Patent Publication Number: US-10761183-B2

Title: Ultrasonic signal triangulation

Description:
TECHNICAL FIELD 
     The present disclosure relates to systems and methods for locating an object using ultrasonic signal triangulation. 
     BACKGROUND 
     Operation of a motor vehicle may include being aware of multiple external factors, such as stationary and moving objects, people, and animals, traffic signals, roadway signage, and so on. As some examples, the external factors may include parked and moving vehicles, bicyclists, pedestrians, one-way street and speed limit signs, and so on. Additionally or alternatively, driving may include maneuvering the vehicle in physically constrained areas or in areas with poor visibility. 
     One or more vehicle object-detection systems, such as radio detection and ranging (RADAR) and light detection and ranging (LIDAR), may be used to detect objects external to the vehicle. In some instances, RADAR and LIDAR systems may be configured to detect external objects, or “targets”, in the vicinity of the vehicle. The vehicle object-detection systems may determine a distance to the external object, i.e., a target range, and speed at which the object is moving toward or away from the vehicle, i.e., a target range rate. The vehicle object-detection systems may be configured to determine a likelihood of collision between the vehicle and the external object. 
     SUMMARY 
     A system for a vehicle includes a trio of ultrasonic sensors, and a controller configured to, responsive to a location of an object identified from a distance between the ultrasonic sensors, a receive time at each of the ultrasonic sensors associated with a same ultrasonic pulse from a transmitter of the object, and an absence of data regarding a send time of the ultrasonic pulse, steer the vehicle to the object. 
     A method for a vehicle includes steering, by a controller, the vehicle to an object responsive to a location of the object identified from a distance between an outer pair of a plurality of ultrasonic sensors on the vehicle, a receive time at each of the ultrasonic sensors associated with a same ultrasonic pulse from a transmitter of the object, and an absence of data regarding a send time of the ultrasonic pulse. 
     A vehicle includes a bumper having sensors thereon, and a controller configured to steer the vehicle to an object based on a location of the object identified from receive times at each of the sensors associated with a same pulse emitted from the object and an absence of data regarding a send time of the pulse. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1A  is a block diagram illustrating a vehicle equipped with an ultrasonic object detection system; 
         FIG. 1B  is a block diagram illustrating a component arrangement of the ultrasonic object detection system; 
         FIG. 2A  is a perspective view of an ultrasonic object detection sensor; 
         FIG. 2B  is a cross-section view of the ultrasonic object detection sensor; 
         FIG. 3A  a block diagram illustrating object positioning using the ultrasonic sensor; 
         FIG. 3B  is a block diagram illustrating ultrasonic sensor object positioning using triangulation; 
         FIG. 4  is a block diagram illustrating an example geometric triangulation approach; 
         FIGS. 5A-5B  are block diagrams illustrating ultrasonic sensor object positioning using triangulation; 
         FIGS. 6A-6B  are block diagrams illustrating object location determination using ultrasonic sensor signal triangulation; and 
         FIGS. 7A-7B  are flowcharts illustrating algorithms for the ultrasonic object detection system. 
     
    
    
