Patent Publication Number: US-2017369083-A1

Title: System and method of vehicle system control

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a continuation of U.S. patent application Ser. No. 14/963,889, filed 9 Dec. 2015, which is a continuation of U.S. patent application Ser. No. 14/169,459, filed 31 Jan. 2014 (the “&#39;459 Application”) and issued as U.S. Pat. No. 9,211,809 on 15 Dec. 2015, which claims priority to U.S. Provisional Application No. 61/790,477, filed 15 Mar. 2013. The &#39;459 Application is related to U.S. application Ser. No. 14/169,580, filed 31 Jan. 2015. The entire disclosures of the foregoing applications are incorporated herein by reference. 
    
    
     FIELD 
     Embodiments of the inventive subject matter described herein relate to controlling the speeds at which axles of a vehicle are rotated to propel the vehicle. 
     DISCUSSION OF ART 
     Some vehicles include powered axles that are rotated to propel the vehicles. To control the speeds at which the axles are rotated, the speed at which the vehicle is traveling is measured. For example, the axles may be rotated at speeds that are based on the measured speed of the vehicle to generate sufficient tractive effort to propel the vehicle. 
     Various approaches have been used to determine a speed of the vehicle. Radar systems have been used, but have been found to be unreliable and prone to mechanical failure when used with vehicles. Additionally, the radar systems have been found to have poor accuracy in measuring vehicle speeds at relatively low speeds. Wheel speed sensors have been used to measure the rotation speeds of wheels of the vehicle. But, exclusive use of these sensors may not be accurate due to slippage between the wheels and the track during motoring and/or braking. Another approach is referred to as a Sampled Axle Speed (SAS) algorithm. SAS involves decreasing the torque applied to one axle of a set of axles of the vehicle to eliminate or avoid slippage of the wheel along a track. The speed of this axle is sampled to acquire a potentially more accurate vehicle speed. This approach, however, decreases the tractive effort generated by the vehicle, and may not work well at higher acceleration rates and/or when a significantly heavy load is being hauled by the vehicle. It may be desirable to have a system and method that differs from those that are currently available. 
     BRIEF DESCRIPTION 
     In an embodiment, a method (e.g., for controlling a vehicle system) includes determining a vehicle reference speed of the vehicle system traveling along a route using an off-board-based input speed and an onboard-based input speed. The off-board-based input speed is representative of a moving speed of the vehicle system and is determined from data received from an off-board device. The onboard-based input speed is representative of the moving speed of the vehicle system and is determined from data obtained from an onboard device. The method may include, based at least in part on using the vehicle reference speed, to at least one of measure determining wheel creep for one or more wheels of the vehicle system or control controlling at least one of torques applied by or rotational speeds of one or more motors of the vehicle system. The rotational speeds may represent or be the same as the rotational speeds of axles that are rotated by the motors. 
     In an embodiment, a vehicle control system includes a vehicle controller configured to obtain an off-board-based input speed and an onboard-based input speed of a vehicle system traveling along a route. The off-board-based input speed is representative of a moving speed of the vehicle system and is determined from data received from an off-board device. The onboard-based input speed is representative of the moving speed of the vehicle system and is determined from data obtained from an onboard device. The vehicle controller also is configured to use the vehicle reference speed to at least one of measure determine wheel creep for one or more wheels of the vehicle system based on the vehicle reference speed or to control at least one of torques applied by or rotational speeds of one or more motors of the vehicle system based on the vehicle reference speed. 
     In an embodiment, a method (e.g., for controlling a vehicle system) includes controlling a rotational speed at which a first axle of a vehicle system is rotated by a first motor based on a throttle setting of the vehicle system and a first vehicle reference speed. The first vehicle reference speed is determined from a group of input speeds that includes an onboard-based input speed and an off-board-based input speed. The method may include controlling a rotational speed at which at least a second axle of the vehicle system is rotated by a second motor based on the throttle setting and a second vehicle reference speed. The second vehicle reference speed is determined from the onboard-based input speed. The rotational speeds of the first axle and the at least a second axle are controlled based on the respective first and second vehicle reference speeds. 
