Patent Publication Number: US-8990001-B2

Title: Vehicle collision monitoring method

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     Related subject matter is disclosed in U.S. patent application Ser. No. 13/743,952, entitled “Vehicle Turn Monitoring System and Method,” filed on Jan. 17, 2013, in U.S. patent application Ser. No. 13/689,452, entitled “Vehicle Intersection Monitoring System and Method,” filed on Nov. 29, 2012, in U.S. patent application Ser. No. 13/689,484 entitled “Vehicle Intersection Monitoring System and Method,” filed on Nov. 29, 2012, in U.S. patent application Ser. No. 13/689,523 entitled “Vehicle Intersection Warning System and Method,” filed on Nov. 29, 2012, and in U.S. patent application Ser. No. 13/689,564 entitled “Vehicle Intersection Monitoring System and Method,” filed on Nov. 29, 2012, all of these applications being incorporated by reference herein. 
     BACKGROUND 
     1. Field of the Invention 
     The present invention generally relates to a vehicle turn monitoring system and method. More particularly, the present invention relates to a system and method that evaluate scenarios in which a host vehicle and a remote vehicle may come in contact at an intersection or while the host vehicle is executing a turn. 
     2. Background Information 
     In recent years, vehicles have become more equipped with features for improving safety. For example, vehicles can be equipped with a collision warning system that identifies the location of the vehicle and the locations of other nearby vehicles to determine whether the vehicle may come into contact with any of the other vehicles. The possibility of contact between vehicles can be particularly high at road intersections in which the travel paths of the vehicle and other nearby vehicles may intersect. If the possibility of contact exists, the system can issue a warning to the driver so that the driver can take the appropriate action 
     Accordingly, a need exists for an improved vehicle collision warning system. 
     SUMMARY 
     In accordance with one aspect of the present invention, a vehicle collision monitoring method comprises preparing a host vehicle message including information pertaining to a host vehicle including a host vehicle location and a host vehicle heading, receiving a remote vehicle message including information pertaining to a remote vehicle including a remote vehicle location and a remote vehicle heading, and evaluating, using a controller, whether the host vehicle heading and the remote vehicle heading are converging paths. The evaluating includes segregating an area surrounding the host vehicle location into a plurality of sectors, determining which of the sectors is a remote vehicle sector including the remote vehicle location, and determining whether the host vehicle heading and the remote vehicle heading are converging paths based on the host vehicle location, the host vehicle heading, the remote vehicle location, the remote vehicle heading and a characteristic relating to the sector that includes the remote vehicle location. 
     These and other objects, features, aspects and advantages of the present invention will become apparent to those skilled in the art from the following detailed description, which, taken in conjunction with the annexed drawings, discloses a preferred embodiment of the present invention. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Referring now to the attached drawings which form a part of this original disclosure: 
         FIG. 1  is a block diagram illustrating an example of a host vehicle equipped with an intersection monitoring system according to embodiments disclosed herein in relation to a remote vehicle and components of a global positioning system (GPS); 
         FIG. 2  is a block diagram of exemplary components of an intersection monitoring system according to disclosed embodiments; 
         FIG. 3  is a block diagram of exemplary components included in the application controller of the intersection monitoring system as shown in  FIG. 2 ; 
         FIGS. 4 through 30  are exemplary diagrams illustrating different intersection scenarios that are handled by the intersection monitoring system according to disclosed embodiments; 
         FIG. 31  is a flowchart illustrating exemplary operations that are performed by the intersection monitoring system to transmit information pertaining to the host vehicle; 
         FIG. 32  is a flowchart illustrating exemplary operations that are performed by the intersection monitoring system to receive information pertaining to the remote vehicle; 
         FIG. 33  is a diagram illustrating an example of the relative positions of the host vehicle and the remote vehicle with respect to each other; 
         FIGS. 34A and 34B  are flowcharts illustrating exemplary operations for determining the intent of the host vehicle and the remote vehicle; 
         FIGS. 35 and 36  are flowcharts illustrating exemplary operations for determining an intersection scenario based on the host vehicle information and the remote vehicle information; 
         FIG. 37  is a flowchart illustrating exemplary operations for calculating a time to contact between the host vehicle and the remote vehicle; 
         FIG. 38  is a flowchart illustrating exemplary operations for issuing a warning to the host vehicle based on the time to contact determined in  FIG. 37 ; 
         FIG. 39  is a flowchart illustrating exemplary operations for issuing a warning to the host vehicle based on the time to contact determined in  FIG. 37  for a host vehicle about to make a left turn with an oncoming remote vehicle travelling straight in an opposite direction as shown in  FIG. 13 ; 
         FIG. 40  is a graph illustrating an example of a range of host vehicle speeds and host vehicle braking levels for which a warning is issued in accordance with the process shown in  FIG. 39 ; 
         FIG. 41  is a flowchart illustrating exemplary operations for determining the intent of the subject (host) vehicle and the remote (target or threat) vehicle according to another embodiment; 
         FIG. 42  is a graph illustrating an example of a four quadrant coordinate system which shows an example of a location of a remote vehicle within the first quadrant with respect to a location of the host vehicle which is at the center of the coordinate system; 
         FIG. 43  is a graph illustrating an example of a location of a remote vehicle within the second quadrant of the four quadrant coordinate system with respect to a location of the host vehicle which is at the center of the coordinate system; 
         FIG. 44  is a graph illustrating an example of a location of a remote vehicle within the third quadrant of the four quadrant coordinate system with respect to a location of the host vehicle which is at the center of the coordinate system; 
         FIG. 45  is a graph illustrating an example of a location of a remote vehicle within the fourth quadrant of the four quadrant coordinate system with respect to a location of the host vehicle which is at the center of the coordinate system; 
         FIGS. 46A and 46B  are flowcharts illustrating exemplary operations for determining whether the paths of the host vehicle and the remote vehicle will cross and also whether the remote vehicle is to the left or right of the host vehicle; 
         FIGS. 47A and 47B  are flowcharts illustrating exemplary operations for determining the crossing path scenario for the host vehicle and the remote vehicle; 
         FIG. 48  is a flowchart illustrating exemplary operations for determining a time that contact will occur between the host vehicle and the remote vehicle; 
         FIG. 49  is a graph illustrating an example of possible converging paths when the host vehicle is travelling north and the remote vehicle is travelling south; 
         FIG. 50  is a graph illustrating an example of possible converging paths when the host vehicle is travelling northeast and the remote vehicle is travelling southwest; 
         FIG. 51  is a graph illustrating an example of possible converging paths when the host vehicle is travelling east and the remote vehicle is travelling west; 
         FIG. 52  is a graph illustrating an example of possible converging paths when the host vehicle is travelling southeast and the remote vehicle is travelling northwest; 
         FIG. 53  is a graph illustrating an example of possible converging paths when the host vehicle is travelling south and the remote vehicle is travelling north; 
         FIG. 54  is a graph illustrating an example of possible converging paths when the host vehicle is travelling southwest and the remote vehicle is travelling northeast; 
         FIG. 55  is a graph illustrating an example of possible converging paths when the host vehicle is travelling west and the remote vehicle is travelling east; and 
         FIG. 56  is a graph illustrating an example of possible converging paths when the host vehicle is travelling northwest and the remote vehicle is travelling southeast. 
     
    
    
     DETAILED DESCRIPTION OF EMBODIMENTS 
     Selected embodiments will now be explained with reference to the drawings. It will be apparent to those skilled in the art from this disclosure that the following descriptions of the disclosed embodiments are provided for illustration only and not for the purpose of limiting the invention as defined by the appended claims and their equivalents. 
       FIG. 1  is a block diagram illustrating a host vehicle (HV)  10  that is equipped with a vehicle intersection monitoring system  12  according, to a disclosed embodiment. As discussed herein, the host vehicle  10  can also be referred to as a subject vehicle (SV). The vehicle intersection monitoring system  12  communicates with at least one remote vehicle (RV)  14  that can also include a vehicle intersection monitoring system  12 . Alternatively, the remote vehicle  14  can include another type of two-way communication system, such as an adaptive cruise control system, that is capable of communicating information about at least the location and speed of the remote vehicle  14  as understood in the art. Also, a remote vehicle  14  can also be referred to as a target vehicle (TV)  14  or a threat vehicle (TV)  14 . 
     The vehicle intersection monitoring system  12  of the host vehicle  10  and the remote vehicle  14  communicates with a two-way wireless communications network  16 . The two-way wireless communications network  16  can include one or more global positioning satellites  18  (only one shown) and one or more roadside units  20  (only one shown) that send and receive signals to and from the vehicle intersection monitoring system  12  of the host vehicle  10  and the remote vehicle  14 . 
     As shown in more detail in  FIGS. 2 and 3 , the vehicle intersection monitoring system  12  includes an application controller  22  that can be referred to simply as a controller  22 . The controller  22  preferably includes a microcomputer with a control program that controls the components of the vehicle intersection monitoring system  12  as discussed below. The controller  22  includes other conventional components such as an input interface circuit, an output interface circuit, and storage devices such as a ROM (Read Only Memory) device and a RAM (Random Access Memory) device. The microcomputer of the controller  22  is at least programmed to control the vehicle intersection monitoring system  12  in accordance with the flow charts of  FIGS. 31 ,  32  and  34  through  39  as discussed below. It will be apparent to those skilled in the art from this disclosure that the precise structure and algorithms for the controller  22  can be any combination of hardware and software that will carry out the functions of the present invention. In other words, “means plus function” clauses as utilized in the specification and claims should include any structure or hardware and/or algorithm or software that can be utilized to carry out the function of the “means plus function” clause. Furthermore, the controller  22  can communicate with the other components of the vehicle intersection monitoring system  12  discussed herein via, for example a controller area network (CAN) bus or in any other suitable manner as understood in the art. 
     As further shown in  FIG. 2 , the vehicle intersection monitoring system  12  includes a navigation system  24 . In this example, the navigation system  24  includes a global positioning system (GPS) that receives signals from the two-way wireless communications network  16  via a GPS receiver  26  that is coupled to a GPS antenna  28 . The GPS receiver  26  can be, for example, any Wide Area Augmentation System (WAAS) enabled National Marine Electronics Association (NMEA) output receiver as known in the art. However, the navigation system  24  can include any other suitable navigation system as understood in the art. The controller  22  can receive electronic horizon information including, for example, augmented digital map data, from the navigation system  24 . As shown in  FIG. 3 , a vehicle-to-vehicle (V2V) application  100 , for example, running on the controller  22  can receive and process the electronic horizon information and host vehicle data, such as information included in the CAN messages as shown in Table 1, as discussed in more detail below. The electronic horizon information will thus enable the controller  22  to detect intersections, in particular, upcoming intersections at which the host vehicle  10  will arrive, from the map data. For example, the electronic horizon information informs the application ECU of an approaching intersection ahead within 300 meters of the center of the intersection. The controller  22  can thus provide details on the intersection. Thus, the controller  22  performs an operation of identifying a road intersection relating to the host vehicle heading and the remote vehicle heading as discussed in more detail below. The identifying can include determining a location of the road intersection based on navigation map data as mentioned above. Moreover, as discussed herein, the determining of the presence of the road intersection includes determining whether the host vehicle  10  and the remote vehicle  14  are travelling on converging paths based on the host vehicle information, the remote vehicle information, or both. 
     The intersection monitoring system  12  further includes a communication device  30 . In this example, the communication device  30  includes a dedicated short range communications (DSRC) device, which can also be referred to in the art as a wireless safety unit (WSU). However, the communication device  30  can be any suitable type of two-way communication device that is capable of communicating with the two-way wireless communications network  16 . In this example, the communications device  30  is coupled to a DSRC antenna  32  to receive 5.9 GHz DSRC signals from the two-way wireless communications network  16 . These DSRC signals can include basic safety messages (BSM) that include information which, under certain circumstances, warns drivers of potential crashes in time for the driver of the host vehicle  10  to take appropriate action to avoid the crash. In the disclosed embodiments, a BSM includes information in accordance with SAE Standard J2735 as can be appreciated by one skilled in the art. Also, the GPS antenna  28  and the DSRC antenna  32  can be configured as a dual frequency DSRC and GPS antenna as understood in the art. 
     As further illustrated, the communications device  30  receives GPS signals from the GPS antenna  20 . The communication device  30  also receives BSM transmissions (BSM Tx) from the controller  22  to be transmitted via the DSCR antenna  32  for receipt by other vehicles, such as a remote vehicle  14 , as discussed in more detail below. For example, at a certain timing (e.g., every 100 msec), a BSM generator  102  (see  FIG. 3 ) running on the controller  22  can collect the data to assemble a packet to transmit a BSM Tx to the communication device  30  for transmission. The BSM generator  102  can collect this data in the form of CAN messages that are communicated over the CAN bus of the host vehicle  10  or in any other suitable manner. For instance, the CAN messages can be communicated from the components of the vehicle  10  over the CAN bus at a certain timing, such as every 20 msec. The BSM generator  102  can thus assembly the data packet and send the data packet to the communication device  30  via, for example, user data protocol (UDP) or in any other suitable manner. Table 1 below describes examples of CAN messages. 
     
       
         
           
               
             
               
                 TABLE 1 
               
             
            
               
                   
               
               
                 Examples of CAN Message 
               
            
           
           
               
               
               
               
               
            
               
                   
                 Signal Name 
                 CAN Name 
                 Resolution 
                 Offset 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 Acceleration (G) 
                 LONG_ACC 
                 0.001 
                 −2.048 
               
               
                   
                 Acceleration (G) 
                 TRANS_ACC 
                 0.001 
                 −2.048 
               
               
                   
                 Yaw Rate (deg/s) 
                 YAW_RATE 
                 0.1 
                 −204.8 
               
               
                   
                 Vehicle Speed 
                 VSO 
                 0.01 
                 0 
               
               
                   
                 (km/h) 
               
               
                   
                 Low Beam 
                 HL_LOW_REQ 
                 — 
                 — 
               
               
                   
                 High Beam 
                 HL_HIGH_REQ 
                 — 
                 — 
               
               
                   
                 Turn Signal 
                 TURN_IND 
                 — 
                 — 
               
               
                   
                 Brake Status 
                 CABRESW 
                 — 
                 — 
               
               
                   
                 Front Wiper 
                 FR_WIP_REQ 
                 — 
                 — 
               
               
                   
                 Throttle Pos (%) 
                 APS1_A 
                 0.39216 
                 0 
               
               
                   
                 Steering Wheel 
                 STRANGLE 
                 0.1 
                 0 
               
               
                   
                 Angle (deg) 
               
               
                   
                 Transmission 
                 CURGP 
                 — 
                 — 
               
               
                   
                 TCS Status 
                 TCSACT 
                 — 
                 — 
               
               
                   
                 VDC Status 
                 VDCACT 
                 — 
                 — 
               
               
                   
                 VDC On/Off 
                 OFF_SW 
                 — 
                 — 
               
               
                   
                 ABS Status 
                 ABSACT 
                 — 
                 — 
               
               
                   
                   
               
            
           
         
       
     
     Accordingly, each BSM either transmitted by the host vehicle  10  or transmitted by a remote vehicle  14  can include the following information pertaining to the vehicle issuing the BSM: a temporary vehicle ID, vehicle latitude, vehicle longitude, vehicle elevation, position accuracy, vehicle speed, vehicle heading, vehicle steering wheel angle, vehicle acceleration (e.g., lateral, longitudinal, vertical and yaw rate), vehicle brake status and vehicle size, to name a few. Naturally, each BSM can include additional or fewer data as necessary or desired. 
     Table 2 below provides examples of certain vehicle data specifications relating to features of the host vehicle  10  and remote vehicle  14  on which data included in the BSMs is based. 
     
       
         
           
               
             
               
                 TABLE 2 
               
             
            
               
                   
               
               
                 Exemplary Vehicle Data Specifications 
               
            
           
           
               
               
            
               
                 Data Element 
                 Element Specifications 
               
               
                   
               
               
                 Transmission State 
                 Ability to differentiate between 
               
               
                   
                 neutral, park, forward and reverse 
               
               
                 Vehicle Speed 
                 0.02 m/s resolution 
               
               
                 Steering Wheel Angle 
                 1.5 degree resolution 
               
               
                 Vehicle Lateral Acceleration 
                 0.01 m/s{circumflex over ( )}2 resolution 
               
               
                 Vehicle Longitudinal Acceleration 
                 0.01 m/s{circumflex over ( )}2 resolution 
               
               
                 Vehicle Yaw Rate 
                 0.01 deg/sec resolution 
               
               
                 Brake Application Status 
                 Ability to determine if brakes 
               
               
                   
                 are applied 
               
               
                 Vehicle Length 
                 0.01 m resolution 
               
               
                 Vehicle Width 
                 0.1 m resolution 
               
               
                   
               
            
           
         
       
     
     Table 3 below provides examples of desired resolution of measurement data that is, for example, included in the BSMs. 
     
       
         
           
               
             
               
                 TABLE 3 
               
             
            
               
                   
               
               
                 Exemplary Positioning Data Specifications 
               
            
           
           
               
               
               
            
               
                   
                 Data Element 
                 Element Specifications 
               
               
                   
                   
               
               
                   
                 Position Latitude 
                   0.1 μdegree resolution 
               
               
                   
                 Position Longitude 
                   0.1 μdegree resolution 
               
               
                   
                 Vehicle Heading 
                 0.0125 deg resolution 
               
               
                   
                   
               
            
           
         
       
     
     As further illustrated, the communication device  30  provides an echo of the above BSM Tx (BSM Tx Echo) to the controller  22  via, for example, a UDP port, with GPS information included in the BSM Tx Echo message. In this example, a message dispatcher  104  running on the controller  22  sends the BSM Tx Echo message to a global share application  106  running on the controller  22 . 
     In addition, the communication device  30  receives BSMs (BSM Rx) that were transmitted by remote vehicles  14  within a certain range of the host vehicle  10 . The communication device  30  provides received BSMs to the controller  22  via, for example, a UDP port. The message dispatcher  104  in this example sends the BSM Rx to a BSM classification application  108  running on the controller  22 . The BSM classification application  108  also receives host vehicle data, such as information included in the CAN messages as shown in Table 1. The BSM classification application  108  can extract information from BSMs that were received from remote vehicles  14  within a certain range of the host vehicle  10 , such as within 300 meters of the host vehicle  10  or at any other suitable distance from the host vehicle  10 . 
     Accordingly, by exchanging the BSMs, the host vehicle  10  and the remote vehicle  14  exchange host vehicle information and remote vehicle information between each other, with the host vehicle information including information pertaining to a host vehicle location, a host vehicle heading and a host vehicle intended next maneuver and the remote vehicle information including information pertaining to a remote vehicle location, a remote vehicle heading and a remote vehicle intended next maneuver. As discussed herein, the intended next maneuver of the remote vehicle  14  can be determined based on a condition of a turn signal on the remote vehicle  14 . Similarly, the intended next maneuver of the host vehicle  10  can be determined based on a condition of a turn signal on the host vehicle  10 . Alternatively, the intended next maneuver of the remote vehicle  14  can be determined based on a set navigation route for the remote vehicle  14  that can be set by, for example, the navigation system  24  on the remote vehicle  14 . Also, the intended next maneuver of the host vehicle  10  can be determined based on a set navigation route for the host vehicle  10  that can be set by, for example, the navigation system  24  on the host vehicle  10 . As discussed in more detail below, the intended next maneuver of the remote vehicle  14  can be determined as a straight movement of the remote vehicle  14  at the intersection, a left turn of the remote vehicle  14  at the intersection or a right turn of the remote vehicle  14  at the intersection. Similarly, the intended next maneuver of the host vehicle  10  can be determined as a straight movement of the host vehicle  10  at the intersection, a left turn of the host vehicle  10  at the intersection or a right turn of the host vehicle  10  at the intersection. 
     The BSM classification application  108  can also, for example, cache BSM messages received from one or more remote vehicles  14  in a cache table, which can also be referred to as a lookup table. The cache table in this example can include up to 16 entries. However, the cache table can be any suitable size. The cache table can include information representing the host vehicle intended next maneuver; the remote vehicle intended next maneuver; the host vehicle location, the remote vehicle location and any other suitable information included in the BSMs which can then be retrieved for use as discussed herein. Also, the controller  22  can receive and process BSMs from many remote vehicles  14  at the same time. For example, the controller  22  can receive and process BSMs from 100 remote vehicles  14 , or any other suitable number of remote vehicles  14 , at the same time. Upon receiving a BSM from a remote vehicle  14 , the controller  22  can determine whether there is a possibility that remote vehicle  14  may contact thus host vehicle  10  and thus represents a potential threat vehicle (TV) to the host vehicle  10 . If the remote vehicle  14  does not represent a threat, the controller  22  can, for example, discard the data included in the BSM. The controller  22  can also discard a BSM from the cached after a period of time, for example, 0.5 seconds or any suitable length of time. 
     As further shown in  FIG. 3 , the message dispatcher  104  can send geometric intersection description (GID) information and signal phase and timing (SPaT) information that is included, for example, in the GPS information received by the communication device  30  to a vehicle-to-interface (V2I) application  110  running on the controller  22 . The V2I application  110  also receives host vehicle data, such as information included in the CAN messages as shown in Table 1. 
     As further shown in  FIG. 2 , the vehicle intersection monitoring system  12  includes a driver-vehicle interface (DVI)  34  and an external input/output (I/O)  36 . As discussed in more detail below, if there are any remote vehicles  14  that the controller  22  identifies as potential threat vehicles requiring DVI action, the controller  22  can send threat information, such as a UDP broadcast packet, to the DVI  34  via the CAN bus for example. For example, as shown in  FIG. 3 , a threat/notify/warn application  112  running on the controller  22  receives information from the V2V application  100  and the V2I application  110 . The V2V application  100  generates this information based on the BSM information received from the BSM classification application  108 , the electronic horizon information, and the host vehicle data as discussed above. The V2I application  110  generates information based on the host vehicle data, GID information, and SPaT information as discussed above. 
     The threat information generated by the threat/notify/warn application  112  can list all of the identified remote vehicles  14  that are threat vehicles and include BSM information from the remote vehicles  14  that are threat vehicles and the types of alerts and warnings attributed to those remote vehicles  14 . As shown in  FIG. 3 , threat/notify/warn application  112  can issue DVI status information, and can further issue DVI outputs via, for example, a DVI output application  114  running on the controller  22 . The DVI  34  can provide an alert and warning information to the driver based on the threat information as discussed in more detail below. The alert can be a visual alert, and audible alert, a tactile alert, or any combination of these types of alerts. The warnings should convey high urgency causing the driver to immediately pause before making the decision to proceed through an intersection. In addition, the warnings should be noticeable to the driver regardless of their head position and distraction level. Thus, the warnings should be distinguishable from ambient noise and so on. 
     For example, an auditory signal can be emitted as a warning from a speaker mounted in front of the driver on the instrument panel. The warning can be about 1 second in length and can include a car horn icon immediately followed by a “warning” spearcon which is created by speeding up a spoken phrase in particular ways. The sound level of the auditory warning is set at a level that is noticeable against ambient road noise and radio. The visual warning is presented using the DVI display described above on, for example, the instrument panel near the drivers forward eye gaze position and includes multiple visual icons corresponding to the different warning scenarios. The auditory warning conveys high urgency and can be the primary warning causing the driver to immediately pause. In addition to the auditory warning, the visual display is also intended to get the driver&#39;s attention and communicates the nature of the warning to the driver once the potential threat has passed. Also, for people with hearing impairment, the DVI display is can serve as the primary source of warning due its location and the large size of the display. 
     The controller  22  can also send messages to actuate other advance driver assistance system (ADAS) applications. The controller  22  can also exchange data with an external device via the I/O  36 . 
     In addition, as discussed in more detail below, the controller  22  can issue commands via the CAN bus, for example, to other vehicle components  38  when the controller  22  determines that one or more of the remote vehicles  14  is a potential threat vehicle. For instance, the controller  22  may issue brake commands over the CAN bus to maintain the host vehicle  10  in a stopped state even when the driver releases the brake in the presence of an approaching remote vehicle  14  as discussed in more detail below. The controller  22  may also issue steering commands to change a steering direction of the host vehicle  10  in the presence of an approaching remote vehicle  14  as discussed in more detail below. Thus, the controller  22  performs a threat mitigation operation by altering a trajectory of the host vehicle  10 . The altering of the trajectory of the host vehicle  10  can be performed by operating a steering wheel to change a steering direction of the host vehicle  10 , operating a brake, accelerator or both to change the speed of the host vehicle, or in any other suitable manner. The other vehicle components  38  can also include one or more safety devices such as a safety belt, an airbag system, and a horn. Thus, the controller  22  can perform a threat mitigation operation by pretensioning a safety belt, deploying an airbag, operating a horn in the host vehicle, or any of these functions. Furthermore, the host vehicle  10  can include one or more on-board sensors  40  such as a RADAR device, a LIDAR device, a SONAR device, a camera and so on that can detect the presence of objects, such as a remote vehicle (RV)  14 , proximate to the host vehicle  10 . The sensor or sensors  40  can communicate with the controller  22  via, for example, the CAN bus or in any other suitable manner. 
     Examples of operations performed by the intersection monitoring system  12  to determine whether a warning should be provided in view of different scenarios in which the host vehicle  10  and remote vehicle  14  are approaching or at an intersection.  FIGS. 4 through 30  are exemplary diagrams illustrating different intersection scenarios that are handled by the intersection monitoring system  12  according to disclosed embodiments. That is, based on the travelling conditions of the host vehicle  10  and remote vehicle  14  (straight, left turn or right turn), there are 27 total intersection scenarios. Out of those 27 scenarios, there are a total of 14 scenarios can result in the host vehicle  10  and remote vehicle  14  coming in contact with each other. The intersection monitoring system  12  can thus issue a warning to the host vehicle  10  during any of these 14 scenarios depending on the operating condition of the host vehicle  10  and the remote vehicle  14  as discussed in more detail below. In this example, the intersection monitoring system  12  determines whether the host vehicle  10  and remote vehicle  14  are travelling straight, turning left or turning right based on the condition of the turn signals of the host vehicle  10  and the remote vehicle  14 . The turn signal conditions of the host vehicle  10  and the remote vehicle  14  can be contained in the information included in the BSMs transmitted by the host vehicle  10  and remote vehicle  14  as discussed above. 
     In this example, the controller  22  can refer to a truth table as shown in Table 4 to determine which of the 27 scenarios exists. The controller  22  can thus determine from the truth table whether the remote vehicle (RV)  14  is a threat vehicle (TV) that may come in contact with the host vehicle  10 . 
     