     DETAILED DESCRIPTION 
     Embodiments of the present disclosure are described herein. It is to be understood, however, that the disclosed embodiments are merely examples and other embodiments may take various and alternative forms. The figures are not necessarily to scale; some features could be exaggerated or minimized to show details of particular components. Therefore, specific structural and functional details disclosed herein are not to be interpreted as limiting, but merely as a representative basis for teaching one skilled in the art to variously employ the present invention. As those of ordinary skill in the art will understand, various features illustrated and described with reference to any one of the figures may be combined with features illustrated in one or more other figures to produce embodiments that are not explicitly illustrated or described. The combinations of features illustrated provide representative embodiments for typical applications. Various combinations and modifications of the features consistent with the teachings of this disclosure, however, could be desired for particular applications or implementations. 
     Vehicle object-detection systems may detect objects external to the vehicle using radio waves, light waves, or some combination thereof. In some examples, vehicles may be equipped with an ultrasonic object-detection system. Operating parameters of a given vehicle object-detection system may include a horizontal field of view spanning a predefined horizontal range, e.g., between twenty-five and twenty-seven degrees, and a vertical field spanning a predefined vertical range, e.g., approximately seven degrees. An operation cycle time of each object-detection system may last a predefined time period, such as, several milliseconds, and may vary based on sensor types. In one example, an ultrasonic sensor may employ three beams and may be configured to operate at a range of zero to ten meters, with an effective detection range of one to eight meters. 
       FIG. 1A  illustrates an example object-detection system  100 -A for a vehicle  102 . The vehicle  102  may be of various types of passenger vehicles, such as crossover utility vehicle (CUV), sport utility vehicle (SUV), truck, recreational vehicle (RV), boat, plane or other mobile machine for transporting people or goods. 
     The vehicle  102  may be equipped with a plurality of ultrasonic sensors  104 . The sensors  104  may be disposed on exterior of the vehicle  102  body. Each sensor or several sensors  104  may include a housing and may be generally oriented outward and away from the vehicle  102 . The sensors  104  may be oriented to send  106  and receive  108  ultrasonic signals emitted in the vicinity of the vehicle  102 . In one example, the sensors  104  include an acoustic transmitter and an acoustic receiver. In some examples, other types of sensors or a combination of acoustic and other sensors may be used. In still other examples, more or fewer sensors  104  may be implemented. 
     The sensors  104  may be configured to send  106  and receive  108  ultrasonic signals from one or more ultrasonic sensors  109  disposed on exterior of an object  110  being detected by the vehicle  102 . The object ultrasonic sensors  109  may be installed on one or more objects in public or private places, e.g., in physically constrained places or in places with poor visibility, such that the sensors  104  of the vehicle  102  may detect the location of the object  110 . As one example, the sensors  104   a ,  104   b  may each send  106   a ,  106   b  and receive  108   a ,  108   b  ultrasonic signals from the object sensors  109   a ,  109   b , respectively, when the vehicle  102  is within a predefined distance of the object  110   a . As another example, the sensors  104   c ,  104   d  may both send  106   c ,  106   d  and receive  108   c ,  108   d  ultrasonic signals from the object sensor  109   c , when the vehicle  102  is within a predefined distance of the object  110   b.    
     Accordingly, ultrasonically sensing, as used herein, may include sending and receiving a positioning signal from the transmission assembly disposed on the object  110  to assist in positioning the vehicle  102  relative to the object  110 . Respective signal waveforms of the sensors  104  may overlap with one another to provide greater accuracy in detection of the presence, movement and location of the object  110 . The sensors  104  may emit and detect ultrasonic signals that reflect off the objects  110 . Based on the sensed signals at the sensors  104 , the operation of the vehicle  102  may be controlled, e.g., reducing speed of the vehicle  102  during a parking or driving maneuver, or resuming a parking or driving maneuver once a precise location of the object has been determined. 
       FIG. 1B  illustrates an example communication system  100 -B of the vehicle  102 . In one example, the sensors  104  may be connected to and in communication with an ultrasonic object detection controller (hereinafter, controller)  112 . The controller  112  may include one or more processors  114  connected with both a memory  116  and a computer-readable storage medium  118  and configured to perform instructions  120 , commands, and other routines in support of the processes described herein. 
     For instance, the controller  112  may be configured to execute instructions of vehicle applications to provide features, such as, but not limited to, object detection, object identification, object movement detection, and so on. In one example, the processor  114  of the controller  112  may be configured to calculate a position of the object  110 , including distance and horizontal offset, in response to signals from the sensor  104 . Such instructions and other data may be maintained in a non-volatile manner using a variety of types of computer-readable storage medium  118 . The computer-readable medium  118  (also referred to as a processor-readable medium or storage) includes any non-transitory (e.g., tangible) medium that participates in providing instructions or other data that may be read by the processor  114  of the controller  112 . Computer-executable instructions  120  may be compiled or interpreted from computer programs created using a variety of programming languages and/or technologies, including, without limitation, and either alone or in combination, Java, C, C++, C #, Objective C, Fortran, Pascal, Java Script, Python, Perl, and PL/SQL. 