     In an embodiment, a method includes obtaining an off-board-based input speed of a vehicle system as the vehicle system travels along a route. The off-board-based input speed is obtained from signals received from one or more off-board devices that are disposed off-board the vehicle system and is representative of a speed of the vehicle system traveling along the route. The method may include measuring one or more onboard-based input speeds of the vehicle system as the vehicle system travels along the route. The one or more onboard-based input speeds are representative of speeds at which one or more wheels of the vehicle system rotate as the vehicle system travels along the route. The method further includes determining a first vehicle reference speed from a group of input speeds that includes at least one of the non-satellite-based input speeds and an estimated velocity of the vehicle system that is derived from the satellite-based input speed. The method includes determining a second vehicle reference speed from the one or more non-satellite-based input speeds and controlling a speed at which a first axle of the vehicle system is rotated by a first motor based on a throttle setting of the vehicle system and the first vehicle reference speed. The method further includes controlling a speed at which at least a second axle of the vehicle system is rotated by a second motor based on the throttle setting and the second vehicle reference speed. The speeds of the first axle and the at least a second axle are concurrently controlled based on the respective first and second vehicle reference speeds. 
     In an embodiment, a vehicle control system includes a vehicle controller, one or more speed sensors, and one or more inverter controllers. The vehicle controller is configured to obtain a satellite-based input speed of a vehicle system as the vehicle system travels along a route. The satellite-based input speed is obtained from signals received from one or more satellites and representative of a speed of the vehicle system traveling along the route. The one or more speed sensors are configured to measure one or more non-satellite-based input speeds of the vehicle system as the vehicle system travels along the route. The one or more non-satellite-based input speeds are representative of speeds at which one or more wheels of the vehicle system rotate as the vehicle system travels along the route. The one or more inverter controllers are configured to control speeds at which at least first and second axles of the vehicle system are rotated by at least first and second respective motors. The vehicle controller also is configured to determine a first vehicle reference speed and a second vehicle reference speed. The first vehicle reference speed is selected from a group of input speeds that includes at least one of the non-satellite-based input speeds and an estimated velocity of the vehicle system that is derived from the satellite-based input speed. The second vehicle reference speed is selected from the one or more non-satellite-based input speeds. The one or more inverter controllers also are configured to concurrently control the speed at which the first axle is rotated by the first motor based on a throttle setting of the vehicle system and the first vehicle reference speed and to control the speed at which at least the second axle of the vehicle system is rotated by the second motor based on the throttle setting and the second vehicle reference speed. 
     In an embodiment, a method includes deriving a first input speed of a vehicle having at least first and second axles and traveling along a route from position and/or speed data obtained by a global positioning system (GPS) receiver, deriving at least a second input speed of the vehicle from a wheel speed of one or more wheels joined to the second axle of the vehicle as the vehicle travels along the route, and controlling a first speed at which the first axle of the vehicle is rotated to propel the vehicle using a first vehicle reference speed. The terms “first” and “second” may refer to any axles or wheels of the vehicle, and do not necessarily refer to the first and second axles or wheels along a direction of travel. Optionally, the first and second axles or wheels may refer to the first and second axles or wheels along a direction of travel. Additionally, the term “position data” may refer to data that represents a geographic location (e.g., coordinates), a location along a route (e.g., milepost), a speed, or other information representative of where an object such as the vehicle is located and/or moving. The first vehicle reference speed is selected from a first group of input speeds that includes the first input speed and the at least a second input speed. The method may include controlling a second speed at which the second axle of the vehicle is concurrently rotated to propel the vehicle using a second vehicle reference speed. The second vehicle reference speed is obtained from a second group of input speeds that excludes the first input speed. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Reference is now made briefly to the accompanying drawings, in which: 