       
         
           
               
             
               
                 TABLE 4 
               
             
            
               
                   
               
               
                 Threat Use Case Truth Table 
               
            
           
           
               
               
               
            
               
                   
                 AB 
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 00 
                 01 
                 11 
                 10 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                 CDEF 
                 0000 
                 0 
                 1 
                 0 
                 X 
               
               
                   
                   
                 0001 
                 1 
                 1 
                 1 
                 X 
               
               
                   
                   
                 0011 
                 1 
                 1 
                 0 
                 X 
               
               
                   
                   
                 0010 
                 X 
                 X 
                 X 
                 X 
               
               
                   
                   
                 0110 
                 X 
                 X 
                 X 
                 X 
               
               
                   
                   
                 0100 
                 1 
                 0 
                 1 
                 X 
               
               
                   
                   
                 0101 
                 1 
                 1 
                 0 
                 X 
               
               
                   
                   
                 0111 
                 1 
                 1 
                 0 
                 X 
               
               
                   
                   
                 1111 
                 1 
                 0 
                 0 
                 X 
               
               
                   
                   
                 1110 
                 X 
                 X 
                 X 
                 X 
               
               
                   
                   
                 1100 
                 0 
                 1 
                 0 
                 X 
               
               
                   
                   
                 1101 
                 0 
                 0 
                 0 
                 X 
               
               
                   
                   
                 1001 
                 X 
                 X 
                 X 
                 X 
               
               
                   
                   
                 1011 
                 X 
                 X 
                 X 
                 X 
               
               
                   
                   
                 1010 
                 X 
                 X 
                 X 
                 X 
               
               
                   
                   
                 1000 
                 X 
                 X 
                 X 
                 X 
               
               
                   
                   
               
            
           
         
       
     
     According to the truth table, the travel condition of the host vehicle  10  is represented by the two digit binary code AB. That is, code AB=00 indicates that the host vehicle  10  intends to travel straight through the intersection, code AB=01 indicates that the host vehicle  10  intends to turn left at the intersection, and code AB=11 indicates that host vehicle  10  intends to turn right at the intersection. The code AB=10 is not used. Furthermore, the travel condition of the remote vehicle  14  is represented by the four digit binary code CDEF. 
     Examples of the relationships between the host vehicle  10  and the remote vehicle  14  based on their respective intentions at the intersection are shown in  FIGS. 4 through 30  and represented in Tables 5 through 7 below. In Table 5, the host vehicle  10  intends to travel straight through the intersection, and the different intentions of the remote vehicle  14  are represented by the different codes CDEF as explained in Table 5. Thus, each of the six digit binary codes ABCDEF is a combination of the two digit code AB and the four digit code CDEF as indicated. The controller  22  therefore determines whether a threat of contact between the host vehicle  10  and remote vehicle  14  exists for each scenario, as represented by a binary 0 for no threat and a binary 1 for a possible threat. 
     
       
         
           
               
             
               
                 TABLE 5 
               
             
            
               
                   
               
               
                 Host Vehicle Travelling Straight 
               
            
           
           
               
               
               
               
               
               
            
               
                 Host 
                 Code 
                 Remote 
                 Code 
                 Full Code 
                   
               
               
                 Vehicle 
                 AB 
                 Vehicle 
                 CDEF 
                 ABCDEF 
                 Threat 
               
               
                   
               
               
                 Straight 
                 00 
                 Straight/ 
                 0000 
                 000000 
                 0 
               
               
                   
                   
                 Opposite 
               
               
                 Straight 
                 00 
                 Straight/Left 
                 0001 
                 000001 
                 1 
               
               
                 Straight 
                 00 
                 Straight/Right 
                 0011 
                 000011 
                 1 
               
               
                 Straight 
                 00 
                 Left turn/ 
                 0100 
                 000100 
                 1 
               
               
                   
                   
                 Opposite 
               
               
                 Straight 
                 00 
                 Left turn/Left 
                 0101 
                 000101 
                 1 
               
               
                 Straight 
                 00 
                 Left turn/ 
                 0111 
                 000111 
                 1 
               
               
                   
                   
                 Right 
               
               
                 Straight 
                 00 
                 Right turn/ 
                 1100 
                 001100 
                 0 
               
               
                   
                   
                 Opposite 
               
               
                 Straight 
                 00 
                 Right turn/ 
                 1101 
                 001101 
                 0 
               
               
                   
                   
                 Left 
               
               
                 Straight 
                 00 
                 Right turn/ 
                 1111 
                 001111 
                 1 
               
               
                   
                   
                 Right 
               
               
                   
               
            
           
         
       
     
     These nine different scenarios are shown graphically in  FIGS. 4 through 12 . For purposes of these examples, the remote vehicle (RV)  14  is referred to as a threat vehicle (TV) whenever a threat of contact between the host vehicle,  10  and remote vehicle  14  exists (i.e. when the threat condition is indicated as 1). That is,  FIG. 4  illustrates Scenario  1  where the host vehicle  10  and remote vehicle  14  are each intending to travel straight through the intersection parallel to each, other in opposite directions. Therefore, no threat of contact exists between the host vehicle  10  and the remote vehicle  14 , and the threat condition is indicated as 0 in Table 5. 
     However,  FIG. 5  illustrates Scenario  2  where the host vehicle  10  is intending to travel straight through the intersection and the remote vehicle  14  is intending to travel straight through the intersection in a direction from the left of the host vehicle  10  which will intersect the travel path of the host vehicle  10 . Therefore, a threat of contact exists between the host vehicle  10  and the remote vehicle  14 , and the threat condition is indicated as 1 in Table 5. Similarly,  FIG. 6  illustrates Scenario  3  where the host vehicle  10  is intending to travel straight through the intersection and the remote vehicle  14  is intending to travel straight through the intersection in a direction from the right of the host vehicle  10  which will intersect the travel path of the host vehicle  10 . Therefore, a threat of contact exists between the host vehicle  10  and the remote vehicle  14 , and the threat condition is indicated as 1 in Table 5. 
       FIG. 7  illustrates Scenario  4  where the host vehicle  10  is intending to travel straight through the intersection and the remote vehicle  14  is travelling in a direction opposite to the host vehicle  10  and intending to turn left through the intersection in a direction which will intersect the travel path of the host vehicle  10 . Therefore, a threat of contact exists between the host vehicle  10  and the remote vehicle  14 , and the threat condition is indicated as 1 in Table 5.  FIG. 8  illustrates Scenario  5  where the host vehicle  10  is intending to travel straight through the intersection and the remote vehicle  14  is travelling in a direction from the left of the host vehicle  10  and intending to turn left through the intersection in a direction which will intersect the travel path of the host vehicle  10 . Therefore, a threat of contact exists between the host vehicle  10  and the remote vehicle  14 , and the threat condition is indicated as 1 in Table 5.  FIG. 9  illustrates Scenario  6  where the host vehicle  10  is intending to travel straight through the intersection and the remote vehicle  14  is travelling in a direction from the right of the host vehicle  10  and intending to turn left through the intersection in a direction which will intersect the travel path of the host vehicle  10 . Therefore, a threat of contact exists between the host vehicle  10  and the remote vehicle  14 , and the threat condition is indicated as 1 in Table 5. 
       FIG. 10  illustrates Scenario  7  where the host vehicle  10  is intending to travel straight through the intersection and the remote vehicle  14  is travelling in a direction opposite to the host vehicle  10  and intending to turn right through the intersection in a direction which will not intersect the travel path of the host vehicle  10 . Therefore, no threat of contact exists between the host vehicle  10  and the remote vehicle  14 , and the threat condition is indicated as 0 in Table 5.  FIG. 11  illustrates Scenario  8  where the host vehicle  10  is intending to travel straight through the intersection and the remote vehicle  14  is travelling in a direction from the left of the host vehicle  10  and intending to turn right through the intersection in a direction which will not intersect the travel path of the host vehicle  10 . Therefore, no threat of contact exists between the host vehicle  10  and the remote vehicle  14 , and the threat condition is indicated as 0 in Table 5.  FIG. 12  illustrates Scenario  9  where the host vehicle  10  is intending to travel straight through the intersection and the remote vehicle  14  is travelling in a direction from the right of the host vehicle  10  and intending to turn right through the intersection in a direction which will intersect the travel path of the host vehicle  10 . Therefore, a threat of contact exists between the host vehicle  10  and the remote vehicle  14 , and the threat condition is indicated as 1 in Table 5. 
     In Table 6, the host vehicle  10  intends to turn left through the intersection, and the different intentions of the remote vehicle  14  are represented by the different codes CDEF as explained in Table 6. The controller  22  therefore determines whether a threat of contact between the host vehicle  10  and remote vehicle  14  exists for each scenario, as represented by a binary 0 for no threat and a binary 1 for a possible threat. 
     
       
         
           
               
             
               
                 TABLE 6 
               
             
            
               
                   
               
               
                 Host Vehicle Turning Left 
               
            
           
           
               
               
               
               
               
               
            
               
                 Subject 
                 Code 
                 Remote 
                 Code 
                 Full Code 
                   
               
               
                 Vehicle 
                 AB 
                 Vehicle 
                 CDEF 
                 ABCDEF 
                 Threat 
               
               
                   
               
               
                 Left turn 
                 01 
                 Straight/ 
                 0000 
                 010000 
                 1 
               
               
                   
                   
                 Opposite 
               
               
                 Left turn 
                 01 
                 Straight/Left 
                 0001 
                 010001 
                 1 
               
               
                 Left turn 
                 01 
                 Straight/Right 
                 0011 
                 010011 
                 1 
               
               
                 Left turn 
                 01 
                 Left turn/ 
                 0100 
                 010100 
                 0 
               
               
                   
                   
                 Opposite 
               
               
                 Left turn 
                 01 
                 Left turn/Left 
                 0101 
                 010101 
                 1 
               
               
                 Left turn 
                 01 
                 Left turn/ 
                 0111 
                 010111 
                 1 
               
               
                   
                   
                 Right 
               
               
                 Left turn 
                 01 
                 Right turn/ 
                 1100 
                 011100 
                 1 
               
               
                   
                   
                 Opposite 
               
               
                 Left turn 
                 01 
                 Right turn/ 
                 1101 
                 011101 
                 0 
               
               
                   
                   
                 Left 
               
               
                 Left turn 
                 01 
                 Right turn/ 
                 1111 
                 011111 
                 0 
               
               
                   
                   
                 Right 
               
               
                   
               
            
           
         
       
     
     These nine different scenarios are shown graphically in  FIGS. 13 through 21 .  FIG. 13  illustrates Scenario  10  where the host vehicle  10  and remote vehicle  14  are travelling in opposite directions to each other, with the remote vehicle  14  intending to travel straight through the intersection and the host vehicle  10  intending to turn left in the intersection across the path of remote vehicle  14 . Therefore, a threat of contact exists between the host vehicle  10  and the remote vehicle  14 , and the threat condition is indicated as 1 in Table 6. 
       FIG. 14  illustrates Scenario  11  where the host vehicle  10  is intending to turn left through the intersection and the remote vehicle  14  is intending to travel straight through the intersection in a direction from the left of the host vehicle  10  which will intersect the travel path of the host vehicle  10 . Therefore, a threat of contact exists between the host vehicle  10  and the remote vehicle  14 , and the threat condition is indicated as 1 in Table 6. Similarly,  FIG. 15  illustrates Scenario  12  where the host vehicle  10  is intending to turn left through the intersection and the remote vehicle  14  is intending to travel straight through the intersection in a direction from the right of the host vehicle  10  which will intersect the travel path of the host vehicle  10 . Therefore, a threat of contact exists between the host vehicle  10  and the remote vehicle  14 , and the threat condition is indicated as 1 in Table 6. 
       FIG. 16  illustrates Scenario  13  where the host vehicle  10  is intending to turn left through the intersection and the remote vehicle  14  is travelling in a direction opposite to the host vehicle  10  and intending to turn left through the intersection in a direction which will not intersect the travel path of the host vehicle  10 . Therefore, no threat of contact exists between the host vehicle  10  and the remote vehicle  14 , and the threat condition is indicated as 0 in Table 6.  FIG. 17  illustrates Scenario  14  where the host vehicle  10  is intending to turn left through the intersection and the remote vehicle  14  is travelling in a direction from the left of the host vehicle  10  and intending to turn left through the intersection in a direction which will intersect the travel path of the host vehicle  10 . Therefore, a threat of contact exists between the host vehicle  10  and the remote vehicle  14 , and the threat condition is indicated as 1 in Table 6.  FIG. 18  illustrates Scenario  15  where the host vehicle  10  is intending to turn left through the intersection and the remote vehicle  14  is travelling in a direction from the right of the host vehicle  10  and intending to turn left through the intersection in a direction which will intersect the travel path of the host vehicle  10 . Therefore, a threat of contact exists between the host vehicle  10  and the remote vehicle  14 , and the threat condition is indicated as 1 in Table 6. 
       FIG. 19  illustrates Scenario  16  where the host vehicle  10  is intending to turn left through the intersection and the remote vehicle  14  is travelling in a direction opposite to the host vehicle  10  and intending to turn right through the intersection in a direction which will intersect the travel path of the host vehicle  10 . Therefore, a threat of contact exists between the host vehicle  10  and the remote vehicle  14 , and the threat condition is indicated as 1 in Table 6.  FIG. 20  illustrates Scenario  17  where the host vehicle  10  is intending to turn left through the intersection and the remote vehicle  14  is travelling in a direction from the left of the host vehicle  10  and intending to turn right through the intersection in a direction which will not intersect the travel path of the host vehicle  10 . Therefore, no threat of contact exists between the host vehicle  10  and the remote vehicle  14 , and the threat condition is indicated as 0 in Table 6.  FIG. 21  illustrates Scenario  18  where the host vehicle  10  is intending to turn left through the intersection and the remote vehicle  14  is travelling in a direction from the right of the host vehicle  10  and intending to turn right through the intersection in a direction which will not intersect the travel path of the host vehicle  10 . Therefore, no threat of contact exists between the host vehicle  10  and the remote vehicle  14 , and the threat condition, is indicated as 0 in Table 6. 
     In Table 7, the host vehicle  10  intends to turn right through the intersection, and the different intentions of the remote vehicle  14  are represented by the different codes CDEF as explained in Table 7. The controller  22  therefore determines whether a threat of contact between the host vehicle  10  and remote vehicle  14  exists for each scenario, as represented by a binary 0 for no threat and a binary 1 for a possible threat. 
     
       
         
           
               
             
               
                 TABLE 7 
               
             
            
               
                   
               
               
                 Host Vehicle Turning Right Use Cases 
               
            
           
           
               
               
               
               
               
               
            
               
                 Subject 
                 Code 
                 Remote 
                 Code 
                 Full Code 
                   
               
               
                 Vehicle 
                 AB 
                 Vehicle 
                 CDEF 
                 ABCDEF 
                 Threat 
               
               
                   
               
               
                 Right turn 
                 11 
                 Straight/ 
                 0000 
                 110000 
                 0 
               
               
                   
                   
                 Opposite 
               
               
                 Right turn 
                 11 
                 Straight/Left 
                 0001 
                 110001 
                 1 
               
               
                 Right turn 
                 11 
                 Straight/Right 
                 0011 
                 110011 
                 0 
               
               
                 Right turn 
                 11 
                 Left turn/ 
                 0100 
                 110100 
                 1 
               
               
                   
                   
                 Opposite 
               
               
                 Right turn 
                 11 
                 Left turn/Left 
                 0101 
                 110101 
                 0 
               
               
                 Right turn 
                 11 
                 Left turn/ 
                 0111 
                 110111 
                 0 
               
               
                   
                   
                 Right 
               
               
                 Right turn 
                 11 
                 Right turn/ 
                 1100 
                 111100 
                 0 
               
               
                   
                   
                 Opposite 
               
               
                 Right turn 
                 11 
                 Right turn/ 
                 1101 
                 111101 
                 0 
               
               
                   
                   
                 Left 
               
               
                 Right turn 
                 11 
                 Right turn/ 
                 1111 
                 111111 
                 0 
               
               
                   
                   
                 Right 
               
               
                   
               
            
           
         
       
     
     These nine different scenarios are shown graphically in  FIGS. 22 through 30 .  FIG. 22  illustrates Scenario  19  where the host vehicle  10  and remote vehicle  14  are travelling in opposite directions to each other, with the remote vehicle  14  intending to travel straight through the intersection and the host vehicle  10  intending to turn right in the intersection without crossing the path of remote vehicle  14 . Therefore, no threat of contact exists between the host vehicle  10  and the remote vehicle  14 , and the threat condition is indicated as 0 in Table 7. 
     However,  FIG. 23  illustrates Scenario  20  where the host vehicle  10  is intending to turn right through the intersection and the remote vehicle  14  is intending to travel straight through the intersection in a direction from the left of the host vehicle  10  which will intersect the travel path of the host vehicle  10 . Therefore, a threat of contact exists between the host vehicle  10  and the remote vehicle  14 , and the threat condition is indicated as 1 in Table 7. Similarly,  FIG. 24  illustrates Scenario  21  where the host vehicle  10  is intending to turn right through the intersection and the remote vehicle  14  is intending to travel straight through the intersection in a direction from the right of the host vehicle  10  which will not intersect the travel path of the host vehicle  10 . Therefore, no threat of contact exists between the host vehicle  10  and the remote vehicle  14 , and the threat condition is indicated as 0 in Table 7. 
       FIG. 25  illustrates Scenario  22  where the host vehicle  10  is intending to turn right through the intersection and the remote vehicle  14  is travelling in a direction opposite to the host vehicle  10  and intending to turn left through the intersection in a direction which will intersect the travel path of the host vehicle  10 . Therefore, a threat of contact exists between the host vehicle  10  and the remote vehicle  14 , and the threat condition is indicated as 1 in Table 7.  FIG. 26  illustrates Scenario  23  where the host vehicle  10  is intending to turn right through the intersection and the remote vehicle  14  is travelling in a direction from the left of the host vehicle  10  and intending to turn left through the intersection in a direction which will not intersect the travel path of the host vehicle  10 . Therefore, no threat of contact exists between the host vehicle  10  and the remote vehicle  14 , and the threat condition is indicated as 0 in Table 7.  FIG. 27  illustrates Scenario  24  where the host vehicle  10  is intending to turn right through the intersection and the remote vehicle  14  is travelling in a direction from the right of the host vehicle  10  and intending to turn left through the intersection in a direction which will not intersect the travel path of the host vehicle  10 . Therefore, no threat of contact exists between the host vehicle  10  and the remote vehicle  14 , and the threat condition is indicated as 0 in Table 7. 
       FIG. 28  illustrates Scenario  25  where the host vehicle  10  is intending to turn right through the intersection and the remote vehicle  14  is travelling in a direction opposite to the host vehicle  10  and intending to turn right through the intersection in a direction which will not intersect the travel path of the host vehicle  10 . Therefore, no threat of contact exists between the host vehicle  10  and the remote vehicle  14 , and the threat condition is indicated as 0 in Table 7.  FIG. 29  illustrates Scenario  26  where the host vehicle  10  is intending to turn right through the intersection and the remote vehicle  14  is travelling in a direction from the left of the host vehicle  10  and intending to turn right through the intersection in a direction which will not intersect the travel path of the host vehicle  10 . Therefore, no threat of contact exists between the host vehicle  10  and the remote vehicle  14 , and the threat condition is indicated as 0 in Table 7.  FIG. 30  illustrates Scenario  27  where the host vehicle  10  is intending to turn right through the intersection and the remote vehicle  14  is travelling in a direction from the right of the host vehicle  10  and intending to turn right through the intersection in a direction which will not intersect the travel path of the host vehicle  10 . Therefore, no threat, of contact exists between the host vehicle  10  and the remote vehicle  14 , and the threat condition is indicated as 0 in Table 7. 
     An example of operations performed by the intersection monitoring system  12  to identify the scenarios shown in  FIGS. 4 through 30  as discussed above will now be described. These operations can be performed by the controller  22  in this example. 
     The flowchart of  FIG. 31  illustrates an example of a process for transmitting a BSM that can include information pertaining to a vehicle which is used to identify the scenarios as discussed above. In this example, it is assumed that the controller  22  is in the intersection monitoring system  12  included in the host vehicle  10  so that the host vehicle  10  can transmit a BSM. 
     When the process begins in step  1000 , the controller  22  initializes the CAN and the UDP interfaces discussed above with regard to  FIGS. 2 and 3  in step  1010 . The process then enters a processing loop beginning in step  1020 . As discussed above, the processing loop repeats, for example, every 100 msec so that the controller  22  can collect the data to assemble a packet to transmit a BSM Tx to the communication device  30  (WSU) for transmission. For example, the controller  22  reads the CAN data in step  1030 , and receives GPS data in step  1040  as discussed above with regard to  FIGS. 2 and 3 . The controller  22  then determines in step  1050  whether the GPS data is valid and fresh, for example, the GPS data is non-zero with a fix and is less than 250 msec old. If the GPS data is not valid or fresh, the processing repeats the loop beginning at step  1020 . However, if the GPS data is valid and fresh, the processing continues to step  1060  where the BSM Tx packet is formatted as a UDP packet. In step  1070 , the UDP packet is then sent to the communication device  30  (WSU) for transmission. 
     The flowchart of  FIG. 32  illustrates an example of a process for receiving a BSM that can include information pertaining to a vehicle which is used to identify the scenarios as discussed above. In this example, it is assumed that the controller  22  is in the intersection monitoring system  12  included in the host vehicle  10  so that the host vehicle  10  can receive a BSM. 
     When the process begins in step  2000 , the controller  22  initializes the UDP interfaces discussed above with regard to  FIGS. 2 and 3  in step  2010 . The process then enters a processing loop beginning in step  2020 . The controller  22  receives a BSM in the form of a UDP packet in step  2030 . The controller  22  then determines in step  2040  whether the UDP packet is a BSM Tx Echo packet. If the UDP packet is a BSM Tx Echo packet, the controller  22  extracts GPS position information in step  2050  and creates GPS position data in step  2060 . 
     However, if the UDP packet is determined to not be a BSM Tx Echo packet in step  2040 , the processing continues to step  2070 . In step  2070 , the processing determines whether the UDP packet is a BSM Rx data packet, that is, a received BSM message. If the UDP packet is determined not to be a BSM Rx data packet in step  2070 , the processing repeats beginning at step  2020 . However, if the UDP packet is determined to be a BSM Rx data packet in step  2070 , the processing continues to step  2080  where the controller processes the BSM Rx data packet as discussed above with regard to  FIGS. 2 and 3 . In particular, the controller  22  can extract the GPS and BSM information from the data packet to use that information to identify the scenario as discussed above with regard to  FIGS. 4 through 30 . 
       FIG. 33  is a diagram illustrating the relationship between the location of the host vehicle  10  and the location of the remote vehicle  14  and the manner in which a point of contact of the host vehicle  10  and the remote vehicle  14  can be calculated based on the respective speed and heading of the host vehicle  10  and the remote vehicle  14 . In this example, φ 1  can represent the latitude of the host vehicle  10 , θ 1  represents the longitude of the host vehicle  10 , φ 2  can represent the latitude of the remote vehicle  14  and θ 2  represents the longitude of the remote vehicle  14 . All of the values for the latitude and longitude can be expressed in radians. 
     Also, δ 1  can represent the heading of the host vehicle  10 , ν 1  can represent the speed of the host vehicle  10 , δ 2  can represent the heading of the remote vehicle  14 , and ν 2  can represent the speed of the remote vehicle  10 . As discussed above, the heading and speed information for a vehicle, such as the host vehicle  10  and remote vehicle  14 , can be obtained from the BSM that the vehicle transmits. Thus, in this example, the heading and speed of the host vehicle  10  can be obtained from the message BSM Tx transmitted by the host vehicle  10  and the heading and speed of the remote vehicle  14  can be obtained from the message BSM Rx that was transmitted by the remote vehicle  14  and received by the host vehicle  10 . For heading, the convention used is as follows: 0 degrees for north, π/2 (90 degrees) for east, π (108 degrees) for south, and 3π/2 (270 degrees) for west. Also, l 1  can represent the travel path of the host vehicle  10 , l 2  can represent the travel path of the remote vehicle  14  and D represents the relative distance between the host vehicle  10  and the remote vehicle  14 . In addition, X represents the east-west distance between two points. Y represents the north-south distance between two points, α 1  represents the angle between the travel path l 1  and the line representing the relative distance D, α 2  represents the angle between the travel path l 2  and the line representing the relative distance D, α 3  represents the angle between travel path l 1  and travel path l 2 , and angle β 1  represents the arc cosine of Y divided by D. Furthermore, φ c  can represent the latitude at which the paths of the host vehicle  10  and the remote vehicle  14  cross, and θ c  can represent the longitude at which the paths of the host vehicle  10  and the remote vehicle  14  cross 
     An example of the process that can be performed by the controller  22  to identify the scenario as discussed above with regard to  FIGS. 4 through 30  will now be described with regard to the flowcharts in  FIGS. 34 through 38 . It should be noted that the information pertaining to the host vehicle  10  and the remote vehicle  14  used in this process can be obtained from the BSMs as discussed above. 
     As shown in the flowcharts of  FIGS. 34A and 34B , when the process begins in step  3000 , the controller  22  determines from the location information pertaining to the host vehicle  10  and the remote vehicle  14  whether a difference in elevation ΔH between the host vehicle  10  and the remote vehicle  14  is above a threshold H threshold  in step  3010 . In other words,H threshold  represents the threshold value that determines whether the remote vehicle  14  should be considered to be a possible threat vehicle. In this example, the value of H threshold =14 ft.±1 ft. However, the value of H threshold  can be any suitable value. Therefore, if the processing determines in step  3010  that the host vehicle  10  and the remote vehicle  14  are at different elevations, the processing determines that the remote vehicle  14  is not a threat to the host vehicle  10  (e.g., the remote vehicle  14  will pass above the host vehicle  10  on an overpass). Hence, the processing can end in step  3020  and return to the beginning in step  3000 . Accordingly, the processing refrains from performing a threat mitigation operation as discussed herein. 
     However, if the difference in elevation ΔH between the host vehicle  10  and the remote vehicle  14  is not above the threshold H threshold , the processing continues to determine whether the left or right turn signals of the host vehicle  10  and the remote vehicle  14  (represented at threat vehicle TV) indicate that either of the vehicles  10  or  14  intend to turn left or right. In step  3030 , the processing determines whether the left turn signal of the host vehicle  10  is activated. If the left turn signal of the host vehicle  10  is activated, the processing continues to step  3040  where the values of binary code AB discussed above with regard to the truth table in Table 4 are set to 01. However, if the left turn signal of the host vehicle  10  is not activated, the processing continues from step  3030  to step  3050 . 
     In step  3050 , the processing determines whether the right turn signal of the host vehicle  10  is activated. If the right turn signal of the host vehicle  10  is activated, the processing continues to step  3060  where the values of binary code AB are set to 11. However, if the right turn signal of the host vehicle  10  is not activated, the processing continues from step  3050  to step  3070  where the values of the binary code AB are set to 00, thus indicating that the host vehicle  10  intends to travel straight without turning. 
     In step  3080 , the processing determines whether the left turn signal of the remote vehicle  14  is activated. If the left turn signal of the remote vehicle  14  is activated, the processing continues to step  3090  where the values of binary code CD discussed above with regard to the truth table in Table 4 are set to 01. However, if the left turn signal of the remote vehicle  14  is not activated, the processing continues from step  3080  to step  3100 . 
     In step  3100 , the processing determines whether the right turn signal of the remote vehicle  14  is activated. If the right turn signal of the remote vehicle  14  is activated, the processing continues to step  3110  where the values of binary code CD are set to 11. However, if the right turn signal of the remote vehicle  14  is not activated, the processing continues from step  3100  to step  3120  where the values of the binary code CD are set to 00, thus indicating that the remote vehicle  14  intends to travel straight without turning. 
     After completing the above processing to determine the values for binary codes AB and CD, the processing continues to step  3130  where the angle β 1  shown in  FIG. 33  is calculated according to the following equation 
               β   1     =       arccos   ⁡     (     Y   D     )       =     arccos   (       (       ϕ   b     -     ϕ   a       )               (       θ   b     -     θ   a       )     2     ⁢     cos   2     ⁢     ϕ   a       +       (       ϕ   b     -     ϕ   a       )     2           )             
where φ a  equals φ 1 , φ b  equals φ 2 , θ a  equals θ 1  and θ b  equals θ 2  discussed above.
 