     The controller  112  may be further configured to communicate with other components of the vehicle  102  via one or more in-vehicle networks  122 . For example, the controller  112  may communicate with a first set of vehicle systems, subsystems, or components over a first in-vehicle network  122   a , and with a second set of vehicle  102  systems, subsystems, or components over a second in-vehicle network  122   b . In other examples, the controller  112  may be connected to more or fewer in-vehicle networks  122 . Additionally or alternately, one or more vehicle  102  systems, subsystem, or components may be connected to the controller  112  via different in-vehicle networks  122  than shown, or directly, e.g., without connection to an in-vehicle network  122 . 
     The in-vehicle networks  122  may include one or more of a vehicle controller area network (CAN), an Ethernet network, or a media oriented system transfer (MOST), as some examples. The in-vehicle networks  122  may allow the controller  112  to communicate with other vehicle  102  systems, such as a global positioning system (GPS) controller  124  and an in-vehicle display  126  configured to provide current vehicle  102  location and heading information, and various vehicle controllers  128  configured to provide other types of information regarding the systems of the vehicle  102 . 
     As some non-limiting possibilities, the vehicle controllers  128  may include a powertrain controller configured to provide control of engine operating components (e.g., idle control components, fuel delivery components, emissions control components, etc.) and monitoring of engine operating components (e.g., status of engine diagnostic codes); a body controller configured to manage various power control functions such as exterior lighting, interior lighting, keyless entry, remote start, and point of access status verification (e.g., closure status of the hood, doors, and/or trunk of the vehicle  102 ); a radio transceiver configured to communicate with key fobs or other local vehicle  102  devices; and a climate control management controller configured to provide control and monitoring of heating and cooling system components (e.g., compressor clutch and blower fan control, temperature sensor information, etc.). 
     The ultrasonic object detection controller  112  may be connected to and in communication with the in-vehicle display  126 . The in-vehicle display may be a dashboard multifunction display or other displays as appropriate. The controller  112  may be configured to provide positional information to a driver via the in-vehicle display  126 , such as, but not limited to, a position of the object  110  and a position of the vehicle  102  with respect to one another. The in-vehicle display  126  may include any appropriate representation of the vehicle  102  positional information to illustrate the vehicle  102  position and orientation, including distance and horizontal offset relative to the object  110 . In response to this information, the driver may more accurately maneuver the vehicle  102  with respect to the object  110 . 
     As one example, the vehicle  102  may be equipped with an auto park system. In such an example, a controller, which may be the controller  112  or other vehicle controllers  128 , may command various vehicle systems to coordinate an automatic parking event. During an automatic parking event, vehicle steering, acceleration, and braking systems (not illustrated) may be automatically controlled to park the vehicle  102  in an appropriate parking location and orientation. The controller  112  and/or vehicle controllers  128  may use the positional information from the sensors  104  to coordinate the various systems and position the vehicle  102  relative to the objects  110 . 
       FIG. 2A  illustrates a perspective view  200 -A of the ultrasonic sensor  104  of the vehicle  102 . The sensor  104  may include a housing  202  configured to retain at least a portion of a connector body  204  and connection terminals  206 . In some instances, the wireless transceiver  150  described in reference to  FIG. 1B  may be disposed within the housing  202  of the sensor  104  and may be configured to send and receive ultrasonic signals. In some other instances, the processor  114  may be connected to the wireless transceiver  150  via the terminals  206  and may monitor and control operation of the wireless transceiver  150  using the same. Additionally or alternatively, the processor  114 , like the wireless transceiver  150 , may be disposed within the housing  202  of the sensor  104  and may use the terminals  206  to transmit signals between the sensor  104  and the in-vehicle networks  122 . 
       FIG. 2B  illustrates a partial cross-section view  200 -B of the ultrasonic sensor  104 . The housing  202  may include a metal case  208 . A layer of piezoelectric material  210  may be sandwiched by thin high conductivity electrode layers, e.g., layers of gold or platinum, with or without an underlying adhesion layer, e.g., a layer of chromium or titanium, and may be connected with the terminals  206 . In one example, generating an excitation within one or both terminals  206  may cause the piezoelectric material  210  to deflect in a predefined pattern, such as, but not limited to, deflect in a longitudinal vibration. In some instances, thickness of the piezoelectric material  210  layer and longitudinal velocity of sound directed toward the material  210  causing corresponding vibrations may influence an anti-resonant frequency value of the sensor  104 . One or more of an absorber  212 , a stiffener  214 , and a damper  216  may form a backing layer of the sensor  104  and may be configured to dampen vibrations of the piezoelectric material  210 . 