         FIG. 1  is a schematic diagram of a vehicle system having an embodiment of a vehicle control system; 
         FIG. 2  is a schematic diagram of an embodiment of a vehicle control system; 
         FIG. 3  illustrates an embodiment of a vehicle controller; 
         FIG. 4  is a flowchart of a method for controlling axles of a vehicle system; 
         FIG. 5  illustrates a schematic diagram of one example of a quality module shown in  FIG. 3 ; 
         FIG. 6  illustrates a schematic diagram of one example of application of a quality function used by the quality module to determine the uncertainty parameter; 
         FIG. 7  is a schematic diagram of a vehicle having an embodiment of a vehicle control system; 
         FIG. 8  illustrates a schematic diagram of one example of the vehicle shown in  FIG. 7  traveling along a segment of a route; 
         FIG. 9  illustrates one example of the vehicle shown in  FIG. 7  traveling toward a switch in the route; 
         FIG. 10  illustrates a top view of the vehicle shown in  FIG. 7  traveling over a curved segment of the route; 
         FIG. 11  is a front view of an embodiment of a vehicle; 
         FIG. 12  illustrates a top view of an embodiment of a vehicle; 
         FIG. 13  illustrates another top view of the vehicle shown in  FIG. 12 ; and 
         FIG. 14  is a top view of an embodiment of a vehicle. 
     
    
    
     DETAILED DESCRIPTION 
     In accordance with one or more embodiments described herein, systems and methods provide for the control of the torque applied to powered axles of a vehicle system. The term “powered axles” refers to axles of a vehicle that generates propulsive force or tractive effort to propel the vehicle by rotating the axles using motors interconnected with the axles. For example, powered axles of a locomotive or other rail vehicle may be rotated by traction motors connected with the axles. The torque that is applied by a motor to the axle, and the speeds at which motors rotate axles to propel the vehicle system may be determined from a selected throttle setting of the vehicle system and a vehicle reference speed. The vehicle reference speed used for the different axles may differ. 
     The vehicle reference speeds for the various axles may differ in that the vehicle reference speed used for at least a first axle may be based on an off-board-based input speed that may be obtained from data signals received from one or more off-board locations disposed off-board of the vehicle system. Suitable off-board sources or locations may include satellites (e.g., global positioning system (GPS) satellites), wayside devices, wifi communications, radio communications, TV communications, cellular communications/towers, and the like. The vehicle reference speeds used for one or more other axles (or all other axles) in the same vehicle may be at least partially based on onboard-based input speeds that may be not obtained or based on data signals received from any off-board location and/or may be obtained or created onboard the vehicle system. For example, the onboard-based input speeds may be wheel speeds that may be measured by onboard devices such as sensors disposed on the vehicle system for one or more wheels connected to these axles. These onboard-based input speeds may be obtained from speed sensors, such as tachometers. The vehicle reference speeds used for these other axles can be determined from a combination of the off-board-based input speeds and the onboard-based input speeds. 
     By controlling the speed at which one or more axles may be rotated by using an off-board-based input speed, the vehicle system may be operated more efficiently. The off-board-based speeds may be more accurate than the onboard-based speeds. For example, the onboard-based speeds may be inaccurate due to poor adhesion between the wheels and the route being traveled by the vehicle system. Slippage of the wheels on the route may cause the onboard-based speeds to be faster than the actual speed of the vehicle system. As a result, the motors may rotate the axles at speeds that may be faster than needed to apply the torque associated with a selected throttle setting. Rotating the axles at speeds that may be faster than necessary can result in increased wheel slippage (and, as a result, increased wear and tear on the wheels), reduced tractive effort being applied to the route, reduced fuel efficiency, increased emission generation, and the like. 
     The off-board-based speeds, on the other hand, may represent the actual speed of the vehicle more accurately than the onboard-based speeds. As a result, rotating the axles at speeds that may be at least partially based on off-board-based input speeds may result in reduced wheel slippage, increased tractive effort being applied to the route, increased fuel efficiency, reduced emission generation, and the like, relative to relying solely on onboard-based input speeds. 