     The processing then continues to step  3140  where the absolute value of the difference between the heading δ 1  of the host vehicle  10 , represented in this flowchart by δ HV , and the heading δ 2  of the remote vehicle  14 , represented in this flowchart by δ RV , is calculated. If the absolute value of the difference is equal to π (180 degrees), the processing continues to step  3150  where the value of the binary code EF discussed above with regard to the truth table in Table 4 are set to 00. This indicates that the host vehicle  10  and the remote vehicle  14  are travelling toward each other. 
     However, if the processing determines in step  3140  that the absolute value of the difference is not equal to π, the processing continues to step  3160 . In step  3160 , the processing determines whether the heading of the host vehicle is less than the angle β 1 . If the heading of the host vehicle is less than the angle β 1 , the processing determines in step  3170  whether the heading of the host vehicle  10  is less than the heading of the remote vehicle  14  which is less than the angle β 1 +π. If the result of step  3170  is yes, the processing returns at step  3180  to step  3000  because the remote vehicle  14  is determined to not be a threat vehicle to the host vehicle  10 . 
     However, if the heading of the host vehicle is not less than the angle β 1 , the processing proceeds from step  3160  to step  3190  and determines whether the heading of the host vehicle  10  is greater than the heading of the remote vehicle  14  which is greater than the angle β 1 +π. If the result of step  3190  is yes, the processing returns at step  3200  to step  3000  because the remote vehicle  14  is determined to not be a threat vehicle to the host vehicle  10 . 
     However, if the result of either step  3170  or  3190  is no, the processing continues from either of those steps to step  3210 . In step  3210 , the processing determines whether the heading of the host vehicle  10  is between the angle β 1  and the value of angle β 1 +π. If the result of step  3210  is yes, the processing continues to step  3220  and sets the value of binary codes EF to 01, indicating that the remote vehicle  14  is coming toward the host vehicle  10  from the left of the host vehicle  10 . However, if the result of step  3210  is no, the processing continues to step  3230  and sets the value of binary codes EF to 11, indicating that the remote vehicle  14  is coming toward the host vehicle  10  from the right of the host vehicle  10 . 
     After completing the above processing in either of steps  3150 ,  3220  or  3230 , the processing continues at step  3240  to the flowchart shown in  FIG. 35 . In the flowchart shown in  FIG. 35 , the processing determines the type of scenario that exists as shown in  FIGS. 4 through 30  and discussed above. 
     Beginning in step  4000 , the processing determines in step  4010  whether the binary codes CD are equal to 00. If they are, the processing determines in step  4020  whether the binary codes EF are equal to 00. If so, the processing determines in step  4030  whether the binary codes AB are equal to 01. Also, if the processing determines in step  4020  that the binary codes EF are not equal to 00, the processing determines in step  4040  whether the binary codes EF are equal to 01. If the processing determines in step  4030  that the binary codes AB are equal to 01, or the processing determines in step  4040  that the binary codes EF are equal to 01, the processing continues to step  4050  where the processing will proceed to the flowchart shown in  FIG. 36  as discussed below. 
     However, if the processing determines in step  4040  that the binary codes EF are not equal to 01, then the processing concludes in step  4060  that the binary codes EF are equal to 11. After doing so, the processing determines in step  4070  whether the binary codes AB are equal to 11. If not, the processing proceeds to step  4050  and to the flowchart in  FIG. 36 . 
     Turning back to step  4010 , if the processing determines that the binary codes CD are not equal to 00, the processing continues to step  4080  where the processing determines if the values of CD are equal to 01. If so, the processing continues to step  4090  to determine whether the binary codes EF are equal to 00. If the binary codes EF are equal to 00, the processing determines in step  4100  whether the binary codes AB are equal to 01. However, if the processing determines in step  4090  that the binary codes EF are not equal to 00, the processing determines in step  4110  whether the binary codes AB are equal to 11. 
     Turning back to step  4080 , if the binary codes CD are not equal to 01, the processing concludes in step  4120  that the binary codes CD are equal to 11. The processing continues to step  4130  to determine whether the binary codes EF are equal to 11. If so, the processing determines in step  4140  whether the binary codes AB are equal to 00. However, if it is determined in step  4130  that the binary codes EF are not equal to 11, the processing determines in step  4150  whether the binary bodes EF are equal to 00. If so, the processing determines in step  4160  whether the binary codes AB are equal to 01. 
     As can be appreciated from the flowchart in  FIG. 35 , if step  4030  determines that the binary codes AB are not equal to 01, or step  4070  determines that binary codes AB are equal to 11, or step  4110  determines that the binary codes AB are equal to 11, or step  4140  determines that the binary codes AB are not equal to 00, or step  4150  determines that the binary codes EF are not equal to 00, or step  4160  determines that binary codes AB are not equal to 01, the processing continues to step  4170 . In step  4170 , the processing concludes that none of the scenarios shown in the truth table in Table 4 are met by the processing performed in the flowcharts of  FIGS. 34A and 34B . Thus, the processing returns at step  4180  to step  3000  and repeats as discussed above. In addition, if step  4030  determines that the binary codes AB are equal to 01, or step  4070  determines that binary codes AB are not equal to 11, or step  4110  determines that the binary codes AB are not equal to 11, or step  4140  determines that the binary codes AB are equal to 00, or step  4160  determines that binary codes AB are equal to 01, the processing continues to step  4050  and to the flowchart in  FIG. 36 . 
     Beginning at step  5000  in the flowchart of  FIG. 36 , the processing determines in step  5010  whether the binary codes ABCD are equal to 0000. If not, the processing determines in step  5020  whether the binary codes ABCD are equal to 0001. If not, the processing determines in step  5030  whether the binary codes ABCD are equal to 0100. If not, the processing determines in step  5040  whether the binary codes ABCD are equal to 0011. If not, the processing determines in step  5050  whether the binary codes ABCD are equal to 1100. If not, the processing determines in step  5060  whether the binary codes ABCD are equal to 0101. If not, the processing concludes in step  5070  that the binary codes ABCD are equal to 0111. However, if any of the inquiries in steps  5010  through  5060  are yes, or after step  5070 , the processing proceeds to step  5080  and continues to the flowchart shown in  FIG. 37 . Thus, by performing the operations in  FIGS. 31 ,  32  and  34  through  36 , the controller  22  selects an intersection scenario from a plurality of intersection scenarios based on the host vehicle information and the remote vehicle information, and monitors a location relationship between the host vehicle  10  and the remote vehicle  14  according to an algorithm that is determined based on the selected intersection scenario. As discussed above, the selecting of the intersection scenario can include determining, based on the remote vehicle intended next maneuver and the host vehicle intended next maneuver, whether the remote vehicle  14  will be moving left in relation to a path of movement of the host vehicle  10  at the intersection, right in relation to the path of movement of the host vehicle  10  at the intersection or across the path of movement of the host vehicle  10  at the intersection. As can be appreciated from the description herein, the location relationship can be a distance between the host vehicle and the remote vehicle. Naturally, the selecting of the intersection scenario includes eliminating some of the plurality of intersection scenarios based on the host vehicle information and the remote vehicle information as demonstrated above. 
     In the flowchart in  FIG. 37 , the processing calculates the time to collision (TTC) beginning in step  6000 . Thus, the processing determines whether to provide a warning to the host vehicle  10  by evaluating an operating condition of the host vehicle  10  while the possibility of contact exists between the host vehicle  10  and the remote vehicle  14 . As will now be discussed, the process determines whether the possibility of contact between the host vehicle  10  and the remote vehicle  14  exists by determining an east-west distance X and a north-south distance Y between the host vehicle  10  and the remote vehicle  14 , determining a relative distance between the host vehicle  10  and the remote vehicle  14  based on the east-west distance X and the north-south distance Y, and determining an angle heading between the host vehicle  10  and the remote vehicle  14 . That is, the processing in step  6010  calculates the values for X, Y and D as shown in  FIG. 33  using the following equations: 
     
       
         
           
             
                 
             
             ⁢ 
             
               X 
               = 
               
                 
                   
                     ( 
                     
                       
                         θ 
                         2 
                       
                       - 
                       
                         θ 
                         1 
                       
                     
                     ) 
                   
                   ⁢ 
                   ρ 
                 
                 = 
                 
                   
                     
                       ( 
                       
                         
                           θ 
                           2 
                         
                         - 
                         
                           θ 
                           1 
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         1 
                         - 
                         f 
                       
                       ) 
                     
                     ⁢ 
                     
                       r 
                       e 
                     
                     ⁢ 
                     cos 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       ϕ 
                       1 
                     
                   
                   
                     
                       
                         
                           sin 
                           2 
                         
                         ⁢ 
                         
                           ϕ 
                           1 
                         
                       
                       + 
                       
                         
                           
                             ( 
                             
                               1 
                               - 
                               f 
                             
                             ) 
                           
                           2 
                         
                         ⁢ 
                         
                           cos 
                           2 
                         
                         ⁢ 
                         
                           ϕ 
                           1 
                         
                       
                     
                   
                 
               
             
           
         
       
       
         
           
             
                 
             
             ⁢ 
             
               Y 
               = 
               
                 
                   
                     ( 
                     
                       
                         ϕ 
                         2 
                       
                       - 
                       
                         ϕ 
                         1 
                       
                     
                     ) 
                   
                   ⁢ 
                   r 
                 
                 = 
                 
                   
                     
                       ( 
                       
                         
                           ϕ 
                           2 
                         
                         - 
                         
                           ϕ 
                           1 
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         1 
                         - 
                         f 
                       
                       ) 
                     
                     ⁢ 
                     
                       r 
                       e 
                     
                   
                   
                     
                       
                         
                           sin 
                           2 
                         
                         ⁢ 
                         
                           ϕ 
                           1 
                         
                       
                       + 
                       
                         
                           
                             ( 
                             
                               1 
                               - 
                               f 
                             
                             ) 
                           
                           2 
                         
                         ⁢ 
                         
                           cos 
                           2 
                         
                         ⁢ 
                         
                           ϕ 
                           1 
                         
                       
                     
                   
                 
               
             
           
         
       
       
         
           
             
                 
             
             ⁢ 
             
               D 
               = 
               
                 
                   ( 
                   
                     1 
                     - 
                     f 
                   
                   ) 
                 
                 ⁢ 
                 
                   r 
                   e 
                 
                 ⁢ 
                 
                   
                     
                       
                         
                           
                             ( 
                             
                               
                                 θ 
                                 2 
                               
                               - 
                               
                                 θ 
                                 1 
                               
                             
                             ) 
                           
                           2 
                         
                         ⁢ 
                         
                           cos 
                           2 
                         
                         ⁢ 
                         
                           ϕ 
                           1 
                         
                       
                       + 
                       
                         
                           ( 
                           
                             
                               ϕ 
                               2 
                             
                             - 
                             
                               ϕ 
                               1 
                             
                           
                           ) 
                         
                         2 
                       
                     
                     
                       
                         
                           sin 
                           2 
                         
                         ⁢ 
                         
                           ϕ 
                           1 
                         
                       
                       + 
                       
                         
                           
                             ( 
                             
                               1 
                               - 
                               f 
                             
                             ) 
                           
                           2 
                         
                         ⁢ 
                         
                           cos 
                           2 
                         
                         ⁢ 
                         
                           ϕ 
                           1 
                         
                       
                     
                   
                 
               
             
             ⁢ 
             
                 
             
           
         
       
       
         
           
             
                 
             
             ⁢ 
             
               
                 where 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   r 
                   e 
                 
                 ⁢ 
                 
                   
                       
                   
                   ⁢ 
                   
                       
                   
                 
                 ⁢ 
                 represents 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 the 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 radius 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 of 
                 ⁢ 
                 
                   
                       
                   
                   ⁢ 
                   
                       
                   
                 
                 ⁢ 
                 the 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 earth 
               
               , 
               
                  
               
               ⁢ 
               
                   
               
               ⁢ 
               
                 
                   which 
                   ⁢ 
                   
                     
                         
                     
                     ⁢ 
                     
                         
                     
                   
                   ⁢ 
                   is 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     r 
                     e 
                   
                 
                 = 
                 
                   6 
                   ⁢ 
                   
                     , 
                   
                   ⁢ 
                   378 
                   ⁢ 
                   
                     , 
                   
                   ⁢ 
                   137 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   m 
                 
               
               , 
               
                 
 
               
               ⁢ 
               
                   
               
               ⁢ 
               
                 f 
                 = 
                 
                   1 
                   298.257223563 
                 
               
               , 
               
                 
 
               
               ⁢ 
               
                   
               
               ⁢ 
               
                 
                   ϕ 
                   1 
                 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 can 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 represent 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 the 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 latitude 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 of 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 the 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 host 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 vehicle 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 10 
               
               , 
               
                 
 
               
               ⁢ 
               
                   
               
               ⁢ 
               
                 
                   θ 
                   1 
                 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 can 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 represent 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 the 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 longitude 
                 ⁢ 
                 
                   
                       
                   
                   ⁢ 
                   
                       
                   
                 
                 ⁢ 
                 of 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 the 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 host 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 vehicle 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 10 
               
               , 
               
                 
 
               
               ⁢ 
               
                   
               
               ⁢ 
               
                 
                   ϕ 
                   2 
                 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 can 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 represent 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 the 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 latitude 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 of 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 the 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 remote 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 vehicle 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 14 
               
               , 
               and 
             
           
         
       
       
         
           
             
               θ 
               2 
             
             ⁢ 
             
                 
             
             ⁢ 
             can 
             ⁢ 
             
                 
             
             ⁢ 
             represent 
             ⁢ 
             
                 
             
             ⁢ 
             the 
             ⁢ 
             
                 
             
             ⁢ 
             longitude 
             ⁢ 
             
                 
             
             ⁢ 
             of 
             ⁢ 
             
                 
             
             ⁢ 
             the 
             ⁢ 
             
                 
             
             ⁢ 
             remote 
             ⁢ 
             
                 
             
             ⁢ 
             vehicle 
             ⁢ 
             
                 
             
             ⁢ 
             14 
             ⁢ 
             
                 
             
             ⁢ 
             as 
             ⁢ 
             
                 
             
             ⁢ 
             discussed 
             ⁢ 
             
                 
             
             ⁢ 
             
               above 
               . 
             
           
         
       
     
     The processing then continues to step  6020  where the processing determines whether the heading of the host vehicle  10  δ HV  (δ 1  in  FIG. 33 ) is less than or equal to the angle β 1 +π. If so, the processing continues to step  6030  and calculates the angle α HV  (α 1  in  FIG. 33 ) as indicated. If not, the processing continues to step  6040  and calculates the angle α HV  as indicated. In addition, after completing step  6010  as discussed above, the processing determines in step  6050  whether the heading of the remote vehicle  14  δ TV  (δ 2  in  FIG. 33 ) is less than or equal to the angle β 1 . If so, the processing continues to step  6060  and calculates the angle α TV  (α 2  in  FIG. 33 ) as indicated. If not, the processing continues to step  6070  and calculates the angle α TV  as indicated. 
     After completing any of the steps  6030 ,  6040 ,  6060  and  6070 , the processing continues to step  6080  and calculates the travel path l HV  (l 1 ) of the host vehicle  10  and the travel path l TV  (l 2 ) of the remote vehicle  14  according to the following equations 
     
       
         
           
             
               
                 
                   
                     l 
                     1 
                   
                   = 
                   
                     D 
                     ⁢ 
                     
                       
                         sin 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           α 
                           2 
                         
                       
                       
                         sin 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           α 
                           3 
                         
                       
                     
                   
                 
               
             
             
               
                 
                   
                     l 
                     2 
                   
                   = 
                   
                     D 
                     ⁢ 
                     
                       
                         sin 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           α 
                           1 
                         
                       
                       
                         sin 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           α 
                           3 
                         
                       
                     
                   
                 
               
             
           
         
       
     
     The processing at step  6090  then calculates the latitude φ c  at which the paths of the host vehicle  10  and the remote vehicle  14  cross, and the longitude θ c  at which the paths of the host vehicle  10  and the remote vehicle  14  cross according to the following equations 
                     ϕ   c     =           (       l   1     ⁢   cos   ⁢           ⁢     δ   1       )     ⁢           sin   2     ⁢     ϕ   1       +         (     1   -   f     )     2     ⁢     cos   2     ⁢     ϕ   1                 (     1   -   f     )     ⁢     r   e         +     ϕ   1                     θ   c     =           (       l   1     ⁢   sin   ⁢           ⁢     δ   1       )     ⁢           sin   2     ⁢     ϕ   1       +         (     1   -   f     )     2     ⁢     cos   2     ⁢     ϕ   1                 (     1   -   f     )     ⁢     r   e     ⁢   cos   ⁢           ⁢     ϕ   1         +     θ   1                   
where the variables are as discussed above.
 
     The processing then continues to step  6100  and calculates the time to collision TTC HV  (TTC 1 ) which represents the time until the host vehicle  10  reaches the collision point, and the time to collision TTC TV  (TTC 2 ) which represents the time until the remote vehicle  14  reaches the collision point according to the following equations 
                     TTC   1     =       l   1       v   1                     TTC   2     =       l   2       v   2                   
where the speed ν 1  of the host vehicle  10  and the speed ν 2  of the remote vehicle  14  are included in the respective BSMs transmitted by the host vehicle  10  and the remote vehicle  14 . Thus, the monitoring of the location relationship discussed above can include monitoring a time until the host vehicle  10  and the remote vehicle  14  contact each other as the location relationship. In other words, the processing that determines whether the possibility of contact between the host vehicle  10  and the remote vehicle  14  exists includes determining respective times for the host vehicle  10  and the remote vehicle  14  to travel from their respective current locations to a contact location proximate the intersection. The processing then calculates an absolute value of the difference between TTC HV  (TTC 1 ) and TTC TV  (TTC 2 ) in step  6110 , and continues in step  6120  to the process for issuing a warning message as shown in the flowchart of  FIG. 38 . Accordingly, as can be appreciated from the above, the processing determines whether the possibility of contact between the host vehicle  10  and the remote vehicle  14  exists by calculating a latitude and longitude of a contact location, determining a first time for the host vehicle  10  to travel a first distance from the current location of the host vehicle  10  to the contact location, determining a second time for the remote vehicle  14  to travel a second distance from the current location of the remote vehicle  14  to the contact location, and calculating a difference between the first and second times to determine whether the vehicles  10  and  14  will be at the contact location at the same time. The TTC is calculated to determine the time for warning the driver. For example, approximately 2.5 seconds may be needed to warn the driver to take action, independent of speed. As discussed above, the warning can, be an audible warning, a visual warning and a tactile warning at the host vehicle  10  while the process determines that the operating condition of the host vehicle  10  can permit contact between the host vehicle  10  and the remote vehicle  14 .
 