       FIG. 3A  illustrates an example signal transmission scheme  300 -A of the ultrasonic sensor  104  signals. The vehicle  102  may include a plurality of ultrasonic sensors  104 . The ultrasonic sensors  104  in communication with the controller  112  may be disposed at predefined locations about exterior of the vehicle  102 , e.g., front portion of the vehicle  102 , proximate to each of the vehicle  102  headlights, and so on. In one example, first, second, and third sensors  104   a ,  104   b ,  104   c , respectively, may be disposed about a front bumper  302  of the vehicle  102 , such that the first and third sensors  104   a ,  104   c  are located about opposite ends of the front bumper  302  and a second sensor  104   b  is disposed between, and equidistant from, the first and third sensors  104   a ,  104   c.    
     Other variations of the above system are also contemplated. For example, the sensors  104  may be operatively coupled to a different exterior or interior portion of the vehicle  102 , rather than the front bumper  302  as illustrated in  FIG. 3A . In one or more variations, the sensors  104  may be operatively coupled to an underbody, sides, roof, windshield of the vehicle  102 . The above and other sensor  104  locations may all be used in conjunction with methods according to the present disclosure. In some examples, the vehicle  102  may be equipped with an automatic parking system, and the positional information is used by an automatic parking system to facilitate hands-free parking. In some other examples, the vehicle  102  may be equipped with an object detection system, an adaptive cruise control system, a lane departure warning system, and so on. 
     The sensors  104   a ,  104   b ,  104   c  may be configured to emit bursts of sound at frequencies outside a range of frequencies perceptible by a human ear. For example, the controller  112  may be configured to issue a command to one or more of the sensors  104   a ,  104   b , and  104   c  to generate an acoustic signal. Responsive to the command, the sensors  104   a ,  104   b , and  104   c  may be configured to transmit signals simultaneously with one another or at different times. Accordingly, the sensors  104   a ,  104   b , and  104   c  may transmit signals to determine whether an object is present in the vicinity of the vehicle  102  and the distance to that object. 
     As one example, the sensors  104   a ,  104   b ,  104   c  may be configured to detect an echo signal returned, e.g., reflected, from the object  110 . The sensors  104  may compute the distance to the object  110  based on a period of time between the initial signal transmission and the receipt of the echo signal. In some cases, the echo signal may be lost or dissipated prior to reaching the sensor  104 , such as when the echo signal is directed away from the sensor  104  due to the orientation of the object  110  relative to the sensor  104  or when the material, from which the object is made, either partially absorbs the transmitted ultrasonic signals or simply serves as a poor reflector of an ultrasonic signal waveform. 
     As another example, the corresponding wireless transceivers  150  of the sensors  104   a ,  104   b ,  104   c  may be configured to detect returned, e.g., reflected, ultrasonic signals from corresponding transceivers of the object sensors  109  disposed about the objects  110 . The object sensors  109  may be disposed on one or more objects  110  likely to be within a path of a maneuvering vehicle  102 , such as, but not limited to, parking meters, street and traffic signage, objects  110  located within physically constrained areas, objects  110  located in areas with poor visibility, and so on. 
     A distance  304  may be indicative of a shortest distance between the sensors  104  and the object sensor  109 , e.g., a distance along a straight line disposed perpendicular to the plane formed by the sensors  104 . A distance  306  may be indicative of a shortest distance, e.g., distance along a straight line, between the corresponding sensor  104  and the object sensor  109 . Thus, a first distance  306   a  may be indicative of a distance between the first sensor  104   a  and the object sensor  109 , a second distance  306   b  may be indicative of a distance between the second sensor  104   b  and the object sensor  109 , a third distance  306   c  may be indicative of a distance between the third sensor  104   c  and the object sensor  109 , and so on. 
     A distance  308  may be indicative of a distance between the outer sensors  104 , i.e., the first and third sensors  104   a  and  104   c , respectively, and the second sensor  104   b  may be equidistant from each of the first and third sensors  104   a  and  104   c . In some instances, the three sensors  104   a ,  104   b ,  104   c  and the object sensor  109  may be arranged to form a triangle, such that a difference in respective arrival times of the ultrasonic signal, transmitted by the object sensor  109 , at each of the sensors  104   a ,  104   h ,  104   c  may be proportional to the corresponding distance  306  between that sensor  104  and the object sensor  109 . 
       FIG. 4  illustrates an example arrangement  400  of points A, B, and C disposed on a same plane and connected with one another to form a triangle ABC  402 , where angle A defines an angle between a first line  404  connecting points A and B and a second line  406  connecting points A and C, angle B defines an angle between a pair of lines  404  and  408  connecting points B and A and points B and C, respectively, and angle C defines an angle between a pair of lines  406  and  408  connecting points C and A and points C and B, respectively. In some instances, medians m a    410 , m b    412 , m c    414  may be indicative of a distance between each of the points A, B, and C and the corresponding one of the points, M a , M b , and M c  disposed about a center of an opposing side. In some other instances, the length of each of the medians m a    410 , m b    412 , and m c    414  may be given according to Apollonius Theorem, such that the length of each median m a    410 , m b    412 , and m c    414  may be based on corresponding lengths of the sides a  408 , b  406 , and c  404  of the triangle  402  as follows: 
     