       FIG. 1  is a schematic diagram of a vehicle system  100  having an embodiment of a vehicle control system  102 . The vehicle system may be shown as a rail vehicle consist comprising a propulsion-generating vehicle  104  and a non-propulsion generating vehicle  106 . The vehicle system may represent a system of vehicles other than rail vehicles, such as other off highway vehicles (e.g., vehicles that may be not permitted or designed for travel on public roadways), mining equipment, automobiles, marine vessels, and the like. The propulsion-generating vehicle may represent a locomotive, but also may represent another type of vehicle that generates tractive effort to propel the vehicle system. The non-propulsion generating vehicle  106  may represent cargo cars, passenger cars, or the like (or another type of vehicle that does not generate tractive effort). The vehicle system includes the vehicles  104 ,  106  connected with each other so that the vehicle system can travel along a route  108  (e.g., a track, road, waterway, or the like). 
     The propulsion-generating vehicle includes two or more axles  110  (e.g., axles  110 A-F) that may be rotated by a propulsion subsystem  112  of the vehicle to generate tractive effort and propel the vehicle along the route. The number and arrangement of the axles  110  may be shown only as an example and may be not intended as limitations on all embodiments described herein. For example, although the axle  110 A may be shown as the front axle along a direction of travel of the vehicle system, alternatively, the axle  110 A may be in another position relative to the other axles  110 B-F. As described below, one embodiment of the propulsion subsystem  112  includes traction motors  126  that may be connected to and rotate the axles and inverters that supply electric energy to the traction motors to power the motors. Wheels may connect to the axles and may be rotated by the axles to propel the vehicle along the route. 
     The vehicle control system, through the propulsion subsystem, may control the torque applied to the axles and the speeds at which the axles may be rotated. In one aspect, the torque applied to the axles and/or the speeds at which the axles may be rotated by the propulsion subsystem  112  may be individually controlled on an axle-by-axle basis. For example, the torque and/or speed of a first axle  110 A may be different than the torque and/or speed of a second axle  110 B during the same time period, which may differ from the torque and/or speed of a third axle  110 C during the same time period, and so on. 
     The vehicle control system determines vehicle reference speeds that may be used to control the torques applied to the axles and the speeds at which the axles may be rotated by the propulsion subsystem. The vehicle control system receives a selected throttle setting from a user input  122 . The selected throttle setting may represent a desired power output or tractive effort that may be to be provided by the vehicle system to travel along the route. The user input may represent a device that may be manually actuated to select the throttle setting, such as a lever, switch, pedal, button, touchscreen, or the like. Additionally or alternatively, the user input may represent a system that automatically designates the selected throttle setting. For example, the user input can include or represent an energy management system that designates throttle settings and/or speeds (from which throttle settings can be automatically determined) of the vehicle system as a function of time and/or distance along the route for a trip. These designated settings and/or speeds may be determined such that operating the vehicle system using the settings and/or speeds results in the vehicle system consuming less fuel and/or producing fewer emissions during a trip over the route than the vehicle system traveling over the same route during the same trip (and arriving at a destination at the same time or within a designated time period) but by traveling according to different settings and/or speeds. 
     The vehicle control system can determine torques that may be applied to the axles and the speeds at which the axles may be to be rotated by the propulsion subsystem to achieve the power output or tractive effort associated with the selected throttle setting. Optionally, the torque applied to a wheel or axle may be determined based on a vehicle speed, such as a vehicle reference speed (which may be based on and/or determined from the onboard-based input speed and/or the off-board-based input speed). In one embodiment, the torque applied to one or more axles may be determined from and/or based on the off-board-based input speed and not any other vehicle reference speed or other vehicle speed (e.g., the onboard-based input speed), or the torque may be determined from and/or based on the onboard-based input speed and not any other vehicle reference speed or other vehicle speed (e.g., the off-board-based input speed). The torques may be determined based on the selected throttle setting (e.g., with greater torques associated with larger throttle settings and lesser torques associated with smaller throttle settings). The speeds at which the axles may be rotated may be determined from the vehicle reference speeds. For example, the vehicle control system may direct the propulsion subsystem to rotate the axles at speeds that may be based on (e.g., related to via one or more mathematical relationships) one or more vehicle reference speeds to apply the torque associated with the selected throttle setting. In one aspect, the vehicle reference speed determination may be performed down to zero vehicle speed. In such an instance, there would be no minimum speed threshold value on the determination function. 