     As will now be discussed with regard to  FIG. 38 , the warning process includes two branches, with one branch controlling warning when the host vehicle  10  is initially in motion and the other warning when the vehicle is initially at a stop. Furthermore, as discussed below, the flowchart in  FIG. 39  illustrates specific operations that are performed when the full code ABCDEF=010000, indicating that the host vehicle  10  is intending to make a left hand turn and the remote vehicle  14  is travelling straight in the opposite direction, as shown in  FIG. 13  and in the first entry in Table 6 above. 
     For the case when the host vehicle  10  is in motion, the process first checks to see if the speed is above a threshold, ν threshold . In this example, the value of ν threshold  can be 5 mph or any other suitable speed. If the speed is not above the threshold, the process exits the loop. If the speed is above the threshold, the process determines if the time for the host vehicle  10  to reach the intersection of the two vehicle paths is less than a threshold, TTC HV     —     th . In this example, the value of TTC HV     —     th =2 sec.±2 sec. However, the value of TTC HV     —     th  can be any suitable value. If the time is not less than the threshold, the process exits the loop. However, if the time is less than the threshold, the process determines if the difference between the times for the host vehicle  10  and the remote vehicle  14  (threat vehicle) to reach the intersection of the two vehicle paths is less than, a threshold ΔTTC th . In this example, the value of ΔTTC th =2 sec.±1 sec. However, the value of ΔTTC th  can be any suitable value. If the difference is not less than the threshold, the process exits the loop. If the difference is less than the threshold, the process checks the status of the warning. If the warning has not been issued, the process issues the warning then loops back to the beginning and continues to issue the warning until the threat is no longer present. Once the threat is gone, the process resets the warning and exits the loop. 
     For the case when the host vehicle  10  is stopped, the application first checks to see if the time for the remote vehicle  14  to reach the intersection of the two vehicle paths is less than a threshold TTC TV     —     th . In this example, the value of TTC TV     —     th =2 sec.±2 sec. However, the value of TTC TV     —     th  can be any suitable value. If the time is not less than the threshold, the process exits the loop. If the time is less than the threshold, the application checks to see if the brakes on the host vehicle are applied. If the brakes are applied, the process exits the loop. If the brakes are not applied, the process maintains brake pressure and issues a warning. The process then continuously checks to see if the brakes have been applied. If the brakes have been applied, the application resets the warning and exits the loop. Thus, the process refrains from providing the warning while the evaluating determines that the operating condition indicates that a brake of the host vehicle  10  is in an engaged condition to retain the host vehicle  10  in a stationary position. If the brakes have not been applied, the process checks to see if the throttle is active. If the throttle is not active, the process loops back to check if the brakes have been applied. However, if the throttle is active, the process releases the brakes, resets the warning and exits the loop. 
     Accordingly, beginning at step  7000 , the process determines in step  7005  whether the full code ABCDEF=010000, indicating that the host vehicle  10  is intending to turn left and the remote vehicle  14  is travelling straight in the opposite direction as shown in  FIG. 13 . If this is the scenario, the process continues to step  7010  to begin the process Warning LTAP/OD as shown in  FIG. 39  and discussed below before the host vehicle  10  begins to execute the left turn. In other words, the process Warning LTAP/OD as shown in  FIG. 39  is performed before the driver of the host vehicle  10  begins to steer the steering wheel of the host vehicle  10  to begin executing the left turn, and thus before the trajectory of the host vehicle  10  moves toward the left turn. However, if this is not the scenario and the host vehicle  10  is not intending to execute a left turn, the processing continues to step  7015  to determine whether the speed of the host vehicle  10  is 0. If the speed is not 0, the processing determines in step  7020  if the speed of the host vehicle  10  is less than a threshold ν threshold . If the speed is not less than the threshold ν threshold , the processing determines in step  7030  whether the time to collision of the host vehicle  10  is less than a time to collision threshold for the host vehicle. If so, the processing determines in step  7040  whether the value ΔTTC calculated in step  6110  as discussed above is less than a change in the time to collision threshold. If so, the processing determines in step  7050  whether a warning has already been issued. If a warning has already been issued, the processing returns to step  7015  and repeats as discussed above. However, if a warning has not been issued, the processing issues a warning in step  7060  and repeats at step  7015 . 
     Also, if the processing determines in step  7020  that the speed of the host vehicle  10  is not less than a threshold ν threshold , if the processing determines in step  7030  that the time to collision of the host vehicle  10  is not less than the time to collision threshold for the host vehicle, or the processing in step  7040  determines that the value calculated in step  6110  is not less than the change in the time to collision threshold, the processing continues to step  7070 . In step  7070 , the processing determines if the warning has been issued. If the warning has not been issued, the processing returns at step  7160  to step  3000  and repeats as discussed above. However, if the warning has been issued, the warning is reset in step  7080  and the processing returns at step  7160  to step  3000  and repeats as discussed above. 
     Returning to step  7015 , if the speed of the host vehicle  10  is determined to be 0, the processing determines in step  7090  whether the time to collision of the remote vehicle  14  is less than a time to collision threshold for the remote vehicle. If so, the processing determines in step  7100  if the brake of the host vehicle  10  has been released. If so, the processing holds the brake in step  7110  and issues a warning in step  7120 . This brake hold is characterized as a haptic warning since the driver can override the brake by applying the accelerator, and is not considered active control, since it occurs under specific conditions. Thus, the process provides the warning while the evaluating determines that the operating condition indicates that a brake of the host vehicle  10  is in a disengaged condition to enable the host vehicle  10  to move from a stationary position and the possibility of contact exists. In this instance, the warning includes operating the brake to change from the disengaged condition to an engaged condition to retain the host vehicle  10  in a stationary position. 
     The processing then determines in step  7130  if the brake of the host vehicle  10  has been activated. If the brake has not been activated, the processing determines in step  7140  whether the throttle of the host vehicle  10  has been activated. If the throttle has not been activated, the processing returns to step  7130  and again checks whether the brake has been activated. However, if the throttle has been activated, the processing releases the brake in step  7150  and resets the warning in step  7080 . The processing continues to step  7160  and returns to step  3000  as discussed above. In addition, if the processing determines in step  7090  that the time to collision of the remote vehicle  14  is not less than the time to collision threshold for the remote vehicle, or the processing determines in step  7100  that the brake of the host vehicle  10  has not been released, the processing continues to step  7070  and repeats as discussed above. 
     As can be appreciated from the flowchart in  FIG. 38 , a determination is made whether to provide a warning for each of the scenarios shown in  FIGS. 4 through 30  that may lead to contact between the host vehicle  10  and the remote vehicle  14 . For instance, if the brakes of the host vehicle  10  are held and the host vehicle  10  is stopped, no warning needs to be given. However, if the brakes of the host vehicle  10  are released, the host vehicle  10  is stopped, and a remote vehicle  14  (threat vehicle) is approaching, the controller  22  can hold the brakes in a braking state and issue a warning. Also, if the speed of the host vehicle is below threshold where the threat will pass, no warning needs to be issued. Thus, the process refrains from providing the warning while the evaluating determines that the operating condition indicates that a speed of the host vehicle  10  will permit the remote vehicle  14  to pass through the intersection without contacting the host vehicle  10 . Furthermore, if the speed of the host vehicle  10  is above a threshold where collision is likely, a warning is issued. Thus, the process provides the warning while the evaluating determines that the operating condition indicates that a speed of the host vehicle  10  can permit the remote vehicle  14  to contact the host vehicle  10 . As can also be appreciated from the above, the process performs a threat mitigation operation while a difference between the host vehicle travel time and the remote vehicle travel time is less than a threshold time value. As discussed above, the process can perform a threat mitigation operation by altering a trajectory of the host vehicle  10 . The altering of the trajectory of the host vehicle  10  can be performed by operating a steering wheel to change a steering direction of the host vehicle  10 , operating a brake, accelerator or both to change the speed of the host vehicle, or in any other suitable manner. The other vehicle components  38  can also include one or more safety devices such as a safety belt, an airbag system, and a horn. Thus, the controller  22  can perform a threat mitigation operation by pretensioning a safety belt, deploying an airbag, operating a horn in the host vehicle, or any of these functions. 
     As discussed above, if the process determines in step  7005  that the full code ABCDEF=010000, indicating that the host vehicle  10  is intending to turn left and the remote vehicle  14  is travelling straight in the opposite direction as shown in  FIG. 13 , the process continues to step  7010  to begin the process Warning LTAP/OD (Left Turn Across Path/Opposite Direction as shown in  FIG. 39 . That is, as can be appreciated from  FIG. 13 , it is desirable to consider certain factors relating to the operation of the host vehicle  10  when determining at what time to issue a warning in the case where the host vehicle  10  is attempting to make a left turn across the path of a remote vehicle  14  approaching the intersection from the opposite direction. For example, when inputs such as yaw rate, lateral acceleration, steering angle, and so are considered, the driver of the host vehicle  10  is typically already committed to the left turn maneuver before a determination can be made whether a warning is necessary. 
     An alternative is to monitor the speed and acceleration of the host vehicle  10  to anticipate the driver&#39;s action. That is, in addition to signaling a left turn, a driver will typically engage in certain pre-turn driving behaviors with regard to speed and acceleration control prior to initiating the turn. It is during this time that a warning, if needed, would be most effective. 
     Accordingly, as will now be described with reference to  FIG. 39 , the vehicle intersection monitoring system  12  in this example uses two speed thresholds and two acceleration thresholds to define a set of conditions in which it is likely that the driver of the host vehicle  10  is preparing to make a left turn. That is, a host vehicle  10  traveling below one speed threshold, ν 1  suggests that the driver intends to stop, but a host vehicle  10  traveling above a second speed threshold, ν 2  suggests the driver intends to continue driving forward. Also, the driver of the host vehicle  10  braking below one acceleration threshold a 1  suggests that the driver intends to continue driving forward, while the driver of the host vehicle  10  braking above a second acceleration threshold a 2  suggests that the driver intends to stop. Therefore, as shown, for example, in  FIG. 40 , the Active Area where the velocity of the host vehicle  10  ranges from ν 1  to ν 2  and the acceleration (braking) ranges from a 1  to a 2  indicates that the likelihood of the driver intending to turn the host vehicle  10  left is high. Again, it should be noted that the operations shown in  FIG. 39  are performed before the host vehicle  10  begins to execute the left turn, that is, before the driver begins to turn the steering wheel of the host vehicle  10  to cause the host vehicle  10  to begin executing the left turn. In other words, the operations shown in  FIG. 39  are performed before the direction of travel of the host vehicle  10  changes in the direction of the left turn. 
     In a manner similar to that discussed above, the controller  22  performs the processes discussed above to detect for the presence of a remote vehicle  14 . The controller  22  also performs the processes discussed above, such as checking the status of the turn signals, to determine the intention of the driver of the host vehicle  10 . As will be appreciated from the following description, many of the operations of the process shown in  FIG. 39  are similar to those shown in  FIG. 38 . 
     When the Warning. LTAP/OD process begins in step  8000  as shown in  FIG. 39 , the process continues to step  8010  to determine whether the speed of the host vehicle  10  is 0. If the speed is not 0, the processing determines in step  8020  if the speed of the host vehicle  10  is less than a threshold v threshold . If the speed is not less than the threshold v threshold , the processing determines in step  8030  whether the time to collision of the host vehicle  10  is less than a time to collision threshold for the host vehicle  10 . 
     That is, the processing determines in step  8030  whether the time to contact TTC of the remote vehicle  14  with the host vehicle  10  is less than a predetermined length of time for the remote vehicle  14  to contact the host vehicle  10  as defined by TTC LTAP2 . The value of TTC LTAP2  can be, for example, any time value within a range of 3 seconds to 5 seconds, or any other suitable value. The controller  22  can determine the presence of a remote vehicle  14  based on, for example, signals received from one or more sensors  40  ( FIG. 2 ), or by using messages received from the remote vehicle  14  that are communicated over a vehicle-to-vehicle communication network as discussed above. From this information, the controller  22  can determine the time to contact (TTC) of the remote vehicle  14  with the host vehicle  10  based on the following equation 
             TTC   =     D       v   HV     +     v   RV               
where D represents the instantaneous distance, between the host vehicle  10  and the remote vehicle  14  either measured directly by one or more of the sensors  40  or calculated by the controller  22  in accordance with the following equation
 
             D   =       (     1   -   f     )     ⁢     r   e     ⁢               (       θ   RV     -     θ   HV       )     2     ⁢     cos   2     ⁢     ϕ   HV       +       (       ϕ   RV     -     ϕ   HV       )     2             sin   2     ⁢     ϕ   HV       +         (     1   -   f     )     2     ⁢     cos   2     ⁢     ϕ     HV   ⁢                               
where
     f=1/298.257223563 (earth flattening);   r e =6,378,137 m (earth equatorial radius);   θ HV =Host Vehicle (HV) longitude;   θ RV =Remote Vehicle (RV) longitude;   φ HV =Host Vehicle (HV) latitude;   φ RV =Remote Vehicle (RV) latitude;   ν HV =Host Vehicle (HV) speed; and   ν RV =Remote Vehicle (RV) speed   

     If the TTC is less than the TTC LTAP2 , the process continues to step  8040  to determine if a warning variable W is equal to 1, thus indicating that a warning should be issued. The warning can generally be referred to as a threat mitigation operation as described herein. 
     In step  8040 , the vehicle intersection monitoring system  12  uses the two speed thresholds and two acceleration thresholds as mentioned above to determine whether the system should warn the driver of the host vehicle  10  (e.g., perform a threat mitigation operation and/or issue a warning) when the on-coming remote vehicle  14  is within a predetermined length of time away from the host vehicle  10  as defined by TTC LTAP2 . The value W is determined by the following equation 
             W   =         1   16     ⁡     [       (         v   -     v   1     +   σ              v   -     v   1            +   σ       +   1     )     ⁢     (           v   2     -   v   +   σ                v   2     -   v          +   σ       +   1     )       ]       ×     [       (         a   -     a   1     +   σ              a   -     a   1            +   σ       +   1     )     ⁢     (           a   2     -   a   +   σ                a   2     -   a          +   σ       +   1     )       ]             
where
 
     ν 1 =the lower speed threshold and thus, if the host vehicle  10  is traveling at a speed less than v1, W=0 because such a speed suggests that the driver is about to stop the host vehicle  10 ; 
     ν 2 =the upper speed threshold and thus, if the host vehicle  10  is traveling at a speed greater than v2, W=0 because such a speed suggests that the driver will allow the host vehicle  10  to proceed straight through the intersection or past the oncoming remote vehicle  14 ; 
     a  1 =the upper brake threshold and thus, if the host vehicle  10  is braking at a level greater than a1, W=0 because such a brake level suggests that the driver will cause the host vehicle  10  to come to a stop; 
     a 2 =the lower brake threshold and thus, if the host vehicle  10  is braking at a level lower than a1, W=0 because such a brake level suggests that the driver will allow the host vehicle  10  to proceed straight through the intersection or past the oncoming remote vehicle  14 ; 
     σ=a constant added to the equation to prevent dividing by 0; and 
             1   16         
is the normalization factor.
 
     If the process determines in step  8040  that the warning variable W is equal to 1, the process determines in step  8050  whether a warning has already been issued. If a warning has already been issued, the processing returns to step  8010  and repeats as discussed above. However, if a warning has not been issued, the process issues a warning in step  8060  and repeats at step  8010 . 
     Also, if the processing determines in step  8020  that the speed of the host vehicle  10  is not less than a threshold v threshold , if the processing determines in step  8030  that the TTC is not less than the TTC LTAP , or the processing in step  8040  determines that the value W is not equal to 1 (e.g., W=0), the processing continues to step  8070 . In step  8070 , the processing determines if the warning has been issued. If the warning has not been issued, the processing returns at step  8160  to step  3000  ( FIGS. 34A and 34B ) and repeats as discussed above. However, if the warning has been issued, the warning is reset in step  8080  and the processing returns at step  8160  to step  3000  and repeats as discussed above. 
     Returning to step  8010 , if the speed of the host vehicle  10  is determined to be 0, the processing determines in step  8090  whether the time to contact TTC of the remote vehicle  14  with the host vehicle  10  is less than a predetermined length of time for the remote vehicle  14  to contact the host vehicle  10  as defined by TTC LTAP1 . The value of TTC LTAP1  can be, for example, any time value within a range of 3 seconds to 5 seconds, or any other suitable value. If TTC is less than TTC LTAP1 , the processing determines in step  8100  if the brake of the host vehicle  10  has been released. If so, the processing holds the brake in step  8110  and issues a warning in step  8120 . As discussed above with regard to  FIG. 38 , this brake hold is characterized as a haptic warning since the driver can override the brake by applying the accelerator, and is not considered active control since it occurs under specific conditions. Thus, the process provides the warning while the evaluating determines that the operating condition indicates that a brake of the host vehicle  10  is in a disengaged condition to enable the host vehicle  10  to move from a stationary position and the possibility of contact exists. In this instance, the warning includes operating the brake to change from the disengaged condition to an engaged condition to retain the host vehicle  10  in a stationary position. 
     The processing then determines in step  8130  if the brake of the host vehicle  10  has been activated. If the brake has not been activated, the processing determines in step  8140  whether the throttle of the host vehicle  10  has been activated. If the throttle has not been activated, the processing returns to step  8130  and again checks whether the brake has been activated. However, if the throttle has been activated, the processing releases the brake in step  8150  and resets the warning in step  8080 . The processing continues to step  8160  and returns to step  3000  ( FIGS. 34A and 34B ) as discussed above. In addition, if the processing determines in step  8090  that the time to contact TTC of the remote vehicle  14  with the host vehicle  10  is less than a predetermined length of time away from the host vehicle  10  as defined by TTC LTAP1 , or the processing determines in step  8100  that the brake of the host vehicle  10  has not been released, the processing continues to step  8070  and repeats as discussed above. 
     In addition, as with the operations described in the flowchart of  FIG. 38 , the process shown in  FIG. 39  can also perform a threat mitigation operation by altering a trajectory of the host vehicle  10 . The altering of the trajectory of the host vehicle  10  can be performed by operating a steering wheel to change a steering direction of the host vehicle  10 , operating a brake, accelerator or both to change the speed of the host vehicle, or in any other suitable manner. The other vehicle components  38  can also include one or more safety devices such as a safety belt, an airbag system, and a horn. Thus, the controller  22  can perform a threat mitigation operation by pretensioning a safety belt, deploying an airbag, operating a horn in the host vehicle, or any of these functions. 
     The following Tables 8 through 16 summarize the different types of warning conditions that may arise depending on the type of scenario as shown in  FIGS. 4 through 30  depending on the state of the host vehicle (HV)  10  and the remote vehicle  14  (threat vehicle TV). 
     
       
         
           
               
             
               
                 TABLE 8 
               
             
            
               
                   
               
               
                 Initial conditions for Straight Crossing Path Scenarios 
               
            
           
           
               
               
               
            
               
                 HV 
                 TV 
                 HV Response 
               
               
                   
               
               
                 Stopped with brakes 
                 Stopped with brakes applied 
                 No warning 
               
               
                 applied 
                 Stopped with brakes released 
                 No warning 
               
               
                   
                 Creeping forward (0 &lt; v TV  &lt; v threshold ) 
                 No warning 
               
               
                   
                 Approaching at speed (v TV  &gt; v threshold ) 
                 No warning 
               
               
                 Stopped with brakes 
                 Stopped with brakes applied 
                 No warning 
               
               
                 released 
                 Stopped with brakes released 
                 No warning 
               
               
                   
                 Creeping forward (0 &lt; v TV  &lt; v threshold ) 
                 No warning 
               
               
                   
                 Approaching at speed (v TV  &gt; v threshold ) 
                 Hold brakes, issue warning 
               
               
                 Creeping forward (0 &lt; 
                 Stopped with brakes applied 
                 No warning 
               
               
                 v HV  &lt; v threshold ) 
                 Stopped with brakes released 
                 No warning 
               
               
                   
                 Creeping forward (0 &lt; v TV  &lt; v threshold ) 
                 No warning 
               
               
                   
                 Approaching at speed (v TV  &gt; v threshold ) 
                 No warning 
               
               
                 Approaching at 
                 Stopped with brakes applied 
                 No warning 
               
               
                 speed (v HV  &gt; v threshold ) 
                 Stopped with brakes released 
                 No warning 
               
               
                   
                 Creeping forward (0 &lt; v TV  &lt; v threshold ) 
                 Issue warning 
               
               
                   
                 Approaching at speed (v TV  &gt; v threshold ) 
                 Issue warning 
               
               
                   
               
            
           
         
       
     
     For the scenarios when the host vehicle  10  is travelling straight and the remote vehicle  14  is travelling in an opposite direction to the host vehicle  10  and making a left turn across the path of the host vehicle  10 , there are a total of 16 possible combinations with three that could produce a warning in the HV. 
     
       
         
           
               
             
               
                 TABLE 9 
               
             
            
               
                   
               
               
                 HV Travelling Straight and TV in Opposite Direction Turning Left 
               
            
           
           
               
               
               
            
               
                 HV 
                 TV 
                 HV Response 
               
               
                   
               
               
                 Stopped with brakes 
                 Stopped with brakes applied 
                 No warning 
               
               
                 applied 
                 Stopped with brakes released 
                 No warning 
               
               
                   
                 Creeping forward (0 &lt; v TV  &lt; v threshold ) 
                 No warning 
               
               
                   
                 Approaching at speed (v TV  &gt; v threshold ) 
                 No warning 
               
               
                 Stopped with brakes 
                 Stopped with brakes applied 
                 No warning 
               
               
                 released 
                 Stopped with brakes released 
                 No warning 
               
               
                   
                 Creeping forward (0 &lt; v TV  &lt; v threshold ) 
                 No warning 
               
               
                   
                 Approaching at speed (v TV  &gt; v threshold ) 
                 Hold brakes, issue warning 
               
               
                 Creeping forward (0 &lt; 
                 Stopped with brakes applied 
                 No warning 
               
               
                 v HV  &lt; v threshold ) 
                 Stopped with brakes released 
                 No warning 
               
               
                   
                 Creeping forward (0 &lt; v TV  &lt; v threshold ) 
                 No warning 
               
               
                   
                 Approaching at speed (v TV  &gt; v threshold ) 
                 No warning 
               
               
                 Approaching at 
                 Stopped with brakes applied 
                 No warning 
               
               
                 speed (v HV  &gt; v threshold ) 
                 Stopped with brakes released 
                 No warning 
               
               
                   
                 Creeping forward (0 &lt; v TV  &lt; v threshold ) 
                 Issue warning 
               
               
                   
                 Approaching at speed (v TV  &gt; v threshold ) 
                 Issue warning 
               
               
                   
               
            
           
         
       
     
     For the scenarios when the host vehicle  10  is travelling straight and the remote vehicle  14  is travelling in a lateral direction to the host vehicle  10  and making a left turn across the path of the host vehicle  10 , there are a total of 16 possible combinations with three that could produce a warning in the HV. 
     
       
         
           
               
             
               
                 TABLE 10 
               
             
            
               
                   
               
               
                 HV Travelling Straight and TV in Lateral Direction Turning Left 
               
            
           
           
               
               
               
            
               
                 HV 
                 TV 
                 HV Response 
               
               
                   
               
               
                 Stopped with brakes 
                 Stopped with brakes applied 
                 No warning 
               
               
                 applied 
                 Stopped with brakes released 
                 No warning 
               
               
                   
                 Creeping forward (0 &lt; v TV  &lt; v threshold ) 
                 No warning 
               
               
                   
                 Approaching at speed (v TV  &gt; v threshold ) 
                 No warning 
               
               
                 Stopped with brakes 
                 Stopped with brakes applied 
                 No warning 
               
               
                 released 
                 Stopped with brakes released 
                 No warning 
               
               
                   
                 Creeping forward (0 &lt; v TV  &lt; v threshold ) 
                 No warning 
               
               
                   
                 Approaching at speed (v TV  &gt; v threshold ) 
                 Hold brakes, issue warning 
               
               
                 Creeping forward (0 &lt; 
                 Stopped with brakes applied 
                 No warning 
               
               
                 v HV  &lt; v threshold ) 
                 Stopped with brakes released 
                 No warning 
               
               
                   
                 Creeping forward (0 &lt; v TV  &lt; v threshold ) 
                 No warning 
               
               
                   
                 Approaching at speed (v TV  &gt; v threshold ) 
                 No warning 
               
               
                 Approaching at 
                 Stopped with brakes applied 
                 No warning 
               
               
                 speed (v HV  &gt; v threshold ) 
                 Stopped with brakes released 
                 No warning 
               
               
                   
                 Creeping forward (0 &lt; v TV  &lt; v threshold ) 
                 Issue warning 
               
               
                   
                 Approaching at speed (v TV  &gt; v threshold ) 
                 Issue warning 
               
               
                   
               
            
           
         
       
     
     For the scenarios when the host vehicle  10  is travelling straight and the remote vehicle  14  is approaching the intersection from a cross street and making a left turn into the path of the host vehicle  10 , there are a total of 16 possible combinations with three that could produce a warning in the HV. 
     
       
         
           
               
             
               
                 TABLE 11 
               
             
            
               
                   
               
               
                 HV Travelling Straight and TV Turning Left from Cross Street 
               
            
           
           
               
               
               
            
               
                 HV 
                 TV 
                 HV Response 
               
               
                   
               
               
                 Stopped with brakes 
                 Stopped with brakes applied 
                 No warning 
               
               
                 applied 
                 Stopped with brakes released 
                 No warning 
               
               
                   
                 Creeping forward (0 &lt; v TV  &lt; v threshold ) 
                 No warning 
               
               
                   
                 Approaching at speed (v TV  &gt; v threshold ) 
                 No warning 
               
               
                 Stopped with brakes 
                 Stopped with brakes applied 
                 No warning 
               
               
                 released 
                 Stopped with brakes released 
                 No warning 
               
               
                   
                 Creeping forward (0 &lt; v TV  &lt; v threshold ) 
                 No warning 
               
               
                   
                 Approaching at speed (v TV  &gt; v threshold ) 
                 Hold brakes, issue warning 
               
               
                 Creeping forward (0 &lt; 
                 Stopped with brakes applied 
                 No warning 
               
               
                 v HV  &lt; v threshold ) 
                 Stopped with brakes released 
                 No warning 
               
               
                   
                 Creeping forward (0 &lt; v TV  &lt; v threshold ) 
                 No warning 
               
               
                   
                 Approaching at speed (v TV  &gt; v threshold ) 
                 No warning 
               
               
                 Approaching at 
                 Stopped with brakes applied 
                 No warning 
               
               
                 speed (v HV  &gt; v threshold ) 
                 Stopped with brakes released 
                 No warning 
               
               
                   
                 Creeping forward (0 &lt; v TV  &lt; v threshold ) 
                 Issue warning 
               
               
                   
                 Approaching at speed (v TV  &gt; v threshold ) 
                 Issue warning 
               
               
                   
               
            
           
         
       
     
     For the scenarios when the host vehicle  10  is travelling straight and the remote vehicle  14  is approaching, the intersection from a cross street and making a right turn into the path of the host vehicle  10 , there are a total of 16 possible combinations with three that could produce a warning in the HV. 
     
       
         
           
               
             
               
                 TABLE 12 
               
             
            
               
                   
               
               
                 HV Travelling Straight and TV Turning Right from Cross Street 
               
            
           
           
               
               
               
            
               
                   
                   
                 HV 
               
               
                 HV 
                 TV 
                 Response 
               
               
                   
               
               
                 Stopped with 
                 Stopped with brakes applied 
                 No warning 
               
               
                 brakes 
                 Stopped with brakes released 
                 No warning 
               
               
                 applied 
                 Creeping forward (0 &lt; v TV  &lt; v threshold ) 
                 No warning 
               
               
                   
                 Approaching at speed (v TV  &gt; v threshold ) 
                 No warning 
               
               
                 Stopped with 
                 Stopped with brakes applied 
                 No warning 
               
               
                 brakes 
                 Stopped with brakes released 
                 No warning 
               
               
                 released 
                 Creeping forward (0 &lt; v TV  &lt; v threshold ) 
                 No warning 
               
               
                   
                 Approaching at speed (v TV  &gt; v threshold ) 
                 Hold brakes, 
               
               
                   
                   
                 issue 
               
               
                   
                   
                 warning 
               
               
                 Creeping forward 
                 Stopped with brakes applied 
                 No warning 
               
               
                 (0 &lt; v HV  &lt; 
                 Stopped with brakes released 
                 No warning 
               
               
                  v threshold ) 
                 Creeping forward (0 &lt; v TV  &lt; v threshold ) 
                 No warning 
               
               
                   
                 Approaching at speed (v TV  &gt; v threshold ) 
                 No warning 
               
               
                 Approaching at 
                 Stopped with brakes applied 
                 No warning 
               
               
                 speed 
                 Stopped with brakes released 
                 No warning 
               
               
                 (v HV  &gt; v threshold ) 
                 Creeping forward (0 &lt; v TV  &lt; v threshold ) 
                 Issue 
               
               
                   
                   
                 warning 
               
               
                   
                 Approaching at speed (v TV  &gt; v threshold ) 
                 Issue 
               
               
                   
                   
                 warning 
               
               
                   
               
            
           
         
       
     
     For the scenarios when the host vehicle  10  is turning left and the remote vehicle  14  is travelling straight in an opposite direction of the host vehicle  10 , there are a total of 16 possible combinations with three that could produce a warning in the HV. 
     
       
         
           
               
             
               
                 TABLE 13 
               
             
            
               
                   
               
               
                 HV Turning Left and TV Travelling Straight 
               
            
           
           
               
               
               
            
               
                   
                   
                 HV 
               
               
                 HV 
                 TV 
                 Response 
               
               
                   
               
               
                 Stopped with 
                 Stopped with brakes applied 
                 No warning 
               
               
                 brakes 
                 Stopped with brakes released 
                 No warning 
               
               
                 applied 
                 Creeping forward (0 &lt; v TV  &lt; v threshold ) 
                 No warning 
               
               
                   
                 Approaching at speed (v TV  &gt; v threshold ) 
                 No warning 
               
               
                 Stopped with 
                 Stopped with brakes applied 
                 No warning 
               
               
                 brakes 
                 Stopped with brakes released 
                 No warning 
               
               
                 released 
                 Creeping forward (0 &lt; v TV  &lt; v threshold ) 
                 No warning 
               
               
                   
                 Approaching at speed (v TV  &gt; v threshold ) 
                 Hold brakes, 
               
               
                   
                   
                 issue 
               
               
                   
                   
                 warning 
               
               
                 Creeping 
                 Stopped with brakes applied 
                 No warning 
               
               
                 forward (0 &lt; 
                 Stopped with brakes released 
                 No warning 
               
               
                 v HV  &lt; v threshold ) 
                 Creeping forward (0 &lt; v TV  &lt; v threshold ) 
                 No warning 
               
               
                   
                 Approaching at speed (v TV  &gt; v threshold ) 
                 No warning 
               
               
                 Approaching at 
                 Stopped with brakes applied 
                 No warning 
               
               
                 speed 
                 Stopped with brakes released 
                 No warning 
               
               
                 (v HV  &gt; v threshold ) 
                 Creeping forward (0 &lt; v TV  &lt; v threshold ) 
                 Issue 
               
               
                   
                   
                 warning 
               
               
                   
                 Approaching at speed (v TV  &gt; v threshold ) 
                 Issue 
               
               
                   
                   
                 warning 
               
               
                   
               
            
           
         
       
     
     For the scenarios when the host vehicle  10  is turning left and the remote vehicle  14  is travelling straight from a cross street, there are a total of 16 possible combinations with three that could produce a warning in the HV. 
     