       
         
           
             
               
                 
                   
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     With reference to  FIG. 3B , the first side, a may be indicative of the distance  308  between the first and third sensors  104   a  and  104   c  and may be known. The second distance  306   b  between the second sensor  104   b  and the object sensor  109  may be said to be the median m a    410  because the second sensor  104   b  is located equidistant from the first and third sensors  104   a  and  104   c . The second and third sides b, c may be indicative of distances between one of the first and third sensors  104   a  and  104   c  and the object sensor  109 . 
     In some instances, the distance x  304  may be indicative of a shortest distance, i.e., a length of a perpendicular line, between the object sensor  109  and the vehicle  102 . The second side, b may be defined based on a sum of lengths x and y, such that
 
 b=x+y   (4)
 
where y may be indicative of a length difference between the shortest distance, x  304  and the second side, b. The third side, c may be defined based on a sum of lengths x and z, such that
 
 c=x+z   (5)
 
where z may be indicative of a length difference between the shortest distance, x  304  and the third side, c. In some examples, y may be greater than z, e.g., y&gt;z.
 
     Substituting values for the second and third sides b, c, expressed according to Equations (4) and (5), into Equation (1) and solving for the shortest distance, x  304  such that 
     
       
         
           
             
               
                 
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     Accordingly, the values of y and z can be determined based on the speed of sound, c and a timestamping difference of the arrival of the ultrasonic pulse at each of the sensors  104 . For example, the controller  112  may detect that a first timestamping time, T1 is a timestamp of the ultrasonic pulse received at the first sensor  104   a , a second timestamping time, T2 is a timestamp of the ultrasonic pulse received at the second sensor  104   b , and a third timestamping time, T3 is a timestamp of the ultrasonic pulse received at the third sensor  104   c.    
     The controller  112  may be configured to compare the timestamping times T1, T2, and T3. In one example, the controller  112  may set a short timestamp T SHORT  equal to a shortest, e.g., smallest, timestamp, set a long timestamp T LONG  equal to a longest, e.g., largest, timestamp, and set a middle timestamp T MID  equal to the timestamp having a value between the short and long timestamps T SHORT  and T LONG , respectively. 
     The controller  112  may be configured to determine the length y based on a difference between the short and long timestamps T SHORT  and T LONG  such that:
 
 Y =( T   LONG   −T   SHORT )× c   (7)
 
where c may be indicative of a speed of sound and may be approximately equal to 343 m/s. The controller  112  may be configured to determine the length z based on a difference between the short and middle timestamps T SHORT  and T MID  such that:
 
 z =( T   MID   −T   SHORT )× c   (8)
 
The controller  112  may be configured to determine the shortest length, x  304  based on the values y and z, as according to Equation (6). The controller  112  may determine the second side, b and the third side, c based on Equations (4) and (5), respectively.
 