     In one aspect, the vehicle control system can direct the propulsion subsystem to rotate an axle at a speed that may be within a designated range of speeds relative to a vehicle reference speed. Although this designated range of speeds may be modified and/or customized depending on a desired outcome, the designated range of speeds may include from about 103% to about 104% of a vehicle reference speed. Alternatively, the designated range of speeds may be a larger range of percentages or fractions of the vehicle reference speed. In another embodiment, the designated range of speeds may include the vehicle reference speed. 
     The vehicle reference speed that may be used to control the speeds at which the axles may be rotated may differ for different axles of the same vehicle. For example, for at least one axle  110 A (or another axle  110 B-F), the vehicle reference speed may be based on an off-board-based input speed. For one or more other axles (or all other axles), the vehicle reference speed may be based on an onboard-based input speed, such as one or more measured wheel speeds and/or a combination of these wheel speeds and the off-board-based input speed. 
     The vehicle control system can obtain the off-board-based input speed from data signals received from one or more off-board devices  116 . These off-board devices  116  can represent or include satellites, wayside devices, cellular towers and/or antennas, wireless network antennas, and the like. A position and/or velocity data receiver  118  (such as GPS satellites, wayside devices, wife communications, radio communications, TV communications, cellular communications/towers, and the like) may receive position and/or velocity data signals  124  from one or more of the off-board devices  116 . The position and/or velocity data signals may be used by the vehicle control system  102  and/or the position and/or velocity data receiver  118  to calculate the off-board-based input speed. The off-board-based input speed can represent the actual speed of the vehicle system and/or the vehicle as the vehicle system actually travels along the route. As one example, the off-board devices can represent satellites. Additionally or alternatively, the off-board-based input speed may be obtained from one or more other devices disposed remote from the vehicle system other than the satellites. For example, stationary wayside devices disposed alongside the route may communicate position and/or velocity data with the vehicle control system as the vehicle control system travels along the route. This position and/or velocity data may represent the position of the devices and/or other information that can be used to calculate the speed of the vehicle system. The vehicle control system can determine the locations of multiple wayside devices as the vehicle system passes the wayside devices or otherwise moves relative to the wayside devices and determine the vehicle reference speed based on the locations of the wayside devices and the movement of the vehicle system relative to the wayside devices. Additionally or alternatively, the vehicle control system may receive the satellite-based input speed from another remote location, such as a dispatch facility or center. 
     Optionally, the off-board-based input speeds may be obtained or derived from at least some data generated or obtained onboard the vehicle system. For example, the position and/or velocity data receiver  118  may include or represent one or more gyroscopes and/or accelerometers that generate data representative of movement of the vehicle system. The position and/or velocity data receiver and/or control system may include a clock, such as an atomic clock, or be in communication with such a clock, to track passage of time relative to a reference time (e.g., the atomic clock). Using the data on the movement of the vehicle system from a known location (e.g., a starting location) and the passage of time from the reference time, the control system may determine current speeds of the vehicle system and use these speeds as off-board-based input speeds. 