       
         
           
               
             
               
                 TABLE 14 
               
             
            
               
                   
               
               
                 HV Turning Left and TV Travelling Straight from Cross Street 
               
            
           
           
               
               
               
            
               
                   
                   
                 HV 
               
               
                 HV 
                 TV 
                 Response 
               
               
                   
               
               
                 Stopped with 
                 Stopped with brakes applied 
                 No warning 
               
               
                 brakes 
                 Stopped with brakes released 
                 No warning 
               
               
                 applied 
                 Creeping forward (0 &lt; v TV  &lt; v threshold ) 
                 No warning 
               
               
                   
                 Approaching at speed (v TV  &gt; v threshold ) 
                 No warning 
               
               
                 Stopped with 
                 Stopped with brakes applied 
                 No warning 
               
               
                 brakes 
                 Stopped with brakes released 
                 No warning 
               
               
                 released 
                 Creeping forward (0 &lt; v TV  &lt; v threshold ) 
                 No warning 
               
               
                   
                 Approaching at speed (v TV  &gt; v threshold ) 
                 Hold brakes, 
               
               
                   
                   
                 issue 
               
               
                   
                   
                 warning 
               
               
                 Creeping 
                 Stopped with brakes applied 
                 No warning 
               
               
                 forward (0 &lt; 
                 Stopped with brakes released 
                 No warning 
               
               
                 v HV  &lt; v threshold ) 
                 Creeping forward (0 &lt; v TV  &lt; v threshold ) 
                 No warning 
               
               
                   
                 Approaching at speed (v TV  &gt; v threshold ) 
                 No warning 
               
               
                 Approaching at 
                 Stopped with brakes applied 
                 No warning 
               
               
                 speed (v HV  &gt; 
                 Stopped with brakes released 
                 No warning 
               
               
                 v threshold ) 
                 Creeping forward (0 &lt; v TV  &lt; v threshold ) 
                 Issue 
               
               
                   
                   
                 warning 
               
               
                   
                 Approaching at speed (v TV  &gt; v threshold ) 
                 Issue 
               
               
                   
                   
                 warning 
               
               
                   
               
            
           
         
       
     
     For the scenarios when the host vehicle  10  is turning left and the remote vehicle  14  is travelling straight from a cross street so that the host vehicle  10  is turning into the path of the remote vehicle  14 , there are a total of 16 possible combinations with three that could produce a warning in the HV. 
     
       
         
           
               
             
               
                 TABLE 15 
               
             
            
               
                   
               
               
                 HV Turning Left and TV Travelling Straight from Cross Street 
               
            
           
           
               
               
               
            
               
                   
                   
                 HV 
               
               
                 HV 
                 TV 
                 Response 
               
               
                   
               
               
                 Stopped with 
                 Stopped with brakes applied 
                 No warning 
               
               
                 brakes 
                 Stopped with brakes released 
                 No warning 
               
               
                 applied 
                 Creeping forward (0 &lt; v TV  &lt; v threshold ) 
                 No warning 
               
               
                   
                 Approaching at speed (v TV  &gt; v threshold ) 
                 No warning 
               
               
                 Stopped with 
                 Stopped with brakes applied 
                 No warning 
               
               
                 brakes 
                 Stopped with brakes released 
                 No warning 
               
               
                 released 
                 Creeping forward (0 &lt; v TV  &lt; v threshold ) 
                 No warning 
               
               
                   
                 Approaching at speed (v TV  &gt; v threshold ) 
                 Hold brakes, 
               
               
                   
                   
                 issue 
               
               
                   
                   
                 warning 
               
               
                 Creeping 
                 Stopped with brakes applied 
                 No warning 
               
               
                 forward (0 &lt; 
                 Stopped with brakes released 
                 No warning 
               
               
                 v HV  &lt; v threshold ) 
                 Creeping forward (0 &lt; v TV  &lt; v threshold ) 
                 No warning 
               
               
                   
                 Approaching at speed (v TV  &gt; v threshold ) 
                 No warning 
               
               
                 Approaching at 
                 Stopped with brakes applied 
                 No warning 
               
               
                 speed 
                 Stopped with brakes released 
                 No warning 
               
               
                 (v HV  &gt; v threshold ) 
                 Creeping forward (0 &lt; v TV  &lt; v threshold ) 
                 Issue 
               
               
                   
                   
                 warning 
               
               
                   
                 Approaching at speed (v TV  &gt; v threshold ) 
                 Issue 
               
               
                   
                   
                 warning 
               
               
                   
               
            
           
         
       
     
     For the scenarios when the host vehicle  10  is turning right and the remote vehicle  14  is travelling straight from a cross street so that the host vehicle  10  is turning into the path of the remote vehicle  14 , there are a total of 16 possible combinations with three that could produce a warning in the HV. 
     
       
         
           
               
             
               
                 TABLE 16 
               
             
            
               
                   
               
               
                 HV Turning Right and TV Travelling Straight from Cross Street 
               
            
           
           
               
               
               
            
               
                   
                   
                 HV 
               
               
                 HV 
                 TV 
                 Response 
               
               
                   
               
               
                 Stopped with 
                 Stopped with brakes applied 
                 No warning 
               
               
                 brakes 
                 Stopped with brakes released 
                 No warning 
               
               
                 applied 
                 Creeping forward (0 &lt; v TV  &lt; v threshold ) 
                 No warning 
               
               
                   
                 Approaching at speed (v TV  &gt; v threshold ) 
                 No warning 
               
               
                 Stopped with 
                 Stopped with brakes applied 
                 No warning 
               
               
                 brakes 
                 Stopped with brakes released 
                 No warning 
               
               
                 released 
                 Creeping forward (0 &lt; v TV  &lt; v threshold ) 
                 No warning 
               
               
                   
                 Approaching at speed (v TV  &gt; v threshold ) 
                 Hold brakes, 
               
               
                   
                   
                 issue 
               
               
                   
                   
                 warning 
               
               
                 Creeping 
                 Stopped with brakes applied 
                 No warning 
               
               
                 forward (0 &lt; 
                 Stopped with brakes released 
                 No warning 
               
               
                 v HV  &lt; v threshold ) 
                 Creeping forward (0 &lt; v TV  &lt; v threshold ) 
                 No warning 
               
               
                   
                 Approaching at speed (v TV  &gt; v threshold ) 
                 No warning 
               
               
                 Approaching at 
                 Stopped with brakes applied 
                 No warning 
               
               
                 speed 
                 Stopped with brakes released 
                 No warning 
               
               
                 (v HV  &gt; v threshold ) 
                 Creeping forward (0 &lt; v TV  &lt; v threshold ) 
                 Issue 
               
               
                   
                   
                 warning 
               
               
                   
                 Approaching at speed (v TV  &gt; v threshold ) 
                 Issue 
               
               
                   
                   
                 warning 
               
               
                   
               
            
           
         
       
     
     An example of another process that can be performed by the controller  22  to identify the scenario as discussed above with regard to  FIGS. 4 through 30  will now be described with regard to the flowchart in  FIG. 41 , the graphs shown in  FIGS. 42 through 45 , and the flowcharts in  FIGS. 46 through 48 . It should be noted that the information pertaining to the host vehicle  10  and the remote vehicle  14  used in this process can be obtained from the BSMs as discussed above. 
     Furthermore, the process shown in the flowchart of  FIG. 41  is essentially identical to the flowcharts shown in  FIGS. 34A and 34B , except that the host vehicle  10  is instead referred to as a subject or host vehicle (HV)  10 . Accordingly, for purposes of convention with the graphs shown in  FIGS. 42 through 45  and the flowcharts in  FIGS. 46 through 48 , the operations will be briefly discussed. 
     In the process of identifying a threat to the host vehicle  10 , the application first minimizes the number of remote vehicles  14  that should be monitored by performing the following operations. Upon receipt of a BSM, the controller  22  can check the turn signal status of the host vehicle  10  and the remote vehicle  14 . This information for the remote vehicle  14  can be located in part 2 of the BSM and the CAN for the host vehicle  10 . For the host vehicle  10 , AB=00 if there is no turn signal, AB=01 if the host vehicle  10  is signaling a left turn, and AB=11 if the host vehicle  10  is signaling a right turn. For the remote vehicle  14 , CD=00 if there is no turn signal, CD=01 if the remote vehicle  14  is signaling a left turn, and CD=11 if the remote vehicle  14  is signaling a right turn. These operations are performed as shown in the flowchart of  FIG. 41 . 
     As shown in the flowchart of  FIG. 41 , when the process begins in step  9000 , the controller  22  determines from the location information pertaining to the host vehicle  10  and the remote vehicle  14  whether a difference in elevation ΔH between the host vehicle  10  and the remote vehicle  14  is above a threshold H threshold  in step  9010 . In other words, H threshold  represents the threshold value that determines whether the remote vehicle  14  should be considered to be a possible threat vehicle. In this example, the value of H threshold =14 ft.±1 ft. However, the value of H threshold  can be any suitable value. Therefore, if the processing determines in step  9010  that the host vehicle  10  and the remote vehicle  14  are at different elevations, the processing determines that the remote vehicle  14  is not a threat to the host vehicle  10  (e.g., the remote vehicle  14  will pass above the host vehicle  10  on an overpass). Hence, the processing can end in step  9020  and return to the beginning in step  9000 . Accordingly, the processing refrains from performing a threat mitigation operation as discussed herein. 
     However, if the difference in elevation ΔH between the host vehicle  10  and the remote vehicle  14  is not above the threshold H threshold , the processing continues to determine whether the left or right turn signals of the host vehicle  10  and the remote vehicle  14  indicate that either of the vehicles  10  or  14  intend to turn left or right. In step  9030 , the processing determines whether the left turn signal of the host vehicle  10  is activated. If the left turn signal of the host vehicle  10  is activated, the processing continues to step  9040  where the values of binary code AB discussed above with regard to the truth table in Table 4 are set to 01. However, if the left turn signal of the host vehicle  10  is not activated, the processing continues from step  9030  to step  9050 . 
     In step  9050 , the processing determines whether the right turn signal of the host vehicle  10  is activated. If the right turn signal of the host vehicle  10  is activated, the processing continues to step  9060  where the values of binary code AB are set to 11. However, if the right turn signal of the host vehicle  10  is not activated, the processing continues from step  9050  to step  9070  where the values of the binary code AB are set to 00, thus indicating that the host vehicle  10  intends to travel straight without turning. 
     In step  9080 , the processing determines whether the left turn signal of the remote vehicle  14  is activated. If the left turn signal of the remote vehicle  14  is activated, the processing continues to step  9090  where the values of binary code CD discussed above with regard to the truth table in Table 4 are set to 01. However, if the left turn signal of the remote vehicle  14  is not activated, the processing continues from step  9080  to step  9100 . 
     In step  9100 , the processing determines whether the right turn signal of the remote vehicle  14  is activated. If the right turn signal of the remote vehicle  14  is activated, the processing continues to step  9110  where the values of binary code CD are set to 11. However, if the right turn signal of the remote vehicle  14  is not activated, the processing continues from step  9100  to step  9120  where the values of the binary code CD are set to 00, thus indicating that the remote vehicle  14  intends to travel straight without turning. 
     Accordingly, as in the previous examples discussed above, the process includes operations of preparing a host vehicle message including information pertaining to a host vehicle  10  including a host vehicle location and a host vehicle heading, and receiving a remote vehicle message including information pertaining to a remote vehicle  14  including a remote vehicle location and a remote vehicle heading. The processing then evaluating, using the controller  22 , whether the host vehicle heading and the remote vehicle heading are converging paths. As will now be discussed, this process includes segregating an area surrounding the host vehicle location into a plurality of sectors, determining which of the sectors is a remote vehicle sector including the remote vehicle location, and determining whether the host vehicle heading and the remote vehicle heading are converging paths based on the host vehicle location, the host vehicle heading, the remote vehicle location, the remote vehicle heading and a characteristic relating to the sector that includes the remote vehicle location. 
     That is, after completing the above processing to determine the values for binary codes AB and CD, the processing continues to step  9130  where the angle β 1  shown in  FIGS. 42 through 45  is calculated according to the following equation 
               β   1     =       π   ⁡     (           θ   RV     -     θ   HV     +   σ                θ   RV     -     θ   HV            +   σ       +   1     )       -         cos     -   1       ⁡     (       (       ϕ   RV     -     ϕ   HV       )               (       θ   RV     -     θ   HV       )     2     ⁢     cos   2     ⁢     ϕ   RV       +       (       ϕ   RV     -     ϕ   HV       )     2           )       ⁢     (         θ   RV     -     θ   HV     +   σ                θ   RV     -     θ   HV            +   σ       )               
where θ RV =longitude of the remote vehicle  14 , θ HV =longitude of the host vehicle  10 , φ RV =latitude of the remote vehicle  14 , φ HV =latitude of the host vehicle  10 , and σ=a constant of very small value (e.g. of a magnitude ˜10 −9 ) added to the equation to prevent dividing by 0.
 
     Examples of possible locations of a remote vehicle  14  are shown in the graphs of  FIGS. 42 through 45 . In these graphs, the heading angle for the host vehicle  10  is represented by δ HV  and the heading angle for the remote vehicle  14  is represented by δ RV  for the remote vehicle  14  with 0 degrees representing north, π/2 (90 degrees) representing east, π (180 degrees) representing south and 3π/2 (270 degrees) representing west. The sectors are adjacently geographically distributed about the host vehicle location which is at the geographic center of the area where each of the sectors meet. Furthermore, the sectors are separated by a north-south directional line and an east-west directional line that intersect at the host vehicle location. In this case, since there are four sectors, they can be referred to as quadrants. 
     As shown in  FIG. 42 , if the remote vehicle  14  is to the north and east of the host vehicle  10 , the remote vehicle is in the 1 st  quadrant. If the remote vehicle  14  is to the north and west of the host vehicle  10 , the remote vehicle is in the 2 nd  quadrant as shown in  FIG. 43 . If the remote vehicle  14  is to the south and west of the host vehicle  10 , the remote vehicle is in the 3 rd  quadrant as shown in  FIG. 44 . As shown in  FIG. 45 , if the remote vehicle  14  is to the south and east of the host vehicle  10 , the remote vehicle is in the 4 th  quadrant. 
     The 1 st  quadrant is defined by the following conditions: 
     
       
         
           
             
               
                 θ 
                 RV 
               
               &gt; 
               
                 θ 
                 HV 
               
             
             ⁢ 
             
               , 
               RV 
             
             ⁢ 
             
               &gt; 
               
                 ϕ 
                 HV 
               
             
             , 
             
               
                 ( 
                 
                   0 
                   ≤ 
                   
                     β 
                     1 
                   
                   &lt; 
                   
                     π 
                     2 
                   
                 
                 ) 
               
               . 
             
           
         
       
     
     Within the 1 st  quadrant, certain headings of the host vehicle  10  and the remote vehicle  14  that result in crossing paths can be determined by the following matrices in Table 17, where δ HV &lt;δ RV  in one matrix and δ HV &gt;δ RV  in the other matrix. 
     
       
         
           
               
             
               
                 TABLE 17 
               
             
            
               
                   
               
               
                 Matrices Representing Possible Crossing Paths in the 1 st  Quadrant 
               
            
           
           
               
               
               
               
               
            
               
                   
                   
                 00 
                 01 
                 11 
               
               
                   
                   
                 0 ≦ 
                 β 1  &lt; 
                 β 1  + π &lt; 
               
               
                 δ HV  &lt; δ RV   
                 YZ 
                 δ RV  ≦ β 1   
                 δ RV  ≦ β 1  + π 
                 δ RV  &lt; 2π 
               
               
                   
               
               
                 WX 
                   
                   
                   
                   
               
               
                 00 
                 0 ≦ δ HV  ≦ β 1   
                 0 
                 0 
                 1 
               
               
                 01 
                 β 1  &lt; δ HV  ≦ β 1  + π 
                 x 
                 1 
                 0 
               
               
                 11 
                 β 1  + π &lt; δ HV  &lt; 2π 
                 x 
                 x 
                 0 
               
               
                 XW 
               
               
                 00 
                 0 ≦ δ HV  ≦ β 1   
                 1 
                 x 
                 x 
               
               
                 01 
                 β 1  &lt; δ HV  ≦ β 1  + π 
                 0 
                 0 
                 x 
               
               
                 11 
                 β 1  + π &lt; δ HV  &lt; 2π 
                 0 
                 0 
                 1 
               
               
                   
               
            
           
         
       
     
     These two matrices identify four cases where paths cross (1), eight cases where paths do not cross (0) and six cases that are not possible (x). For example, if the heading angle δ HV  of the host vehicle  10  is greater than β 1  and the heading angle δ RV  of the remote vehicle  14  is less than β 1 , then δ HV  cannot be less than δ RV  (wxyz=0100 for δ HV &lt;δ RV ). It can also be seen that when the remote vehicle  14  is in the 1 st  quadrant, the remote vehicle  14  will be to the left of the host vehicle  10  (EF=01) when the heading angle of the host vehicle  10  is greater than β 1  and less than β 1 +π(β 1 &lt;δ HV &lt;β 1 +π), otherwise the remote vehicle  14  will be to the right (EF=11) of the host vehicle  10  (i.e. when β 1 +π&lt;δ HV &lt;β 1 ). 
     The 2 nd  quadrant is defined by the following conditions: 
     
       
         
           
             
               
                 θ 
                 RV 
               
               &lt; 
               
                 θ 
                 HV 
               
             
             , 
             
               
                 ϕ 
                 RV 
               
               &gt; 
               
                 ϕ 
                 HV 
               
             
             , 
             
               
                 ( 
                 
                   
                     
                       3 
                       2 
                     
                     ⁢ 
                     π 
                   
                   ≤ 
                   
                     β 
                     1 
                   
                   &lt; 
                   
                     2 
                     ⁢ 
                     π 
                   
                 
                 ) 
               
               . 
             
           
         
       
     
     Within the 1 st  quadrant, certain headings of the host vehicle  10  and the remote vehicle  14  that result in crossing paths can be determined by the following matrices in Table 18, where δ HV &lt;δ RV  in one matrix and δ HV &gt;δ RV  in the other matrix. 
     
       
         
           
               
             
               
                 TABLE 18 
               
             
            
               
                   
               
               
                 Matrices Representing Possible Crossing Paths in the 2 nd  Quadrant 
               
            
           
           
               
               
               
               
               
            
               
                   
                   
                 00 
                 01 
                 11 
               
               
                   
                   
                 0 ≦ 
                 β 1  − π &lt; 
                 β 1  &lt; 
               
               
                 δ HV  &lt; δ RV   
                 YZ 
                 δ RV  ≦ β 1  − π 
                 δ RV  ≦ β 1   
                 δ RV  &lt; 2π 
               
               
                   
               
               
                 WX 
                   
                   
                   
                   
               
               
                 00 
                 0 ≦ δ HV  ≦ β 1  − π 
                 1 
                 0 
                 0 
               
               
                 01 
                 β 1  − π &lt; δ HV  ≦ β 1   
                 x 
                 0 
                 0 
               
               
                 11 
                 β 1  &lt; δ HV  &lt; 2π 
                 x 
                 x 
                 1 
               
               
                 WX 
               
               
                 00 
                 0 ≦ δ HV  ≦ β 1  − π 
                 0 
                 x 
                 x 
               
               
                 01 
                 β 1  − π &lt; δ HV  ≦ β 1   
                 0 
                 1 
                 x 
               
               
                 11 
                 β 1  &lt; δ HV  &lt; 2π 
                 1 
                 0 
                 0 
               
               
                   
               
            
           
         
       
     
     The two matrices identify four cases where paths cross (1), eight cases where paths do not cross (0) and six cases that are not possible (x). For example, if the heading angle δ HV  of the host vehicle  10  is greater than β 1 , and the heading angle δ RV  of the remote vehicle  14  is less than β 1 −π, then δ HV  cannot be less than δ RV  (wxyz=1100 for δ HV &lt;δ RV ). It can also be seen that when the remote vehicle  14  is in the 2 nd  quadrant, the remote vehicle  14  will be to the right (EF=11) of the host vehicle  10  when the heading angle of the host vehicle  10  is greater than β 1 −π and less than β 1  (β 1 −π&lt;δ HV &lt;β 1 ) otherwise the remote vehicle  14  will be to the left (EF=01) of the host vehicle  10  (i.e., when β 1 &lt;δ HV &lt;β 1 −π). 
     The 3 rd  quadrant is defined by the following conditions: 
     
       
         
           
             
               
                 θ 
                 RV 
               
               &lt; 
               
                 θ 
                 HV 
               
             
             , 
             
               
                 ϕ 
                 RV 
               
               &lt; 
               
                 ϕ 
                 HV 
               
             
             , 
             
               
                 ( 
                 
                   π 
                   ≤ 
                   
                     β 
                     1 
                   
                   &lt; 
                   
                     
                       3 
                       2 
                     
                     ⁢ 
                     π 
                   
                 
                 ) 
               
               . 
             
           
         
       
     
     Within the 3 rd  quadrant, certain headings of the host vehicle  10  and the remote vehicle  14  that result in crossing paths can be determined by the following matrices in Table 19, where δ HV &lt;δ RV  in one matrix and δ HV &gt;δ RV  in the other matrix. 
     
       
         
           
               
             
               
                 TABLE 19 
               
             
            
               
                   
               
               
                 Matrices Representing Possible Crossing Paths in the 3 rd  Quadrant 
               
            
           
           
               
               
               
               
               
            
               
                   
                   
                 00 
                 01 
                 11 
               
               
                   
                   
                 0 ≦ 
                 β 1  − π &lt; 
                 β 1  &lt; 
               
               
                 δ HV  &lt; δ RV   
                 YZ 
                 δ RV  ≦ β 1  − π 
                 δ RV  ≦ β 1   
                 δ RV  &lt; 2π 
               
               
                   
               
               
                 WX 
                   
                   
                   
                   
               
               
                 00 
                 0 ≦ δ HV  ≦ β 1  − π 
                 1 
                 0 
                 0 
               
               
                 01 
                 β 1  − π &lt; δ HV  ≦ β 1   
                 x 
                 0 
                 0 
               
               
                 11 
                 β 1  &lt; δ HV  &lt; 2π 
                 x 
                 x 
                 1 
               
               
                 WX 
               
               
                 00 
                 0 ≦ δ HV  ≦ β 1  − π 
                 0 
                 x 
                 x 
               
               
                 01 
                 β 1  − π &lt; δ HV  ≦ β 1   
                 0 
                 1 
                 x 
               
               
                 11 
                 β 1  &lt; δ HV  &lt; 2π 
                 1 
                 0 
                 0 
               
               
                   
               
            
           
         
       
     
     The two matrices again identify four cases where paths cross (1), eight cases where paths do not cross (0) and six cases that are not possible (x). It should be noted that these matrices are the same as those for the 3 rd  quadrant. It can also be seen that when the remote vehicle  14  is in the 3 rd  quadrant, the remote vehicle  14  will be to the right (EF=11) of the host vehicle  10  when the heading angle of the host vehicle  10  is greater than β 1 −π and less than β 1  (β 1 −π&lt;δ HV &lt;β 1 ), otherwise the remote vehicle  14  will be to the left (EF=01) of the host vehicle  10  (i.e., when β 1 &lt;δ HV &lt;β 1 −π). This is also the same as if the remote vehicle  14  were in the 2 nd  quadrant. 
     The 4 th  quadrant is defined by the following conditions: 
     
       
         
           
             
               
                 θ 
                 RV 
               
               &gt; 
               
                 θ 
                 HV 
               
             
             , 
             
               
                 ϕ 
                 RV 
               
               &lt; 
               
                 ϕ 
                 HV 
               
             
             , 
             
               
                 ( 
                 
                   
                     π 
                     2 
                   
                   ≤ 
                   
                     β 
                     1 
                   
                   &lt; 
                   π 
                 
                 ) 
               
               . 
             
           
         
       
     
     Within the 4 th  quadrant, certain headings of the host vehicle  10  and the remote vehicle  14  that result in crossing paths can be determined by the following matrices in Table 20 where δ HV &lt;δ RV  in one matrix and δ HV &gt;δ RV  in the other matrix. 
     