       FIGS. 5A-5B  illustrate example triangulation diagrams  500 -A and  500 -B, respectively, for varying a position of the object sensor  109  and maintaining fixed a position of the vehicle  102 , i.e., ultrasonic sensors  104   a ,  104   b , and  104   c . A first pair of adjacent sensors may include the first and second ultrasonic sensors  104   a ,  104   b  and a second pair of adjacent sensors may include the second and third ultrasonic sensors  104   b ,  104   c . In some instances, an absolute value of a difference between signal times of the sensors  104  of a given adjacent pair may be proportional to an absolute value of a difference in distance between the sensors  104  of that pair and the object sensor  109 . 
     With reference to  FIG. 5A , for the first adjacent pair, if the first sensor  104   a  receives the signal at t1 and the second sensor  104   b  receives the signal at t2, then |t1−t2| may be proportional to an absolute value of a difference between respective distances  502 ,  504 , e.g., |d1−d2|. As another example, for the second adjacent pair, if the second sensor  104   b  receives the signal at t2 and the third sensor  104   c  receives the signal at t3, then |t2−t3| may be proportional to an absolute value of a difference between respective distances  504 ,  506 , e.g., |d2−d3|. 
     Referring now to  FIG. 5B , for the first adjacent pair, if the first sensor  104   a  receives the signal at t1 and the second sensor  104   b  receives the signal at t2, then |t1−t2| may be proportional to an absolute value of a difference between respective distances  510 ,  512 , e.g., |d4−d5|. As another example, for the second adjacent pair, if the second sensor  104   b  receives the signal at t2 and the third sensor  104   c  receives the signal at t3, then |t2−t3| may be proportional to an absolute value of a difference between respective distances  512 ,  514 , e.g., |d5−d6|. 
       FIGS. 6A-6B  illustrate example triangulation diagrams  600 -A and  600 -B, respectively, for varying a position of the vehicle  102 , i.e., a position of the ultrasonic sensors  104   a ,  104   b , and  104   c  and keeping fixed a position of the object sensor  109 . In one example, if arrival timestamps T of at least two sensors  104  are approximately equal, then the respective distances d between the object sensor  109  and those sensors  104  may be approximately equal to one another. With reference to  FIG. 6A , distance x between the first sensor  104   a  and the object sensor  109  may be approximately equal to distance y between the third sensor  104   c  and the object sensor  109  when respective differences between associated signal timestamps T of the pairs of adjacent sensors  104  are approximately equal to one another, e.g., (T1−T2)≈(T3−T2). 
     As still another example, differences between a shortest (or smallest value) signal timestamp T SHORT  and each of a medium signal timestamp T MID  and a longest (or largest value) signal timestamp T LONG  may be proportional to differences in distance between the sensors  104  associated with the shortest, middle, and longest timestamps T SHORT , T MID , and T LONG , respectively, and the object sensor  109 . 
     With reference to  FIG. 6B , a shortest signal timestamp T SHORT  may be associated with the first sensor  104   a , a medium signal timestamp T MID  may be associated with the second sensor  104   b , and a longest (or largest value) signal timestamp T LONG  may be associated with the third sensor  104   c . Accordingly, (T MID −T SHORT ) may be proportional to a difference between distance e of the first sensor  104   a  and the object sensor  109  and distance f of the second sensor  104   b  and the object sensor  109 . Additionally or alternatively, (T LONG −T SHORT ) may be proportional to a difference between distance f of the second sensor  104   b  and the object sensor  109  and distance g of the third sensor  104   c  and the object sensor  109 . 
       FIG. 7A  illustrates an example process  700 -A for determining a position of the object  110  with respect to the vehicle  102  using triangulation. The process  700 -A may begin at block  702  where the controller  112  detects timestamps T1, T2, and T3 associated with a same signal emitted by a transceiver associated with object sensor  109  and received by the first, second, and third sensors  104   a ,  104   b , and  104   c , respectively. At one or more of blocks  704 - 732  the controller  112  may compare values of the timestamps T1, T2, and T3 with one another and set a shortest (or smallest value) timestamp equal to T SHORT , a longest (or largest value) timestamp equal to T LONG , and a middle (or medium value) timestamp equal to T MID , such that each timestamp T1, T2, and T3 is associated with only one of T SHORT , T LONG , and T MID . 
     The controller  112  at block  734  may determine values y and z according to Equations (7) and (8), respectively. At block  736  the controller  112  may determine a shortest distance x based on the values y and z, where the distance x may be indicative of a shortest distance between the sensors  104   a ,  104   b ,  104   c  and the object sensor  109  and/or indicative of a height of a triangle formed between the sensors  104   a ,  104   b ,  104   c  and the object sensor  109 . In one example, the controller  112  may determine the shortest distance x based on the values y and z and a distance a between the nonadjacent sensors  104 , e.g., distance between the first and third sensors  104   a ,  104   c , as described, for example, in reference to Equation (6). Additionally or alternatively, the controller  112  at block  736  may determine sides b and c of the triangle formed between the sensors  104   a ,  104   b ,  104   c  and the object sensor  109 , as described, for example, in reference to Equations (4) and (5), respectively. 
       FIG. 7B  illustrates an example process  700 -B for determining a position of the object  110  with respect to the vehicle  102  using triangulation. In some instances, the controller  112  may complete the process  700 -B instead of completing the process  700 -A or vice versa. In some other instances, the controller  112  may complete portions of the process  700 -B prior to and/or after completing portions of the process  700 -A. 
     The process  700 -B may begin at block  738  where the controller  112  detects timestamps T1, T2, and T3, each received by one of the first, second, and third sensors  104   a ,  104   b , and  104   c , where T3 is a longest (or largest in value) timestamp, T2 is a middle (or medium value) timestamp, and T1 is a shortest (or smallest value) timestamp. At block  740 , the controller  112  may determine differences y and z, such that:
 