     The vehicle control system can obtain the onboard-based input speeds from one or more sensors that do not receive signals from remote locations (e.g., the off-board devices) to measure the speed of the vehicle system. For example, the vehicle control system may receive measured wheel speeds of the wheels of the vehicle system as the vehicle system travels along the route. The wheel speeds may be measured by speed sensors  120 , such as tachometers or other devices that measure the speeds at which the wheels and/or axles rotate. Additionally or alternatively, the onboard-based input speeds may be obtained from another type of sensor that may be disposed onboard the vehicle system and that measures movement of one or more components of the vehicle system to determine the onboard-based input speeds. 
     For at least one axle  110 A (or one or more of axles), the vehicle control system determines the vehicle reference speed that may be used to control the speed at which the axle  110 A may be rotated from a group of input speeds that includes the off-board-based input speed. For example, the vehicle reference speed that may be used to determine the speed at which the axle  110 A may be rotated may be selected or calculated from a group of input speeds that includes the off-board-based input speed and the onboard-based input speeds associated with one or more other axles. As described in more detail below, such a vehicle reference speed may be selected as the input speed in the group that may be faster than one or more other input speeds in the group, or as the fastest input speed in the group, when the vehicle may be braking (e.g., generating braking effort to slow or stop movement of the vehicle and/or vehicle system). The vehicle reference speed for the axle  110 A may be selected as the input speed in the group that may be slower than one or more other input speeds in the group, or as the slowest input speed in the group, when the vehicle may be motoring (e.g., generating tractive effort to propel the vehicle and/or vehicle system). A faster input speed may be used as the vehicle reference speed when the vehicle may be braking so that the vehicle reference speed may be less likely to be based on wheel slip, since slower rotating wheels (e.g., onboard-based input speed) during braking may be more likely to be the result of the wheels slipping relative to the route during braking than faster moving wheels. A slower input speed may be used as the vehicle reference speed when the vehicle may be motoring so that the vehicle reference speed may be less likely to be based on wheel slip, since faster rotating wheels (e.g., onboard-based input speed) during motoring may be more likely to be the result of the wheels slipping relative to the route  108  during motoring than slower moving wheels. 
     For one or more other axles, the vehicle control system can determine the vehicle reference speed that may be used to control the speeds at which the other axles may be rotated from a group of onboard-based input speeds. For example, the vehicle reference speed for the axles may be selected as the median or average of the onboard-based input speeds in this group of input speeds. Alternatively, another calculation or technique may be used to select the vehicle reference speed from this group of onboard-based input speeds. 
     The vehicle reference speeds may be used by the vehicle control system to determine the speeds at which the axles may be rotated by motors of the propulsion subsystem. For example, to generate the torque associated with a selected throttle setting, the propulsion subsystem may be directed by the vehicle control system to rotate the axles at speeds that may be within the designated range of speeds relative to the vehicle reference speed. As one example, the designated range of speeds for an axle can include a range of speeds of a vehicle reference speed, such as x toy percent of the vehicle reference speed associated with the axle  110 . As described above, x can represent 103% and y can represent 104%, although other amounts may be used for x or y. Therefore, for the axle  110 A associated with the satellite-based input speed, the propulsion subsystem  112  may be directed to rotate the axle  110 A at a speed that may be within x toy percent of the satellite-based input speed. For the axles, the propulsion subsystem  112  may be directed to rotate the axles at speeds that may be within x toy percent of the vehicle reference speed selected from the group of reference speeds, as described above. 
       FIG. 2  is a schematic diagram of an embodiment of a vehicle control system  200 . The vehicle control system  200  may represent the vehicle control system shown in  FIG. 1 . The vehicle control system  200  includes a vehicle controller  202  that may include or represent hardware circuitry or circuits that include and/or are connected to one or more processors, microcontrollers, or other logic-based devices. The vehicle controller  202  obtains the input speeds and determines the vehicle reference speeds described above. For example, the vehicle controller  202  may communicate with the position and/or velocity data receiver  118  to receive the position and/or velocity data transmitted by the off-board devices  116  (shown in  FIG. 1 ). From the data received by the position and/or velocity data receiver  118 , the vehicle controller  202  can calculate the off-board-based input speed of the vehicle (shown in  FIG. 1 ). 