       
         
           
               
             
               
                 TABLE 20 
               
             
            
               
                   
               
               
                 Matrices Representing Possible Crossing Paths in the 4 th  Quadrant 
               
            
           
           
               
               
               
               
               
            
               
                   
                   
                 00 
                 01 
                 11 
               
               
                   
                   
                 0 ≦ 
                 β 1  &lt; 
                 β 1  + π &lt; 
               
               
                 δ HV  &lt; δ RV   
                 YZ 
                 δ RV  ≦ β 1   
                 δ RV  ≦ β 1  + π 
                 δ RV  &lt; 2π 
               
               
                   
               
               
                 WX 
                   
                   
                   
                   
               
               
                 00 
                 0 ≦ δ HV  ≦ β 1   
                 0 
                 0 
                 1 
               
               
                 01 
                 β 1  &lt; δ HV  ≦ β 1  + π 
                 x 
                 1 
                 0 
               
               
                 11 
                 β 1  + π &lt; δ HV  &lt; 2π 
                 x 
                 x 
                 0 
               
               
                 XW 
               
               
                 00 
                 0 ≦ δ HV  ≦ β 1   
                 1 
                 x 
                 x 
               
               
                 01 
                 β 1  &lt; δ HV  ≦ β 1  + π 
                 0 
                 0 
                 x 
               
               
                 11 
                 β 1  + π &lt; δ HV  &lt; 2π 
                 0 
                 0 
                 1 
               
               
                   
               
            
           
         
       
     
     The two matrices identify four cases where paths cross (1), eight cases where paths do not cross (0) and six cases that are not possible (x). These matrices are the same as those for the 1 st  quadrant. It can also be seen that when the remote vehicle  14  is in the 4 th  quadrant, the remote vehicle  14  will be to the left (EF=01) of the host vehicle  10  when the heading angle of the host vehicle  10  is greater than β 1  and less than β 1 +π (β 1 &lt;δ HV &lt;β 1 +π), otherwise the remote vehicle  14  will be to the right (EF=11) of the host vehicle  10  (i.e., when β 1 +π&lt;δ HV &lt;β 1 ). This also is the same as if the remote vehicle  14  were in the 1 st  quadrant. 
     Thus, the characteristic relating to the quadrant that includes the remote vehicle location is different from at least one other characteristic relating to at least one other of the quadrants. 
     Moreover, as can be appreciated from the above, the processing determines the quadrant in which the remote vehicle  14  is present by determining a linear direction between the host vehicle  10  and the remote vehicle  14  at a moment in time, determining an angle between a predetermined direction and the linear direction at the moment in time, and determining the quadrant in which the remote vehicle  14  is present based on the angle. Operations for determining a threat based on the remote vehicle sector and a comparison between a heading angle of the host vehicle  10  in relation to a predetermined direction and a heading angle of the remote vehicle  14  in relation to the predetermined direction will now be further discussed. 
     After calculating the angle β 1  in step  9130  of the flowchart in  FIG. 41 , the processing then continues to step  9140  where the process shown in the flowcharts of  FIGS. 46A and 46B  is performed as will now be described. The information that is determined as discussed above is then used to model logic that identifies whether the paths of the host vehicle  10  and the remote vehicle  14  will cross and also whether the remote vehicle  14  is to the left or right of the host vehicle  10 . As will be appreciated from the following, the processing determines the conditions set for in Tables 17through 20. 
     When the controller  22  performs the process shown in  FIGS. 46A and 46B  beginning in step  10000 , the process determines in step  10010  whether the difference between the heading δ HV  of the host vehicle  10  and the heading δ RV  of the remote vehicle  14  is equal to zero. If the different is equal to zero, the processing determines that the remote vehicle  14  is not a threat to the host vehicle  10  (e.g., the remote vehicle  14  and the host vehicle  10  are travelling in the same direction and their paths will not converge). Hence, the processing can end in step  10020  and return to step  9000  in  FIG. 41 . Accordingly, the processing refrains from performing a threat mitigation operation as discussed herein. 
     If the difference is not equal to zero, the processing determines in step  10030  whether the absolute value of the difference between the heading δ HV  of the host vehicle  10  and the heading δ RV  of the remote vehicle  14  is equal to π. If the absolute value is equal to π, the processing continues to step  10040  where the value of EF is set to 00, which indicates that the host vehicle  10  and the remote vehicle  14  are travelling toward each other. However, if the absolute value of the difference is not equal to π, the processing continues to step  10050  where it is determined if θ RV &gt;θ HV . If so, the processing continues to step  10060  where it is determined if δ HV ≦δ RV . If so, the processing continues to step  10070  to determine whether β 1 &lt;δ HV ≦β 1 +π. It is noted that in accordance with normal convention, π equals 180 degrees. If the determination in step  10070  is yes, the processing continues to step  10080  where it is determined whether β 1 &lt;δ RV ≦β 1 +π. If so, the processing continues to step  10090  where it is again determined whether β 1 &lt;δ HV ≦β 1 +π. If not, the processing determines that the remote vehicle  14  is not a threat to the host vehicle  10 . Hence, the processing can end in step  10100  and return to step  9000  in  FIG. 41 . Accordingly, the processing refrains from performing a threat mitigation operation as discussed herein. 
     If the determination in step  10090  is yes, the processing continues to step  10110  where the value of EF is set to 01, indicating that the remote vehicle  14  is coming toward the host vehicle  10  from the left of the host vehicle  10 . However, if the determination in step  10090  is no, the processing continues to step  10120  where the value of EF is set to 11, indicating that the remote vehicle  14  is coming toward the host vehicle  10  from the right of the host vehicle  10 . 
     Referring back to step  10070  discussed above, if the determination is no, the processing continues to step  10130  where it is determined whether δ HV &lt;β 1 . If so, the processing continues to step  10140 , where it is determined whether δ RV &gt;β 1 +π. If so, the processing proceeds to step  10090  and continues as discussed above. If not, the processing determines that the remote vehicle  14  is not a threat to the host vehicle  10 . Hence, the processing can end in step  10100  and return to step  9000  in  FIG. 41 . Accordingly, the processing refrains from performing a threat mitigation operation as discussed herein. 
     Referring back to step  10060  discussed above, if the determination is no, the processing continues to step  10150  where it is determined whether δ HV &lt;β 1 +π. If not, the processing continues to step  10160  where it is determined whether δ HV &lt;β 1 . If the determination in step  10160  is no, the processing determines that the remote vehicle  14  is not a threat to the host vehicle  10 . Hence, the processing can end in step  10100  and return to step  9000  in  FIG. 41 . Accordingly, the processing refrains from performing a threat mitigation operation as discussed herein. However, if the determination in step  10160  is yes, the processing continues to step  10170  where it is determined whether δ HV &lt;β 1 . If not, the processing determines that the remote vehicle  14  is not a threat to the host vehicle  10 . Hence, the processing can end in step  10100  and return to step  9000  in  FIG. 41 . Accordingly, the processing refrains from performing a threat mitigation operation as discussed herein. However, if the determination in step  10170  is yes, the processing proceeds to step  10090  and continues as discussed above. 
     Referring back to step  10150 , if the determination is yes, the processing continues to step  10180  where it is determined whether δ RV &gt;β 1 +π. If so, the processing proceeds to step  10090  and continues as discussed above. However, if the determination in step  10180  is no, the processing determines that the remote vehicle  14  is not a threat to the host vehicle  10 . Hence, the processing can end in step  10100  and return to step  9000  in  FIG. 41 . Accordingly, the processing refrains from performing a threat mitigation operation as discussed herein. 
     Referring back to step  10050 , if the determination is no, the processing continues to step  10190  where it is determined whether δ HV &lt;δ RV . If so, the processing continues to step  10200  where it is determined whether δ HV &lt;β 1 −π. If determination made in step  10200  is yes, the processing continues to step  10210  where it is determined whether δ HV &lt;β 1 −π. If the determination in step  10210  is no, the processing determines that the remote vehicle  14  is not a threat to the host vehicle  10 . Hence, the processing can end in step  10100  and return to step  9000  in  FIG. 41 . Accordingly, the processing refrains from performing a threat mitigation operation as discussed herein. However, if the determination in step  10210  is yes, the processing continues to step  10220  were it is determined whether β 1 −π&lt;δ HV ≦β 1 . If the determination in step  10220  is no, the processing continues to step  10230  where the value of EF is set to 01. However, if the determination in step  10220  is yes, the processing continues to step  10240  where the value of EF is set to 11. 
     Referring back to step  10200 , if the determination is no, the processing continues to step  10250  where it is determined whether δ HV &lt;β 1 . If the determination is no, the processing determines that the remote vehicle  14  is not a threat to the host vehicle  10 . Hence, the processing can end in step  10100  and return to step  9000  in  FIG. 41 . Accordingly, the processing refrains from performing a threat mitigation operation as discussed herein. However, if the determination is yes, the processing continues to step  10260  where it is determined whether δ RV &lt;β 1 . If the determination in step  10260  is no, the processing determines that the remote vehicle  14  is not a threat to the host vehicle  10 . Hence, the processing can end in step  10100  and return to step  9000  in  FIG. 41 . Accordingly, the processing refrains from performing a threat mitigation operation as discussed herein. However, if the determination in step  10260  is yes, the processing continues to step  10220  and proceeds as discussed above. 
     Referring back to step  10190 , if the determination is no, the processing continues to step  10270  where it is determined whether δ HV &gt;β 1 . If the determination is no, the processing continues to step  10280  where it is determined whether β 1 −π&lt;δ HV ≦β 1 . If the determination in step  10280  is yes, the processing determines that the remote vehicle  14  is not a threat to the host vehicle  10 . Hence, the processing can end in step  10100  and return to step  9000  in  FIG. 41 . Accordingly, the processing refrains from performing a threat mitigation operation as discussed herein. 
     However, if the determination in step  10280  is no, the processing continues to step  10290  where it is determined whether δ RV &lt;β 1 −π. If the determination in step  10290  is no, the processing determines that the remote vehicle  14  is not a threat to the host vehicle  10 . Hence, the processing can end in step  10100  and return to step  9000  in  FIG. 41 . Accordingly, the processing refrains from performing a threat mitigation operation as discussed herein. However, if the determination in step  10290  is yes, the processing proceeds to step  10220  and continues as discussed above. 
     Referring back to step  10270 , if the determination is yes, the processing proceeds to step  10300  where it is determined whether δ RV &lt;β 1 −π. If the determination in step  10300  is no, the processing determines that the remote vehicle  14  is not a threat to the host vehicle  10 . Hence, the processing can end in step  10100  and return to step  9000  in  FIG. 41 . Accordingly, the processing refrains from performing a threat mitigation operation as discussed herein. However, if the determination in step  10300  is yes, the processing proceeds to step  10220  and continues as discussed above. 
     As can be appreciated from the above, the values for EF=01 and EF=11 can be determined according to Table 21 below: 
     
       
         
           
               
             
               
                 TABLE 21 
               
             
            
               
                   
               
               
                 Remote Vehicle Relative to Host vehicle 
               
            
           
           
               
               
               
               
               
            
               
                   
                 1 st  quadrant 
                 2 nd  quadrant 
                 3 rd  quadrant 
                 4 th  quadrant 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
            
               
                 EF = 01 
                 β 1  &lt; δ HV  &lt; β 1  + π 
                 β 1  &lt; δ HV  &lt; β 1  − π 
                 β 1  &lt; δ HV  &lt; β 1  − π 
                 β 1  &lt; δ HV  &lt; β 1  + π 
               
               
                 EF = 11 
                 β 1  + π &lt; δ HV  &lt; β 1   
                 β 1  − π &lt; δ HV  &lt; β 1   
                 β 1  − π &lt; δ HV  &lt; β 1   
                 β 1  + π &lt; δ HV  &lt; β 1   
               
               
                   
               
            
           
         
       
     
     Also, the potential crossing paths can be determined according to Table 22 below: 
     
       
         
           
               
             
               
                 TABLE 22 
               
               
                   
               
               
                 Potential Crossing Paths 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 β 1  + π &lt; δ HV  ≦ 2π 
                 0 &lt; δ HV  ≦ β 1   
                 0 &lt; δ HV  ≦ β 1   
                 β 1  &lt; δ HV  ≦ β 1  + π 
               
               
                 1 st  &amp; 4 th  quadrants 
                 β 1  + π &lt; δ RV  ≦ 2π 
                 β 1  + π &lt; δ RV  ≦ 2π 
                 0 &lt; δ RV  ≦ β 1   
                 β 1  &lt; δ RV  ≦ β 1  + π 
               
               
                   
               
               
                 δ HV  &gt; δ RV   
                 1 
                 1 
                 1 
                 0 
               
               
                 δ HV  &lt; δ RV   
                 0 
                 1 
                 0 
                 1 
               
               
                   
               
               
                   
                 β 1  &lt; δ HV  ≦ 2π 
                 β 1  &lt; δ HV  ≦ 2π 
                 0 &lt; δ HV  ≦ β 1  − π 
                 β 1  − π &lt; δ HV  ≦ β 1   
               
               
                 2 nd  &amp; 3 rd  quadrants 
                 β 1  &lt; δ RV  ≦ 2π 
                 0 &lt; δ RV  ≦ β 1  − π 
                 0 &lt; δ HV  ≦ β 1  − π 
                 β 1  − π &lt; δ RV  ≦ β 1   
               
               
                   
               
               
                 δ HV  &gt; δ RV   
                 0 
                 1 
                 0 
                 1 
               
               
                 δ HV  &lt; δ RV   
                 1 
                 1 
                 1 
                 0 
               
               
                   
               
            
           
         
       
     
     Accordingly, as can be appreciated from the above, the determining of whether the host vehicle heading and the remote vehicle heading are converging paths includes comparing the host vehicle location, the host vehicle heading, the remote vehicle location, the remote vehicle heading and the characteristic of the remote vehicle sector to determine whether the host vehicle  10  and the remote vehicle  14  are travelling on converging paths. 
     Once the determination has been made based on the flowcharts shown in  FIGS. 46A and 46B  that the paths of the host vehicle  10  and the remote vehicle  14  may cross, the controller  22  can perform a process for determining the appropriate crossing path scenario. That is, after performing steps  10040 ,  10110 ,  10120 ,  10230  or  10240  as discussed above, the processing can continue to perform the operations shown in the flowcharts of  FIG. 47A and 47B . This process is similar to that shown in the flowcharts of  FIGS. 35 and 36  as discussed above. 
     Beginning in step  11000 , the processing determines in step  11010  whether the binary codes CD are equal to 00. If they are, the processing determines in step  11020  whether the binary codes EF are equal to 00. If so, the processing determines in step  11030  whether the binary codes AB are equal to 01. Also, if the processing determines in step  11020  that the binary codes EF are not equal to 00, the processing determines in step  11040  whether the binary codes EF are equal to 01. If the processing determines in step  11030  that the binary codes AB are equal to 01, or the processing determines in step  11040  that the binary codes EF are equal to 01, the processing continues to step  11050  as discussed below. 
     However, if the processing determines in step  11040  that the binary codes EF are not equal to 01, then the processing concludes in step  11060  that the binary codes EF are equal to 11. After doing so, the processing determines in step  11070  whether the binary codes AB are equal to 11. If not, the processing proceeds to step  11050  and continues as discussed below. 
     Turning back to step  11010 , if the processing determines that the binary codes CD are not equal to 00, the processing continues to step  11080  where the processing determines if the values of CD are equal to 01. If so, the processing continues to step  11090  to determine whether the binary codes EF are equal to 00. If the binary codes EF are equal to 00, the processing determines in step  11100  whether the binary codes AB are equal to 01. However, if the processing determines in step  11090  that the binary codes EF are not equal to 00, the processing determines in step  11110  whether the binary codes AB are equal to 11. 
     Turning back to step  11080 , if the binary codes CD are not equal to 01, the processing concludes in step  11120  that the binary codes CD are equal to 11. The processing continues to step  11130  to determine whether the binary codes EF are equal to 11. If so, the processing determines in step  11140  whether the binary codes AB are equal to 00. However, if it is determined in step  11130  that the binary codes EF are not equal to 11, the processing determines in step  11150  whether the binary bodes EF are equal to 00. If so, the processing determines in step  11160  whether the binary codes AB are equal to 01. 
     Referring back to step  11030 , if it is determined in step  11030  that the binary codes AB are not equal to 01, or in step  11070  that binary codes AB are equal to 11, or in step  11110  that the binary codes AB are equal to 11, or in step  11140  that the binary codes AB are not equal to 00, or in step  11150  that the binary codes EF are not equal to 00, or in step  11160  that binary codes AB are not equal to 01, the processing continues to step  11170 . In step  11170 , the processing concludes that none of the scenarios shown in the truth table in Table 4 are met by the processing performed in the flowcharts of  FIGS. 46A and 46B . Thus, the processing returns at step  11180  to step  9000  and repeats as discussed above with regard to  FIGS. 46A and 46B . In addition, if step  11030  determines that the binary codes AB are equal to 01, or step  11070  determines that binary codes AB are not equal to 11, or step  11110  determines that the binary codes AB are not equal to 11, or step  11140  determines that the binary codes AB are equal to 00, or step  11160  determines that binary codes AB are equal to 01, the processing continues to step  11050 . 
     Referring to step  11050 , the processing determines whether the binary codes ABCD are equal to 0000. If not, the processing determines in step  11190  whether the binary codes ABCD are equal to 0001. If not, the processing determines in step  11200  whether the binary codes ABCD are equal to 0100. If not, the processing determines in step  11210  whether the binary codes ABCD are equal to 0011. If not, the processing determines in step  11220  that the binary codes ABCD are equal to 1100. The processing then continues to step  11230  where it is determined that the scenario RTIP (Right Turn Into Path) exists. Also, if the processing determined in step  11210  that the binary codes ABCD are equal to 0011, the processing continues to step  11230  where it is determined that the scenario RTIP exists. 
     Referring back to step  11050 , if the processing determines that the binary codes ABCD are equal to 0000, the processing continues to step  11240  where it is determined that the scenario SCP (Straight Crossing Path) exists. 
     Referring back to step  11190 , if the processing determines that the binary codes ABCD are equal to 0001, the processing continues to step  11250 . Also, if the processing determines in step  11200  that the binary codes ABCD are equal to 0100, the processing continues to step  11250 . In step  11250 , the processing determines if EF=00. If so, the processing determines in step  11260  that the scenario LTPA/OD exists. However, if the processing determines in step  11250  that EF is not equal to 00, the processing determines in step  11270  that the scenario LTAP/LD LTIP (Left Turn Across Path/Lateral Directional Left Turn Into Path) exists. 
     Thus, the process can determine whether the host vehicle  10  and the remote vehicle  14  are travelling on converging paths includes identifying a current convergence scenario from a plurality of possible convergence scenarios based on the host vehicle location, the host vehicle heading, the remote vehicle location, the remote vehicle heading and the characteristic. Once the crossing path scenario has been determined by performing the processing discussed above, in particular, steps  11230 ,  11240 ,  11260  or  11270 , the processing proceeds to step  11280  where the controller  22  can perform the processing shown in the flowchart of  FIG. 48  to calculate the time to contact. 
     That is, upon beginning in step  12000 , the processing determines in step  12010  whether the scenario LTAP/OD exists. If so, the processing continues to step  12020  to calculate the values of D, TTC and W. Then, the processing continues to step  12030  and can perform a warning process such as that shown, for example, in the flowchart of  FIG. 38  as discussed above. Thus, the warning can be generated while the host vehicle heading and the remote vehicle heading are determined to be converging paths. More particularly, as can be appreciated from the discussions herein, the information pertaining to the host vehicle location and the remote vehicle location also indicates the elevation of the host vehicle  10  and the remote vehicle  14 . Thus, the processing can inherently determine whether the host vehicle  10  and the remote vehicle  14  are within a predetermined elevation difference. The processing can thus generate the warning while the host vehicle heading and the remote vehicle heading are determined to be converging paths, the host vehicle location and the remote vehicle location are determined to be within the predetermined distance from each other, and the host vehicle elevation and the remote vehicle elevation are within the predetermined elevation difference. Also, the warning can be generated while the host vehicle heading and the remote vehicle heading are determined to be converging paths, and the host vehicle location and the remote vehicle location are determined to be within the predetermined distance from each other. 
     However, if the processing determines in step  12010  that the scenario LTAP/OD does not exist, the processing calculates the values for X, Y, D and β 1  in step  12040 . The processing then determines in step  12050  whether θ RV &gt;θ HV . If so, the processing continues to step  12060  where the processing determines whether β 1 +π&lt;δ HV ≦2π. If the determination in step  12060  is yes, the processing continues to step  12070  where α HV  is set equal to 2π+(β 1 −δ HV ). The processing then continues to step  12080  where the values of l HV , l RV , φ C , θ C , TTC HV , TTC RV  and ΔTTC. The process then continues to step  12030  and a warning process as shown in  FIG. 38  can be performed. 
     However, if the determination in step  12060  is no, the value of α HV  is set to |β 1 −δ HV | in step  12090 . The processing then proceeds to step  12080  and continues as discussed above. 
     Referring back to step  12050 , if the determination in step  12050  is yes, the processing also continues to step  12100  where a determination is made as to whether 0&lt;δ RV ≦β 1 . If the determination is yes, the processing proceeds to step  12110  where the value of α RV  is set to |δ RV −β 1 +π|. The processing then proceeds to step  12080  and continues as discussed above. However, if the determination in step  12100  is no, the processing continues to step  12120  where the value of α RV  is set to |(β 1 +π)−δ RV |. The processing proceeds to step  12080  and continues as discussed above. 
     Referring back to step  12050 , if the determination in step  12050  is no, the processing continues to step  12130  where it is determined whether 0&lt;δ HV ≦β 1 −π. If so, the processing proceeds to step  12140  where the value of α HV  is set to 2π+(β 1 −δ HV ). The processing then proceeds to step  12080  and continues as discussed above. However, if the determination in step  12130  is no, then the processing proceeds to step  12150  where the value of α HV  is set to |β 1 −δ HV |. The processing then proceeds to step  12080  and continues as discussed above. 
     Referring back to step  12050 , if the determination in step  12050  is no, the processing also continues to step  12160  where it is determined whether β 1 &lt;δ RV ≦2π. If the determination in step  12160  is yes, the processing continues to step  12170  where the value of α RV  is set to (β 1 +π)−δ RV . The processing then proceeds to step  12080  and continues as discussed above. However, if the determination in step  12160  is no, the processing proceeds to step  12180  where the value of α RV  is set to |(β 1 −π)−δ RV |. The processing then proceeds to step  12080  and continues as discussed above. 
     In addition to the above, the process shown and described with regard to the flowcharts in  FIGS. 41 ,  46 ,  47  and  48  can be performed as will now be described with regard to  FIGS. 49 through 56  and the equations discussed below. 
     In this example, the processing does not need to rely on logic flows in order to determine if a potential contact between the host vehicle  10  and the remote vehicle  14  exists. Instead, the processing employs a series of mathematical expressions to directly assess if potential threats exist and, if a threat does exist, immediately determine the specific threat type, making this method much more efficient. 
     The processing discussed below uses the convention discussed above with regard to  FIGS. 42 through 45 , and obtains the information pertaining to the subject (host) vehicle  10  and the remote vehicle  14  in any of the manners discussed above. Also, as with the above example, it is assumed that the host vehicle  10  is always located at the center of the coordinate system shown in  FIGS. 42 through 45 . The angle β 1  given by the following equation defines the relative position between the host vehicle  10  and the remote vehicle  14  and is used extensively in defining the mathematical expressions used to identify converging and crossing paths. 
               β   1     =       π   ⁡     [           θ   HV     -     θ   RV     -   σ                θ   HV     -     θ   RV            +   σ       +   1     ]       -         cos     -   1       ⁡     (       (       ϕ   RV     -     ϕ   HV       )               (       θ   RV     -     θ   HV       )     2     ⁢     cos   2     ⁢     ϕ   RV       +       (       ϕ   RV     -     ϕ   HV       )     2           )       ⁡     [         θ   HV     -     θ   RV     -   σ                θ   HV     -     θ   RV            +   σ       ]               
where θ RV =longitude of the remote vehicle  14 , θ HV =longitude of the host vehicle  10 , φ RV =latitude of the remote vehicle  14 , θ HV =latitude of the host vehicle  10 , and σ=a constant of very small value (e.g. a magnitude of ˜10 −9 ) added to the equation to prevent dividing by 0.
 
     As discussed above, if the remote vehicle  14  is to the north φ RV &gt;φ HV  and east θ RV &gt;θ HV  of the host vehicle  10 , the remote vehicle is said to be in the 1 st  quadrant as illustrated in  FIG. 42 . As indicated, the heading angle δ HV  of the host vehicle  10  and the heading angle δ RV  of the remote vehicle  14  can fall in one of three ranges defined according to the heading angles and β 1 . When the remote vehicle  14  is located in the 1 st  quadrant, the three ranges are defined as follows: Range 1: 0≦δ&lt;β 1 ; Range 2: β 1 ≦δ&lt;β 1 +π, and Range 3: β 1 +π≦δ&lt;2π. These three ranges for δ HV  and δ RV  respectively result in nine possible combinations. Additionally, the HV heading angle can either be less than (δ HV &lt;δ RV ) or greater than (δ HV &gt;δ RV ) the RV heading angle. Also, δ HV  can equal δ RV , but under this circumstance, the host vehicle  10  and the remote vehicle  14  would be following one another. A crossing path thus could not occur, so this condition is not addressed in detail here. 
     Combining these two conditions with the nine range combinations results in eighteen combinations that are used are used to build the truth table shown in Table 23 below. 
     
       
         
           
               
             
               
                 TABLE 23 
               
             
            
               
                   
               
               
                 Regions Where Crossing Paths Occur In The 1 st  Quadrant 
               
            
           
           
               
               
               
               
            
               
                   
                 0 ≦ δ RV  &lt; 
                 β 1  ≦ δ RV  &lt; 
                 β 1  + π ≦ 
               
               
                   
                 β 1   
                 β 1  + π 
                 δ RV  &lt; 2π 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
            
               
                 0 ≦ δ HV  &lt; β 1   
                 δ HV  &lt; δ RV   
                 0 
                 0 
                 1 
               
               
                 β 1  ≦ δ HV  &lt; β 1  + π 
                 δ HV  &lt; δ RV   
                 x 
                 1 
                 0 
               
               
                 β 1  + π ≦ δ HV  &lt; 2π 
                 δ HV  &lt; δ RV   
                 x 
                 x 
                 0 
               
               
                 0 ≦ δ HV  &lt; β 1   
                 δ HV  &gt; δ RV   
                 1 
                 x 
                 x 
               
               
                 β 1  ≦ δ HV  &lt; β 1  + π 
                 δ HV  &gt; δ RV   
                 0 
                 0 
                 x 
               
               
                 β 1  + π ≦ δ HV  &lt; 2π 
                 δ HV  &gt; δ RV   
                 0 
                 0 
                 1 
               
               
                   
               
            
           
         
       
     
     Table 23 identifies four cases where paths cross (1) and eight cases where paths do not cross (0). Table 23 also identifies six cases that are not possible (x). For example, δ HV  cannot be less than δ RV , when δ HV  is greater than β 1  and δ RV  is less than β 1 . Also, it can be seen from  FIG. 42  that when the remote vehicle  14  is in the 1 st  quadrant, it will be to the left of the host vehicle  10  (EF=01) when β 1 ≦δ HV &lt;β 1 +π, otherwise the remote vehicle  14  will be to the right (EF=11) of the host vehicle  10  (i.e. when β 1 +π≦δ HV &lt;2π or 0≦δ HV &lt;β 1 ). 
     As further discussed above, if the remote vehicle  14  is to the north φ RV &gt;φ HV  and west θ RV &lt;θ HV  of the host vehicle  10 , the remote vehicle  14  is said to be in the 2 nd  quadrant as illustrated in  FIG. 43 . It can be seen that the heading angles of the host vehicle  10  and the remote vehicle  14  (δ HV  and δ RV ) can fall in one of three ranges defined according to the heading angles and β 1 . When the remote vehicle  14  is located in the 2 nd  quadrant, the three ranges are defined as follows: Range 1: 0≦δ&lt;β 1 −π; Range 2: β 1 −π≦δ&lt;β 1 ; and Range 3: β 1 ≦δ&lt;2π. These three ranges for δ HV  and δ RV  result in nine possible combinations. Additionally, the host vehicle  10  heading angle can either be less than (δ HV &lt;δ RV ) or greater than (δ HV &gt;δ RV ) the remote vehicle  14  heading angle. Combining these two conditions with the nine range combinations results in eighteen combinations that are used are used to build the truth table shown in Table 24 below. 
     