 y =( T 3− T 1)× c   (9)
 
and
 
 z =( T 2− T 1)× c,   (10)
 
where c is a representative of a speed of sound and may be approximately equal to 343 m/s.
 
     At block  742  the controller  112  may determine a shortest distance x based on the values y and z, where the distance x may be indicative of a shortest distance between the sensors  104   a ,  104   b ,  104   c  and the object sensor  109  and/or indicative of a height of a triangle formed between the sensors  104   a ,  104   b ,  104   c  and the object sensor  109 . In one example, the controller  112  may determine the shortest distance x based on the values y and z and a distance a between the first and third sensors  104   a ,  104   c , as described, for example, in reference to Equation (6). Additionally or alternatively, the controller  112  at block  742  may determine sides b and c of the triangle formed between the sensors  104   a ,  104   b ,  104   c  and the object sensor  109 , as described, for example, in reference to Equations (4) and (5), respectively. 
     At block  744  the controller  112  may set distance b to a distance between the object  110  and the sensor  104  associated with the timestamp T2. In one example, the controller  112  may be configured to, responsive to detecting at block  738  the timestamps T1, T2, and T3, associate each sensor  104  with one of the timestamps T1, T2, and T3 based on the timestamp at which the return signal is received at that sensor  104 . At block  746  the controller  112  may set distance c to a distance between the object  110  and the sensor  104  associated with the timestamp T3. The controller  112  at block  748  may determine position of the object  110  based on the distances a, b, and c. That is, the controller  112  may determine the position of the object  110  without any data as to when the signal output by the object sensor  109  was sent. 
     The processes, methods, or algorithms disclosed herein may be deliverable to or implemented by a processing device, controller, or computer, which may include any existing programmable electronic control unit or dedicated electronic control unit. Similarly, the processes, methods, or algorithms may be stored as data and instructions executable by a controller or computer in many forms including, but not limited to, information permanently stored on non-writable storage media such as ROM devices and information alterably stored on writeable storage media such as floppy disks, magnetic tapes, CDs, RAM devices, and other magnetic and optical media. The processes, methods, or algorithms may also be implemented in a software executable object. Alternatively, the processes, methods, or algorithms may be embodied in whole or in part using suitable hardware components, such as Application Specific Integrated Circuits (ASICs), Field-Programmable Gate Arrays (FPGAs), state machines, controllers or other hardware components or devices, or a combination of hardware, software and firmware components. 
     The words used in the specification are words of description rather than limitation, and it is understood that various changes may be made without departing from the spirit and scope of the disclosure. As previously described, the features of various embodiments may be combined to form further embodiments of the invention that may not be explicitly described or illustrated. While various embodiments could have been described as providing advantages or being preferred over other embodiments or prior art implementations with respect to one or more desired characteristics, those of ordinary skill in the art recognize that one or more features or characteristics may be compromised to achieve desired overall system attributes, which depend on the specific application and implementation. These attributes may include, but are not limited to cost, strength, durability, life cycle cost, marketability, appearance, packaging, size, serviceability, weight, manufacturability, ease of assembly, etc. As such, embodiments described as less desirable than other embodiments or prior art implementations with respect to one or more characteristics are not outside the scope of the disclosure and may be desirable for particular applications.