       
         
           
               
             
               
                 TABLE 24 
               
             
            
               
                   
               
               
                 Regions Where Crossing Paths Occur In The 2 nd  Quadrant 
               
            
           
           
               
               
               
               
            
               
                   
                 0 ≦ δ RV  &lt; 
                 β 1  − π ≦ 
                 β 1  ≦ 
               
               
                   
                 β 1  − π 
                 δ RV  &lt; β 1   
                 δ RV  &lt; 2π 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
            
               
                 0 ≦ δ HV  &lt; β 1  − π 
                 δ HV  &lt; δ RV   
                 1 
                 0 
                 0 
               
               
                 β 1  − π ≦ δ HV  &lt; β 1   
                 δ HV  &lt; δ RV   
                 x 
                 0 
                 0 
               
               
                 β 1  ≦ δ HV  &lt; 2π 
                 δ HV  &lt; δ RV   
                 x 
                 x 
                 1 
               
               
                 0 ≦ δ HV  &lt; β 1  − π 
                 δ HV  &gt; δ RV   
                 0 
                 x 
                 x 
               
               
                 β 1  − π ≦ δ HV  &lt; β 1   
                 δ HV  &gt; δ RV   
                 0 
                 1 
                 x 
               
               
                 β 1  ≦ δ HV  &lt; 2π 
                 δ HV  &gt; δ RV   
                 1 
                 0 
                 0 
               
               
                   
               
            
           
         
       
     
     Table 24 identifies four cases where paths cross (1) and eight cases where paths do not cross (0). Table 24 also identifies six cases that are not possible (x). For example, δ HV  cannot be greater than δ RV  when δ HV  is greater than β 1  and δ RV  is less than β 1 −π. Also, when the remote vehicle  14  is in the 2 nd  quadrant, the remote vehicle  14  will be to the right (EF=11) of the host vehicle  10  when β 1 −π&lt;δ HV &lt;β 1 . Otherwise, the remote vehicle  14  will be to the left (EF=01) of the host vehicle  10  (i.e. when β 1 ≦δ HV &lt;2π or 0≦δ HV &lt;β 1 −π). 
     As further discussed above, if the remote vehicle  14  is to the south φ RV &lt;φ HV  and west θ RV &lt;θ HV  of the host vehicle  10 , the remote vehicle  14  is said to be in the 3 rd  quadrant as illustrated in  FIG. 44 . It can be seen that the heading angles of the host vehicle  10  and the remote vehicle  14  (δ HV  and δ RV , respectively) can fall in one of three ranges defined according to the heading angles and β 1 . When the remote vehicle  14  is located in the 3 rd  quadrant, the three ranges are defined as follows: Range 1: 0≦δ&lt;β 1 −π, Range 2: β 1 −π≦δ&lt;β 1 ; and Range 3: β 1 ≦δ&lt;2π. These three ranges for δ HV  and δ RV  result in nine possible combinations. Additionally, the host vehicle  10  heading angle can either be less than (δ HV &lt;δ RV ) or greater than (δ HV &gt;δ RV ) the remote vehicle  14  heading angle. Combining these two conditions with the nine range combinations results in eighteen combinations that are used are used to build the truth table shown in Table 25 below. 
     
       
         
           
               
             
               
                 TABLE 25 
               
             
            
               
                   
               
               
                 Regions Where Crossing Paths Occur In The 3 rd  Quadrant 
               
            
           
           
               
               
               
               
            
               
                   
                 0 ≦ 
                 β 1  − π ≦ 
                 β 1  ≦ 
               
               
                   
                 δ RV  &lt; β 1  − π 
                 δ RV  &lt; β 1   
                 δ RV  &lt; 2π 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
            
               
                 0 ≦ δ HV  &lt; β 1  − π 
                 δ HV  &lt; δ RV   
                 1 
                 0 
                 0 
               
               
                 β 1  − π ≦ δ HV  &lt; β 1   
                 δ HV  &lt; δ RV   
                 x 
                 0 
                 0 
               
               
                 β 1  ≦ δ HV  &lt; 2π 
                 δ HV  &lt; δ RV   
                 x 
                 x 
                 1 
               
               
                 0 ≦ δ HV  &lt; β 1  − π 
                 δ HV  &gt; δ RV   
                 0 
                 x 
                 x 
               
               
                 β 1  − π ≦ δ HV  &lt; β 1   
                 δ HV  &gt; δ RV   
                 0 
                 1 
                 x 
               
               
                 β 1  ≦ δ HV  &lt; 2π 
                 δ HV  &gt; δ RV   
                 1 
                 0 
                 0 
               
               
                   
               
            
           
         
       
     
     Table 25 identifies four cases where paths cross (1) and eight cases where paths do not cross (0). Table 25 also identifies six cases that are not possible (x). It should also be noted that Table 25 is identical to Table 24 for the 2 nd  quadrant. Similar to the 2 nd  quadrant, when the remote vehicle  14  is in the 3 rd  quadrant, the remote vehicle  14  will be to the right (EF=11) of the host vehicle  10  when β 1 −π≦δ HV &lt;β 1  otherwise the remote vehicle  14  will be to the left (EF=01) of the host vehicle  10  (i.e. when β 1 ≦δ HV &lt;2π or 0≦δ HV &lt;β 1 −π). 
     As further discussed above, if the remote vehicle  14  is to the south φ RV &lt;φ HV  and east θ RV &gt;θ HV  of the host vehicle  10 , the remote vehicle  14  is said to be in the 4 th  quadrant as illustrated in  FIGS. 46A and 46B  discussed above. It can be seen that the heading angles of the host vehicle  10  and the remote vehicle  14  (δ HV  and δ RV , respectively) can fall in one of three ranges defined according to the heading angles and β 1 . When the remote vehicle  14  is located in the 4 th  quadrant, the three ranges are defined as follows: Range 1: 0≦δ&lt;β 1 ; Range 2: β 1 ≦δ&lt;β 1 +π, and Range 3: β 1 +π≦δ&lt;2π. These three ranges for δ HV  and δ RV  result in nine possible combinations. Additionally, the host vehicle  10  heading angle can either be less than (δ HV &lt;δ RV ) or greater than (δ HV &gt;δ RV ) the remote vehicle  14  heading angle. Also, δ HV  can also equal δ RV , but under this circumstance the host vehicle  10  and remote vehicle  14  would be following one another. Thus, a crossing path could not occur, so this condition is not addressed. 
     Combining these two conditions with the nine range combinations results in eighteen combinations that are used are used to build the truth table shown in Table 26 below. 
     
       
         
           
               
             
               
                 TABLE 26 
               
             
            
               
                   
               
               
                 Regions Where Crossing Paths Occur In The 4 th  Quadrant 
               
            
           
           
               
               
               
               
            
               
                   
                 0 ≦ 
                 β 1  ≦ 
                 β 1  + π ≦ 
               
               
                   
                 δ RV  &lt; β 1   
                 δ RV  &lt; β 1  + π 
                 δ RV  &lt; 2π 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
            
               
                 0 ≦ δ HV  &lt; β 1   
                 δ HV  &lt; δ RV   
                 0 
                 0 
                 1 
               
               
                 β 1  ≦ δ HV  &lt; β 1  + π 
                 δ HV  &lt; δ RV   
                 x 
                 1 
                 0 
               
               
                 β 1  + π ≦ δ HV  &lt; 2π 
                 δ HV  &lt; δ RV   
                 x 
                 x 
                 0 
               
               
                 0 ≦ δ HV  &lt; β 1   
                 δ HV  &gt; δ RV   
                 1 
                 x 
                 x 
               
               
                 β 1  ≦ δ HV  &lt; β 1  + π 
                 δ HV  &gt; δ RV   
                 0 
                 0 
                 x 
               
               
                 β 1  + π ≦ δ HV  &lt; 2π 
                 δ HV  &gt; δ RV   
                 0 
                 0 
                 1 
               
               
                   
               
            
           
         
       
     
     Table 26 identifies four cases where paths cross (1) and eight cases where paths do not cross (0). Table 26 also identifies six cases that are not possible (x). It should also be noted that Table 26 is identical to Table 23 for the 1 st  quadrant. Similar to the 1 st  quadrant, when the remote vehicle  14  is in the 4 th  quadrant, the remote vehicle will be to the left of the host vehicle  10  (EF=01) when β 1 ≦δ HV ≦β 1 +π. Otherwise, the remote vehicle  14  will be to the right (EF=11) of the host vehicle  10  (i.e. when β 1 +π≦ HV &lt;2π or 0≦δ HV &lt;β 1 ). 
     As discussed above, the ranges for the heading angles δ HV  of the host vehicle  10  and the heading angle δ RV  for the remote vehicle  14  were defined relative to the angle β 1 . Those ranges can also be expressed in mathematical form in Table 27 below. 
     
       
         
           
               
             
               
                 TABLE 27 
               
             
            
               
                   
               
               
                 Threat Assessment Equations for Crossing Paths 
               
            
           
           
               
               
            
               
                 HV 
                 RV 
               
               
                   
               
               
                 
                   
                     
                       
                         
                           H 
                           1 
                         
                         = 
                         
                           
                             1 
                             2 
                           
                           ⁡ 
                           
                             [ 
                             
                               
                                 
                                   
                                     β 
                                     1 
                                   
                                   - 
                                   
                                     δ 
                                     HV 
                                   
                                   - 
                                   σ 
                                 
                                 
                                   
                                      
                                     
                                       
                                         β 
                                         1 
                                       
                                       - 
                                       
                                         δ 
                                         HV 
                                       
                                     
                                      
                                   
                                   + 
                                   σ 
                                 
                               
                               + 
                               1 
                             
                             ] 
                           
                         
                       
                     
                   
                 
                 
                   
                     
                       
                         
                           R 
                           1 
                         
                         = 
                         
                           
                             1 
                             2 
                           
                           ⁡ 
                           
                             [ 
                             
                               
                                 
                                   
                                     β 
                                     1 
                                   
                                   - 
                                   
                                     δ 
                                     RV 
                                   
                                   - 
                                   σ 
                                 
                                 
                                   
                                      
                                     
                                       
                                         β 
                                         1 
                                       
                                       - 
                                       
                                         δ 
                                         RV 
                                       
                                     
                                      
                                   
                                   + 
                                   σ 
                                 
                               
                               + 
                               1 
                             
                             ] 
                           
                         
                       
                     
                   
                 
               
               
                   
               
               
                 
                   
                     
                       
                         
                           H 
                           2 
                         
                         = 
                         
                           
                             
                               1 
                               4 
                             
                             ⁡ 
                             
                               [ 
                               
                                 
                                   
                                     
                                       δ 
                                       HV 
                                     
                                     - 
                                     
                                       β 
                                       1 
                                     
                                     + 
                                     σ 
                                   
                                   
                                     
                                        
                                       
                                         
                                           δ 
                                           HV 
                                         
                                         - 
                                         
                                           β 
                                           1 
                                         
                                       
                                        
                                     
                                     + 
                                     σ 
                                   
                                 
                                 + 
                                 1 
                               
                               ] 
                             
                           
                           × 
                           
                             [ 
                             
                               
                                 
                                   
                                     ( 
                                     
                                       
                                         β 
                                         1 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                   - 
                                   
                                     δ 
                                     HV 
                                   
                                   - 
                                   σ 
                                 
                                 
                                   
                                      
                                     
                                       
                                         ( 
                                         
                                           
                                             β 
                                             1 
                                           
                                           + 
                                           π 
                                         
                                         ) 
                                       
                                       - 
                                       
                                         δ 
                                         HV 
                                       
                                     
                                      
                                   
                                   + 
                                   σ 
                                 
                               
                               + 
                               1 
                             
                             ] 
                           
                         
                       
                     
                   
                 
                 
                   
                     
                       
                         
                           R 
                           2 
                         
                         = 
                         
                           
                             
                               1 
                               4 
                             
                             ⁡ 
                             
                               [ 
                               
                                 
                                   
                                     
                                       δ 
                                       RV 
                                     
                                     - 
                                     
                                       β 
                                       1 
                                     
                                     + 
                                     σ 
                                   
                                   
                                     
                                        
                                       
                                         
                                           δ 
                                           RV 
                                         
                                         - 
                                         
                                           β 
                                           1 
                                         
                                       
                                        
                                     
                                     + 
                                     σ 
                                   
                                 
                                 + 
                                 1 
                               
                               ] 
                             
                           
                           × 
                           
                             [ 
                             
                               
                                 
                                   
                                     ( 
                                     
                                       
                                         β 
                                         1 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                   - 
                                   
                                     δ 
                                     RV 
                                   
                                   - 
                                   σ 
                                 
                                 
                                   
                                      
                                     
                                       
                                         ( 
                                         
                                           
                                             β 
                                             1 
                                           
                                           + 
                                           π 
                                         
                                         ) 
                                       
                                       - 
                                       
                                         δ 
                                         RV 
                                       
                                     
                                      
                                   
                                   + 
                                   σ 
                                 
                               
                               + 
                               1 
                             
                             ] 
                           
                         
                       
                     
                   
                 
               
               
                   
               
               
                 
                   
                     
                       
                         
                           H 
                           3 
                         
                         = 
                         
                           
                             
                               1 
                               4 
                             
                             ⁡ 
                             
                               [ 
                               
                                 
                                   
                                     
                                       δ 
                                       HV 
                                     
                                     - 
                                     
                                       ( 
                                       
                                         
                                           β 
                                           1 
                                         
                                         + 
                                         π 
                                       
                                       ) 
                                     
                                     + 
                                     σ 
                                   
                                   
                                     
                                        
                                       
                                         
                                           δ 
                                           HV 
                                         
                                         - 
                                         
                                           ( 
                                           
                                             
                                               β 
                                               1 
                                             
                                             + 
                                             π 
                                           
                                           ) 
                                         
                                       
                                        
                                     
                                     + 
                                     σ 
                                   
                                 
                                 + 
                                 1 
                               
                               ] 
                             
                           
                           × 
                           
                             [ 
                             
                               
                                 
                                   
                                     2 
                                     ⁢ 
                                     π 
                                   
                                   - 
                                   
                                     δ 
                                     HV 
                                   
                                   - 
                                   σ 
                                 
                                 
                                   
                                      
                                     
                                       
                                         2 
                                         ⁢ 
                                         π 
                                       
                                       - 
                                       
                                         δ 
                                         HV 
                                       
                                     
                                      
                                   
                                   + 
                                   σ 
                                 
                               
                               + 
                               1 
                             
                             ] 
                           
                         
                       
                     
                   
                 
                 
                   
                     
                       
                         
                           R 
                           3 
                         
                         = 
                         
                           
                             
                               1 
                               4 
                             
                             ⁡ 
                             
                               [ 
                               
                                 
                                   
                                     
                                       δ 
                                       RV 
                                     
                                     - 
                                     
                                       ( 
                                       
                                         
                                           β 
                                           1 
                                         
                                         + 
                                         π 
                                       
                                       ) 
                                     
                                     + 
                                     σ 
                                   
                                   
                                     
                                        
                                       
                                         
                                           δ 
                                           RV 
                                         
                                         - 
                                         
                                           ( 
                                           
                                             
                                               β 
                                               1 
                                             
                                             + 
                                             π 
                                           
                                           ) 
                                         
                                       
                                        
                                     
                                     + 
                                     σ 
                                   
                                 
                                 + 
                                 1 
                               
                               ] 
                             
                           
                           × 
                           
                             [ 
                             
                               
                                 
                                   
                                     2 
                                     ⁢ 
                                     π 
                                   
                                   - 
                                   
                                     δ 
                                     RV 
                                   
                                   - 
                                   σ 
                                 
                                 
                                   
                                      
                                     
                                       
                                         2 
                                         ⁢ 
                                         π 
                                       
                                       - 
                                       
                                         δ 
                                         RV 
                                       
                                     
                                      
                                   
                                   + 
                                   σ 
                                 
                               
                               + 
                               1 
                             
                             ] 
                           
                         
                       
                     
                   
                 
               
               
                   
               
               
                 
                   
                     
                       
                         
                           H 
                           4 
                         
                         = 
                         
                           
                             1 
                             2 
                           
                           ⁡ 
                           
                             [ 
                             
                               
                                 
                                   
                                     ( 
                                     
                                       
                                         β 
                                         1 
                                       
                                       - 
                                       π 
                                     
                                     ) 
                                   
                                   - 
                                   
                                     δ 
                                     HV 
                                   
                                   - 
                                   σ 
                                 
                                 
                                   
                                      
                                     
                                       
                                         ( 
                                         
                                           
                                             β 
                                             1 
                                           
                                           - 
                                           π 
                                         
                                         ) 
                                       
                                       - 
                                       
                                         δ 
                                         HV 
                                       
                                     
                                      
                                   
                                   + 
                                   σ 
                                 
                               
                               + 
                               1 
                             
                             ] 
                           
                         
                       
                     
                   
                 
                 
                   
                     
                       
                         
                           R 
                           4 
                         
                         = 
                         
                           
                             1 
                             2 
                           
                           ⁡ 
                           
                             [ 
                             
                               
                                 
                                   
                                     ( 
                                     
                                       
                                         β 
                                         1 
                                       
                                       - 
                                       π 
                                     
                                     ) 
                                   
                                   - 
                                   
                                     δ 
                                     RV 
                                   
                                   - 
                                   σ 
                                 
                                 
                                   
                                      
                                     
                                       
                                         ( 
                                         
                                           
                                             β 
                                             1 
                                           
                                           - 
                                           π 
                                         
                                         ) 
                                       
                                       - 
                                       
                                         δ 
                                         RV 
                                       
                                     
                                      
                                   
                                   + 
                                   σ 
                                 
                               
                               + 
                               1 
                             
                             ] 
                           
                         
                       
                     
                   
                 
               
               
                   
               
               
                 
                   
                     
                       
                         
                           H 
                           5 
                         
                         = 
                         
                           
                             
                               1 
                               4 
                             
                             ⁡ 
                             
                               [ 
                               
                                 
                                   
                                     
                                       δ 
                                       HV 
                                     
                                     - 
                                     
                                       ( 
                                       
                                         
                                           β 
                                           1 
                                         
                                         - 
                                         π 
                                       
                                       ) 
                                     
                                     + 
                                     σ 
                                   
                                   
                                     
                                        
                                       
                                         
                                           δ 
                                           HV 
                                         
                                         - 
                                         
                                           ( 
                                           
                                             
                                               β 
                                               1 
                                             
                                             - 
                                             π 
                                           
                                           ) 
                                         
                                       
                                        
                                     
                                     + 
                                     σ 
                                   
                                 
                                 + 
                                 1 
                               
                               ] 
                             
                           
                           × 
                           
                             [ 
                             
                               
                                 
                                   
                                     β 
                                     1 
                                   
                                   - 
                                   
                                     δ 
                                     HV 
                                   
                                   - 
                                   σ 
                                 
                                 
                                   
                                      
                                     
                                       
                                         β 
                                         1 
                                       
                                       - 
                                       
                                         δ 
                                         HV 
                                       
                                     
                                      
                                   
                                   + 
                                   σ 
                                 
                               
                               + 
                               1 
                             
                             ] 
                           
                         
                       
                     
                   
                 
                 
                   
                     
                       
                         
                           R 
                           5 
                         
                         = 
                         
                           
                             
                               1 
                               4 
                             
                             ⁡ 
                             
                               [ 
                               
                                 
                                   
                                     
                                       δ 
                                       RV 
                                     
                                     - 
                                     
                                       ( 
                                       
                                         
                                           β 
                                           1 
                                         
                                         - 
                                         π 
                                       
                                       ) 
                                     
                                     + 
                                     σ 
                                   
                                   
                                     
                                        
                                       
                                         
                                           δ 
                                           RV 
                                         
                                         - 
                                         
                                           ( 
                                           
                                             
                                               β 
                                               1 
                                             
                                             - 
                                             π 
                                           
                                           ) 
                                         
                                       
                                        
                                     
                                     + 
                                     σ 
                                   
                                 
                                 + 
                                 1 
                               
                               ] 
                             
                           
                           × 
                           
                             [ 
                             
                               
                                 
                                   
                                     β 
                                     1 
                                   
                                   - 
                                   
                                     δ 
                                     RV 
                                   
                                   - 
                                   σ 
                                 
                                 
                                   
                                      
                                     
                                       
                                         β 
                                         1 
                                       
                                       - 
                                       
                                         δ 
                                         RV 
                                       
                                     
                                      
                                   
                                   + 
                                   σ 
                                 
                               
                               + 
                               1 
                             
                             ] 
                           
                         
                       
                     
                   
                 
               
               
                   
               
               
                 
                   
                     
                       
                         
                           H 
                           6 
                         
                         = 
                         
                           
                             
                               1 
                               4 
                             
                             ⁡ 
                             
                               [ 
                               
                                 
                                   
                                     
                                       δ 
                                       HV 
                                     
                                     - 
                                     
                                       β 
                                       1 
                                     
                                     + 
                                     σ 
                                   
                                   
                                     
                                        
                                       
                                         
                                           δ 
                                           HV 
                                         
                                         - 
                                         
                                           β 
                                           1 
                                         
                                       
                                        
                                     
                                     + 
                                     σ 
                                   
                                 
                                 + 
                                 1 
                               
                               ] 
                             
                           
                           × 
                           
                             [ 
                             
                               
                                 
                                   
                                     2 
                                     ⁢ 
                                     π 
                                   
                                   - 
                                   
                                     δ 
                                     HV 
                                   
                                   - 
                                   σ 
                                 
                                 
                                   
                                      
                                     
                                       
                                         2 
                                         ⁢ 
                                         π 
                                       
                                       - 
                                       
                                         δ 
                                         HV 
                                       
                                     
                                      
                                   
                                   + 
                                   σ 
                                 
                               
                               + 
                               1 
                             
                             ] 
                           
                         
                       
                     
                   
                 
                 
                   
                     
                       
                         
                           R 
                           6 
                         
                         = 
                         
                           
                             
                               1 
                               4 
                             
                             ⁡ 
                             
                               [ 
                               
                                 
                                   
                                     
                                       δ 
                                       RV 
                                     
                                     - 
                                     
                                       β 
                                       1 
                                     
                                     + 
                                     σ 
                                   
                                   
                                     
                                        
                                       
                                         
                                           δ 
                                           RV 
                                         
                                         - 
                                         
                                           β 
                                           1 
                                         
                                       
                                        
                                     
                                     + 
                                     σ 
                                   
                                 
                                 + 
                                 1 
                               
                               ] 
                             
                           
                           × 
                           
                             [ 
                             
                               
                                 
                                   
                                     2 
                                     ⁢ 
                                     π 
                                   
                                   - 
                                   
                                     δ 
                                     RV 
                                   
                                   - 
                                   σ 
                                 
                                 
                                   
                                      
                                     
                                       
                                         2 
                                         ⁢ 
                                         π 
                                       
                                       - 
                                       
                                         δ 
                                         RV 
                                       
                                     
                                      
                                   
                                   + 
                                   σ 
                                 
                               
                               + 
                               1 
                             
                             ] 
                           
                         
                       
                     
                   
                 
               
               
                   
               
            
           
         
       
     
     Although these expressions appear complex, the resulting values for each expression is either 0 or 1. These expressions are used to define an intersection scenario as either being a threat or a non-threat. In the case of the scenario being a threat, the equations are also used to define the specific threat scenario (i.e. straight crossing path, left turn across path/opposite direction, etc.). While thirty six combinations of H m  and R n  (where m and n=1-6) are possible, only the following eight combinations are relevant to crossing paths H 1 ×R 1 ; H 1 ×R 3 ; H 2 ×R 2 ; H 3 ×R 3 ; H 4 ×R 4 ; H 5 ×R 5 ; H 6 ×R 4 ; and H 6 ×R 6 . 
     Referring back to Tables 23 through 26, it can be seen that for m and n=1, 2, 3 the remote vehicle  14  is to the east of the host vehicle  10  (θ HV &lt;θ RV ). This condition can be expressed mathematically as follows: 
               Θ   1     =       1   2     ⁡     [           θ   RV     -     θ   HV     +   σ                θ   RV     -     θ   HV            +   σ       +   1     ]             
where Θ 1 =1 when θ HV &lt;θ RV  and Θ=0 when θ HV &gt;θ RV .
 
     Also from Tables 23 through 26, it can be seen that for m and n=4, 5, 6 the remote vehicle  14  is to the west of the host vehicle  10  (θ HV &gt;θ RV ). This condition can be expressed mathematically as follows: 
               Θ   2     =       1   2     ⁡     [           θ   HV     -     θ   RV     +   σ                θ   HV     -     θ   RV            +   σ       +   1     ]             
where Θ 2 =1 when θ HV &gt;θ RV  and Θ 2 =0 when θ HV &lt;θ RV . Thus, the eight combinations become: H 1 ×R 1 ×Θ 1 ; H 1 ×R 3 ×Θ 1 ; H 2 ×R 2 ×Θ 1 ; H 3 ×R 3 ×Θ 1 ; H 4 ×R 4 ×Θ 2 ; H 5 ×R 5 ×Θ 2 ; H 6 ×R 4 ×Θ 2 ; and H 6 ×R 6 ×Θ 2 .
 
     Referring back to Tables 23 through 26, it can be seen that the occurrence of a crossing path depends on the heading angle δ HV  of the host vehicle  10  and the heading angle δ RV  of the remote vehicle  14 . In some cases, crossing paths occur when δ HV &lt;δ RV  and in other cases crossing paths occur when δ HV &gt;δ RV . These crossing path cases are defined in Tables 23 through 26 as discussed above. Also, the condition δ HV &lt;δ RV  can be expressed mathematically as follows: 
               Δ   1     =       1   2     ⁡     [           δ   RV     -     δ   HV     -   σ                δ   RV     -     δ   HV            +   σ       +   1     ]             
where Δ 1 =1 when δ HV &lt;δ RV  and Δ 1 =0 when δ HV &gt;δ RV .
 
     The condition δ HV &gt;δ RV  can also be expressed mathematically as follows: 
               Δ   2     =       1   2     ⁡     [           δ   HV     -     δ   RV     -   σ                δ   HV     -     δ   RV            +   σ       +   1     ]             
where Δ 2 =1 when δ HV &gt;δ RV  and Δ 2 =0 when δ HV &lt;δ RV . Thus the eight combinations become: C 1 =H 1 ×R 1 ×Θ 1 ×Δ 2 ; C 2 =H 1 ×R 3 ×Θ 1 ; C 3 =H 2 ×R 2 ×Θ 1 ×Δ 1 ; C 4 =H 3 ×R 3 ×Θ 1 ×Δ 2 ; C 5 =H 4 ×R 4 ×Θ 2 ×Δ 1 ; C 6 =H 5 ×R 5 ×Θ 2 ×Δ 2 ; C 7 =H 6 ×R 4 ×Θ 2 ; and C 8 =H 6 ×R 6 ×Θ 2 ×Δ 1 . It can be noted that expressions C 2  and C 7  do not include either the Δ 1  or Δ 2  term. This is because under the conditions described by H 1  and R 3  or H 6  and R 4 , there will be a crossing path regardless of the value of δ HV  and δ RV . These expressions are based solely on the GPS coordinates and heading angles of the host vehicle  10  and the remote vehicle  14 . If any one of the eight expressions equals 1, a crossing path will occur.
 
     Accordingly, as can be appreciated from the above, the determining of whether the host vehicle heading and the remote vehicle heading are converging paths includes comparing the host vehicle location, the host vehicle heading, the remote vehicle location, the remote vehicle heading and the characteristic of the remote vehicle sector to determine whether the host vehicle  10  and the remote vehicle  14  are travelling on converging paths. The comparing includes performing a plurality of separate mathematical comparisons of the host vehicle location, the host vehicle heading, the remote vehicle location, the remote vehicle heading and the characteristic of the remote vehicle sector to generate a plurality of results, and determining that the host vehicle heading and the remote vehicle heading are converging paths when any of the results has a particular characteristic. The controller  22  can perform the plurality of separate mathematical comparisons simultaneously to simultaneously generate the plurality of results, or the controller  22  can perform the separate mathematical comparisons in any order. 
     Converging paths are treated differently from crossing paths and can be analyzed in this example according to  FIGS. 49 through 56   
     As shown in  FIG. 49 , the host vehicle  10  is traveling north while the remote vehicle  14  is traveling south. Initially, the absolute value of the difference between the host vehicle  10  heading angle δ HV  and β 1  is greater than 3π/2 radians as the paths of the two vehicles converge toward one another. At some point in time, the absolute value of the difference between the host vehicle  10  heading angle δ HV  and β 1  becomes equal to 3π/2 radians at the moment the two vehicles pass each other. From this point on, the absolute value of the difference between the host vehicle  10  heading angle δ HV  and β 1  is less than 3π/2 radians as the paths of the two vehicles diverge. 
     As shown in  FIG. 50 , the host vehicle  10  is traveling northeast while the remote vehicle  14  is traveling southwest. Initially, the absolute value of the difference between the host vehicle  10  heading angle δ HV  and β 1  is less than π/2 radians as the paths of the two vehicles converge toward one another. At some point in time, the absolute value of the difference between the host vehicle  10  heading angle δ HV  and β 1  becomes greater than 3π/2 radians as the vehicles continue to converge toward one another. At the moment the two vehicles pass each other, the absolute value of the difference between the host vehicle  10  heading angle δ HV  and β 1  becomes equal to 3π/2 radians. From this point on, the absolute value of the difference between the host vehicle  10  heading angle δ HV  and β 1  is less than 3π/2 radians as the paths of the two vehicles diverge. 
     As shown in  FIG. 51 , the host vehicle  10  is traveling east while the remote vehicle  14  is traveling west. Initially, the absolute value of the difference between the host vehicle  10  heading angle δ HV  and β 1  is less than π/2 radians as the paths of the two vehicles converge toward one another. At some point in time, the absolute value of the difference between the host vehicle  10  heading angle δ HV  and β 1  is equal to π/2 radians at the moment the two vehicles pass each other. From this point on, the absolute value of the difference between the host vehicle  10  heading angle δ HV  and β 1  is less than 3π/2 radians as the paths of the two vehicles diverge. 
     As shown in  52 , the host vehicle  10  is traveling southeast while the remote vehicle  14  is traveling northwest. Initially, the absolute value of the difference between the host vehicle  10  heading angle δ HV  and β 1  is less than π/2 radians as the paths of the two vehicles converge toward one another. At the moment the two vehicles pass each other, the absolute value of the difference between the host vehicle  10  heading angle δ HV  and β 1  becomes equal to π/2 radians. As two vehicles continue along their respective paths, the absolute value of the difference between the host vehicle  10  heading angle δ HV  and β 1  becomes greater than π/2 radians as the vehicles diverge away from one another. At some point, the absolute value of the difference between the host vehicle  10  heading angle δ HV  and β 1  becomes less than 3π/2 radians as the paths of the two vehicles continue to diverge. 
     As shown in  FIG. 53 , the host vehicle  10  is traveling south while the remote vehicle  14  is traveling north. Initially, the absolute value of the difference between the host vehicle  10  heading angle δ HV  and β 1  is less than π/2 radians as the paths of the two vehicles converge toward one another. At some point in time, the absolute value of the difference between the host vehicle  10  heading angle δ HV  and β 1  becomes equal to π/2 radians at the moment the two vehicles pass each other. From this point on, the absolute value of the difference between the host vehicle  10  heading angle δ HV  and β 1  is less than 3π/2 radians as the paths of the two vehicles diverge. 
     As shown in  FIG. 54 , the host vehicle  10  is traveling southwest while the remote vehicle  14  is traveling northeast. Initially, the absolute value of the difference between the host vehicle  10  heading angle δ HV  and β 1  is less than π/2 radians as the paths of the two vehicles converge toward one another. At some point in time, the absolute value of the difference between the host vehicle  10  heading angle δ HV  and β 1  becomes equal to π/2 radians at the moment the two vehicles pass each other. From this point on, the absolute value of the difference between the host vehicle  10  heading angle δ HV  and β 1  is less than 3π/2 radians as the paths of the two vehicles diverge. 
     As shown in  FIG. 55 , the host vehicle  10  is traveling west while the remote vehicle  14  is traveling east. Initially, the absolute value of the difference between the host vehicle  10  heading angle δ HV  and β 1  is less than π/2 radians as the paths of the two vehicles converge toward one another. At some point in time, the absolute value of the difference between the host vehicle  10  heading angle δ HV  and β 1  becomes equal to π/2 radians at the moment the two vehicles pass each other. From this point on, the absolute value of the difference between the host vehicle  10  heading angle δ HV  and β 1  is less than 3π/2 radians as the paths of the two vehicles diverge. 
     As shown in  FIG. 56 , the host vehicle  10  is traveling northwest while the remote vehicle  14  is traveling southeast. Initially, the absolute value of the difference between the host vehicle  10  heading angle δ HV  and β 1  is less than π/2 radians as the paths of the two vehicles converge toward one another. At some point in time, the absolute value of the difference between the host vehicle  10  heading angle δ HV  and β 1  becomes equal to π/2 radians at the moment the two vehicles pass each other. From this point on, the absolute value of the difference between the host vehicle  10  heading angle δ HV  and β 1  is less than 3π/2 radians as the paths of the two vehicles diverge. 
     From these eight examples, it can be seen that for any configuration the paths of the two vehicles are converging if the absolute value of the difference between the host vehicle  10  heading angle δ HV  and β 1  is either less than π/2 radians or greater than 3π/2 radians. Conversely the paths of the two vehicles are diverging if the absolute value of the difference between the host vehicle  10  heading angle δ HV  and β 1  is either greater than π/2 radians or less than 3π/2 radians thus:
         Converging paths: |δ HV −β 1 |&lt;π/2 or |δ HV −β 1 |&gt;3π/2   Diverging paths: |δ HV −β 1 |&gt;π/2 or |δ HV −β 1 |&gt;3π/2       

     The converging path condition is expressed mathematically as follows: 
             B   =         1   2     ⁡     [             (       1   /   2     -   φ     )     ⁢   π     -            δ   HV     -     β   1            +   σ                  (       1   /   2     -   φ     )     ⁢   π     -            δ   HV     -     β   1                   +   σ       +   1     ]       +       1   2     ⁡     [                  δ   HV     -     β   1            -       (       3   /   2     -   φ     )     ⁢   π     +   σ                       δ   HV     -     β   1            -       (       3   /   2     -   φ     )     ⁢   π            +   σ       +   1     ]               
where φ is used to define a minimum value for the upper and lower limits for the threshold angles.
 
     To determine that the host vehicle  10  and the remote vehicle  14  are converging along a path from opposing directions the following expression is used: 
               Δ   3     =         1   2     ⁡     [                  δ   HV     -     δ   RV            -       (     1   -   φ     )     ⁢   π     +   σ                       δ   HV     -     δ   RV            -       (     1   -   φ     )     ⁢   π            +   σ       +   1     ]       ×       1   2     ⁡     [             (     1   +   φ     )     ⁢   π     -            δ   HV     -     β   1                           (     1   +   φ     )     ⁢   π     -            δ   HV     -     β   1                   +   σ       +   1     ]               
where φ is used to define a ± range to either side of the reference angle value of π radians.
 
     Multiplying B and Δ 3  results in the following expression:
 
 C   9   =B×Δ   3  
 
     As can be understood from these equations, when C 9  is equal to 1, the host vehicle  10  and remote vehicle  14  are converging along a path from opposing directions. 
     Accordingly, as with the examples discussed above, when the host vehicle  10  receives a BSM, the application being run by the controller  22  on board the host vehicle  10  extracts information regarding GPS location, heading and turn signal status of the remote vehicle  14 . The application also obtains GPS location, heading and turn signal status of the host vehicle  10 . As in the above examples, for the host vehicle  10 , AB=00 if there is no turn signal; AB=01 if the host vehicle  10  is signaling a left turn; and AB=11 if the host vehicle  10  is signaling a right turn. For the remote vehicle  14 , CD=00 if there is no turn signal; CD=01 if the remote vehicle  14  is signaling a left turn; and CD=11 if the remote vehicle  14  is signaling a right turn. 
     Also as discussed above, the application can determine the position of the remote vehicle  14  relative to the host vehicle  10  such that EF=00 if there remote vehicle  14  is approaching the host vehicle  10  from the opposite direction; EF=01 if the remote vehicle  14  is approaching the host vehicle  10  from the left; and EF=11 if the remote vehicle  14  is approaching the host vehicle  10  from the right. 
     When the host vehicle  10  and remote vehicle  14  approach an intersection, there are 27 possible outcomes as shown in  FIGS. 4 through 30 . As discussed above, 14 of these outcomes result in crossing paths while the remaining 13 do not. If any one of the above equations for C 1  through C 9  equals 1, a threat exists. Multiplying the equations for for C 1  through C 9  by the FEDCBA threat code will specify the threat scenario as shown in Tables 28 through 36 below. 
     
       
         
           
               
             
               
                 TABLE 28 
               
             
            
               
                   
               
               
                 C 1  = 1 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
            
               
                   
                   
                   
                   
                   
                   
                   
                   
                 Decimal 
                   
               
               
                 C 1   
                   
                 F 
                 E 
                 D 
                 C 
                 B 
                 A 
                 value 
                 Threat 
               
               
                   
               
               
                 1 
                 x 
                 1 
                 1 
                 0 
                 0 
                 0 
                 0 
                 48 
                 SCP 
               
               
                 1 
                 x 
                 1 
                 1 
                 0 
                 0 
                 0 
                 1 
                 49 
                 LTIP 
               
               
                 1 
                 x 
                 1 
                 1 
                 0 
                 0 
                 1 
                 1 
                 51 
                 No threat 
               
               
                 1 
                 x 
                 1 
                 1 
                 0 
                 1 
                 0 
                 0 
                 52 
                 LTAP/LD 
               
               
                 1 
                 x 
                 1 
                 1 
                 0 
                 1 
                 0 
                 1 
                 53 
                 L/L 
               
               
                 1 
                 x 
                 1 
                 1 
                 0 
                 1 
                 1 
                 1 
                 55 
                 No threat 
               
               
                 1 
                 x 
                 1 
                 1 
                 1 
                 1 
                 0 
                 0 
                 60 
                 RTIP 
               
               
                 1 
                 x 
                 1 
                 1 
                 1 
                 1 
                 0 
                 1 
                 61 
                 No threat 
               
               
                 1 
                 x 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 63 
                 No threat 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 29 
               
             
            
               
                   
               
               
                 C 2  = 1 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
            
               
                   
                   
                   
                   
                   
                   
                   
                   
                 Decimal 
                   
               
               
                 C 2   
                   
                 F 
                 E 
                 D 
                 C 
                 B 
                 A 
                 value 
                 Threat 
               
               
                   
               
               
                 1 
                 x 
                 1 
                 1 
                 0 
                 0 
                 0 
                 0 
                 48 
                 SCP 
               
               
                 1 
                 x 
                 1 
                 1 
                 0 
                 0 
                 0 
                 1 
                 49 
                 LTIP 
               
               
                 1 
                 x 
                 1 
                 1 
                 0 
                 0 
                 1 
                 1 
                 51 
                 No threat 
               
               
                 1 
                 x 
                 1 
                 1 
                 0 
                 1 
                 0 
                 0 
                 52 
                 LTAP/LD 
               
               
                 1 
                 x 
                 1 
                 1 
                 0 
                 1 
                 0 
                 1 
                 53 
                 L/L 
               
               
                 1 
                 x 
                 1 
                 1 
                 0 
                 1 
                 1 
                 1 
                 55 
                 No threat 
               
               
                 1 
                 x 
                 1 
                 1 
                 1 
                 1 
                 0 
                 0 
                 60 
                 RTIP 
               
               
                 1 
                 x 
                 1 
                 1 
                 1 
                 1 
                 0 
                 1 
                 61 
                 No threat 
               
               
                 1 
                 x 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 63 
                 No threat 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 30 
               
             
            
               
                   
               
               
                 C 3  = 1 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
            
               
                   
                   
                   
                   
                   
                   
                   
                   
                 Decimal 
                   
               
               
                 C 3   
                   
                 F 
                 E 
                 D 
                 C 
                 B 
                 A 
                 value 
                 Threat 
               
               
                   
               
               
                 1 
                 x 
                 0 
                 1 
                 0 
                 0 
                 0 
                 0 
                 16 
                 SCP 
               
               
                 1 
                 x 
                 0 
                 1 
                 0 
                 0 
                 0 
                 1 
                 17 
                 LTAP/LD 
               
               
                 1 
                 x 
                 0 
                 1 
                 0 
                 0 
                 1 
                 1 
                 19 
                 RTIP 
               
               
                 1 
                 x 
                 0 
                 1 
                 0 
                 1 
                 0 
                 0 
                 20 
                 LTIP 
               
               
                 1 
                 x 
                 0 
                 1 
                 0 
                 1 
                 0 
                 1 
                 21 
                 L/L 
               
               
                 1 
                 x 
                 0 
                 1 
                 0 
                 1 
                 1 
                 1 
                 23 
                 No threat 
               
               
                 1 
                 x 
                 0 
                 1 
                 1 
                 1 
                 0 
                 0 
                 28 
                 No threat 
               
               
                 1 
                 x 
                 0 
                 1 
                 1 
                 1 
                 0 
                 1 
                 29 
                 No threat 
               
               
                 1 
                 x 
                 0 
                 1 
                 1 
                 1 
                 1 
                 1 
                 31 
                 No threat 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 31 
               
             
            
               
                   
               
               
                 C 4  = 1 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
            
               
                   
                   
                   
                   
                   
                   
                   
                   
                 Decimal 
                   
               
               
                 C 4   
                   
                 F 
                 E 
                 D 
                 C 
                 B 
                 A 
                 value 
                 Threat 
               
               
                   
               
               
                 1 
                 x 
                 1 
                 1 
                 0 
                 0 
                 0 
                 0 
                 48 
                 SCP 
               
               
                 1 
                 x 
                 1 
                 1 
                 0 
                 0 
                 0 
                 1 
                 49 
                 LTIP 
               
               
                 1 
                 x 
                 1 
                 1 
                 0 
                 0 
                 1 
                 1 
                 51 
                 No threat 
               
               
                 1 
                 x 
                 1 
                 1 
                 0 
                 1 
                 0 
                 0 
                 52 
                 LTAP/LD 
               
               
                 1 
                 x 
                 1 
                 1 
                 0 
                 1 
                 0 
                 1 
                 53 
                 L/L 
               
               
                 1 
                 x 
                 1 
                 1 
                 0 
                 1 
                 1 
                 1 
                 55 
                 No threat 
               
               
                 1 
                 x 
                 1 
                 1 
                 1 
                 1 
                 0 
                 0 
                 60 
                 RTIP 
               
               
                 1 
                 x 
                 1 
                 1 
                 1 
                 1 
                 0 
                 1 
                 61 
                 No threat 
               
               
                 1 
                 x 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 63 
                 No threat 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 32 
               
             
            
               
                   
               
               
                 C 5  = 1 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
            
               
                   
                   
                   
                   
                   
                   
                   
                   
                 Decimal 
                   
               
               
                 C 5   
                   
                 F 
                 E 
                 D 
                 C 
                 B 
                 A 
                 value 
                 Threat 
               
               
                   
               
               
                 1 
                 x 
                 0 
                 1 
                 0 
                 0 
                 0 
                 0 
                 16 
                 SCP 
               
               
                 1 
                 x 
                 0 
                 1 
                 0 
                 0 
                 0 
                 1 
                 17 
                 LTAP/LD 
               
               
                 1 
                 x 
                 0 
                 1 
                 0 
                 0 
                 1 
                 1 
                 19 
                 RTIP 
               
               
                 1 
                 x 
                 0 
                 1 
                 0 
                 1 
                 0 
                 0 
                 20 
                 LTIP 
               
               
                 1 
                 x 
                 0 
                 1 
                 0 
                 1 
                 0 
                 1 
                 21 
                 L/L 
               
               
                 1 
                 x 
                 0 
                 1 
                 0 
                 1 
                 1 
                 1 
                 23 
                 No threat 
               
               
                 1 
                 x 
                 0 
                 1 
                 1 
                 1 
                 0 
                 0 
                 28 
                 No threat 
               
               
                 1 
                 x 
                 0 
                 1 
                 1 
                 1 
                 0 
                 1 
                 29 
                 No threat 
               
               
                 1 
                 x 
                 0 
                 1 
                 1 
                 1 
                 1 
                 1 
                 31 
                 No threat 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 33 
               
             
            
               
                   
               
               
                 C 6  = 1 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
            
               
                   
                   
                   
                   
                   
                   
                   
                   
                 Decimal 
                   
               
               
                 C 6   
                   
                 F 
                 E 
                 D 
                 C 
                 B 
                 A 
                 value 
                 Threat 
               
               
                   
               
               
                 1 
                 x 
                 1 
                 1 
                 0 
                 0 
                 0 
                 0 
                 48 
                 SCP 
               
               
                 1 
                 x 
                 1 
                 1 
                 0 
                 0 
                 0 
                 1 
                 49 
                 LTIP 
               
               
                 1 
                 x 
                 1 
                 1 
                 0 
                 0 
                 1 
                 1 
                 51 
                 No threat 
               
               
                 1 
                 x 
                 1 
                 1 
                 0 
                 1 
                 0 
                 0 
                 52 
                 LTAP/LD 
               
               
                 1 
                 x 
                 1 
                 1 
                 0 
                 1 
                 0 
                 1 
                 53 
                 L/L 
               
               
                 1 
                 x 
                 1 
                 1 
                 0 
                 1 
                 1 
                 1 
                 55 
                 No threat 
               
               
                 1 
                 x 
                 1 
                 1 
                 1 
                 1 
                 0 
                 0 
                 60 
                 RTIP 
               
               
                 1 
                 x 
                 1 
                 1 
                 1 
                 1 
                 0 
                 1 
                 61 
                 No threat 
               
               
                 1 
                 x 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 63 
                 No threat 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 34 
               
             
            
               
                   
               
               
                 C 7  = 1 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
            
               
                   
                   
                   
                   
                   
                   
                   
                   
                 Decimal 
                   
               
               
                 C 7   
                   
                 F 
                 E 
                 D 
                 C 
                 B 
                 A 
                 value 
                 Threat 
               
               
                   
               
               
                 1 
                 x 
                 0 
                 1 
                 0 
                 0 
                 0 
                 0 
                 16 
                 SCP 
               
               
                 1 
                 x 
                 0 
                 1 
                 0 
                 0 
                 0 
                 1 
                 17 
                 LTAP/LD 
               
               
                 1 
                 x 
                 0 
                 1 
                 0 
                 0 
                 1 
                 1 
                 19 
                 RTIP 
               
               
                 1 
                 x 
                 0 
                 1 
                 0 
                 1 
                 0 
                 0 
                 20 
                 LTIP 
               
               
                 1 
                 x 
                 0 
                 1 
                 0 
                 1 
                 0 
                 1 
                 21 
                 L/L 
               
               
                 1 
                 x 
                 0 
                 1 
                 0 
                 1 
                 1 
                 1 
                 23 
                 No threat 
               
               
                 1 
                 x 
                 0 
                 1 
                 1 
                 1 
                 0 
                 0 
                 28 
                 No threat 
               
               
                 1 
                 x 
                 0 
                 1 
                 1 
                 1 
                 0 
                 1 
                 29 
                 No threat 
               
               
                 1 
                 x 
                 0 
                 1 
                 1 
                 1 
                 1 
                 1 
                 31 
                 No threat 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 35 
               
             
            
               
                   
               
               
                 C 8  = 1 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
            
               
                   
                   
                   
                   
                   
                   
                   
                   
                 Decimal 
                   
               
               
                 C 8   
                   
                 F 
                 E 
                 D 
                 C 
                 B 
                 A 
                 value 
                 Threat 
               
               
                   
               
               
                 1 
                 x 
                 0 
                 1 
                 0 
                 0 
                 0 
                 0 
                 16 
                 SCP 
               
               
                 1 
                 x 
                 0 
                 1 
                 0 
                 0 
                 0 
                 1 
                 17 
                 LTAP/LD 
               
               
                 1 
                 x 
                 0 
                 1 
                 0 
                 0 
                 1 
                 1 
                 19 
                 RTIP 
               
               
                 1 
                 x 
                 0 
                 1 
                 0 
                 1 
                 0 
                 0 
                 20 
                 LTIP 
               
               
                 1 
                 x 
                 0 
                 1 
                 0 
                 1 
                 0 
                 1 
                 21 
                 L/L 
               
               
                 1 
                 x 
                 0 
                 1 
                 0 
                 1 
                 1 
                 1 
                 23 
                 No threat 
               
               
                 1 
                 x 
                 0 
                 1 
                 1 
                 1 
                 0 
                 0 
                 28 
                 No threat 
               
               
                 1 
                 x 
                 0 
                 1 
                 1 
                 1 
                 0 
                 1 
                 29 
                 No threat 
               
               
                 1 
                 x 
                 0 
                 1 
                 1 
                 1 
                 1 
                 1 
                 31 
                 No threat 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 36 
               
             
            
               
                   
               
               
                 C 9  = 1 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
            
               
                   
                   
                   
                   
                   
                   
                   
                   
                 Decimal 
                   
               
               
                 C 9   
                   
                 F 
                 E 
                 D 
                 C 
                 B 
                 A 
                 value 
                 Threat 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
            
               
                 1 
                 x 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 No threat 
               
               
                 1 
                 x 
                 0 
                 0 
                 0 
                 0 
                 0 
                 1 
                 1 
                 LTAP/OD 
               
               
                 1 
                 x 
                 0 
                 0 
                 0 
                 0 
                 1 
                 1 
                 3 
                 No threat 
               
               
                 1 
                 x 
                 0 
                 0 
                 0 
                 1 
                 0 
                 0 
                 4 
                 LTAP/OD 
               
               
                 1 
                 x 
                 0 
                 0 
                 0 
                 1 
                 0 
                 1 
                 5 
                 No threat 
               
               
                 1 
                 x 
                 0 
                 0 
                 0 
                 1 
                 1 
                 1 
                 7 
                 R/L 
               
               
                 1 
                 x 
                 0 
                 0 
                 1 
                 1 
                 0 
                 0 
                 12 
                 No threat 
               
               
                 1 
                 x 
                 0 
                 0 
                 1 
                 1 
                 0 
                 1 
                 13 
                 L/R 
               
               
                 1 
                 x 
                 0 
                 0 
                 1 
                 1 
                 1 
                 1 
                 15 
                 No threat 
               
               
                   
               
            
           
         
       
     
     As can be appreciated from the above, the embodiments described herein provide a system and method that evaluate scenarios in which a host vehicle and a remote vehicle may come in contact at an intersection or while the host vehicle is executing a turn. The processing can perform logic flows that can determine if a potential contact between the host vehicle  10  and the remote vehicle  14  exists. Alternatively, the processing can employ a series of mathematical expressions to directly assess if potential threats exist and, if a threat does exist, immediately determine the specific threat type, making this method much more efficient. 
     GENERAL INTERPRETATION OF TERMS 
     In understanding the scope of the present invention, the term “comprising” and its derivatives, as used herein, are intended to be open ended terms that specify the presence of the stated features, elements, components, groups, integers, and/or steps, but do not exclude the presence of other unstated features, elements, components, groups, integers and/or steps. The foregoing also applies to words having similar meanings such as the terms, “including”, “having” and their derivatives. Also, the terms “part,” “section,” “portion,” “member” or “element” when used in the singular can have the dual meaning of a single part or a plurality of parts. The term “detect” as used herein to describe an operation or function carried out by a component, a section, a device or the like includes a component, a section, a device or the like that does not require physical detection, but rather includes determining, measuring, modeling, predicting or computing or the like to carry out the operation or function. The term “configured” as used herein to describe a component, section or part of a device includes hardware and/or software that is constructed and/or programmed to carry out the desired function. 
     While only selected embodiments have been chosen to illustrate the present invention, it will be apparent to those skilled in the art from this disclosure that various changes and modifications can be made herein without departing from the scope of the invention as defined in the appended claims. For example, the size, shape, location or orientation of the various, components can be changed as needed and/or desired. Components that are shown directly connected or contacting each other can have intermediate structures disposed between them. The functions of one element can be performed by two, and vice versa. The structures and functions of one embodiment can be adopted in another embodiment. It is not necessary for all advantages to be present in a particular embodiment at the same time. Every feature which is unique, from the prior art, alone or in combination with other features, also should be considered a separate description of further inventions by the applicant, including the structural and/or functional concepts embodied by such feature(s). Thus, the foregoing descriptions of the embodiments according to the present invention are provided for illustration only, and not for the purpose of limiting the invention as defined by the appended claims and their equivalents.