     The vehicle control system  200  includes the speed sensors  120  that may be operatively connected with the wheels  114  and/or axles of the vehicle. The speed sensors  120  can include or represent tachometers that may be disposed relatively close to the wheels  114  and/or axles, or that may be mechanically connected with the wheels  114  and/or axles, so that the speed sensors  120  can measure the speed at which the wheels  114  and/or axles rotate during movement of the vehicle. 
     Several inverter controllers  204  (e.g., inverter controllers  204 A-F) of the vehicle control system  200  determine the speeds at which to rotate the respective axles. The inverter controllers  204  can include or represent one or more processors, microcontrollers, or other logic-based devices. The inverter controllers  204  can be communicatively coupled with a propulsion subsystem  210  to control the speeds at which the axles may be rotated. The propulsion subsystem  210  is similar to the propulsion subsystem shown in  FIG. 1 . The inverter controllers  204  may connect with inverters  206  of the propulsion subsystem  210 . The inverters  206  control the supply of electric current to motors  208  (e.g., motors  208 A-F) of the propulsion subsystem  210 . The motors  208  may be operatively connected with the axles, such as by being directly coupled with the axles or interconnected with the axles by one or more gears, pinions, and the like. The inverters  206  control the speed at which the motors  208  rotate the axles by controlling the electric current supplied to the motors  208 , such as by controlling a frequency of alternating current that may be supplied to the motors  208 . 
     The inverter controllers  204  receive the torques that may be to be applied to the axles by the inverters  206  and the vehicle reference speed(s) from the vehicle controller  202 . As described above, the vehicle controller  202  can identify a first vehicle reference speed for the axle  110 A (or another axle  110 ) from a group of input speeds that includes the off-board-based input speed and one or more of the onboard-based input speeds. The vehicle controller  202  can identify a second vehicle reference speed (which may differ from the first vehicle reference speed or be the same as the first vehicle reference speed) for the axles from a group of input speeds that includes the onboard-based input speeds, but that may not include the off-board-based input speed. 
     The inverter controllers  204  determine the speeds at which to rotate the axles based on the received vehicle reference speeds for the respective axles. For example, the inverter controllers  204  can direct the inverters  206  to supply current to the motors  208  that causes the motors  208  to rotate the axles at speeds that may be within a designated range of the vehicle reference speed for the respective axle  110 . The inverter controller  204 A can direct the inverter  206 A to supply the motor  208 A with current that causes the motor  208 A to rotate the axle  110 A at a speed that may be within a designated range (e.g., 103 to 104%) of the vehicle reference speed for the axle  110 A, and the inverter controllers  204 B-F can direct the respective inverters  206 B-F to supply current to the respective motors  208 B-F that causes the motors  208 B-F to rotate the respective axles at speeds that may be within the designated range of the vehicle reference speed associated with the axles. 
       FIG. 3  illustrates an embodiment of a vehicle controller  300 . The vehicle controller  300  may represent the vehicle controller  202  shown in  FIG. 2 . The vehicle controller  300  includes several modules that represent hardware and/or software used to perform the functions of the vehicle controller  300  described herein. The modules may represent one or more circuits or circuitry that includes and/or may be connected to one or more processors, controllers, microcontrollers, circuitry, and/or other hardware, and/or associated software that directs the processors, controllers, microcontrollers, circuitry, and/or other hardware to perform the functions and operations described herein. Additionally or alternatively, the modules may represent one or more tangible and non-transitory computer readable media that stores one or more sets of instructions for directing the operations of one or more processors, controllers, or other logic-based devices. 
     A filter module  302  receives input speeds (“Axle Speeds” in  FIG. 3 ) associated with the axles (shown in  FIG. 1 ). For example, the filter module  302  can receive the onboard-based input speed associated with the axles. The filter module  302  examines these input speeds and identifies a slow input speed (“Min” in  FIG. 3 ) and/or a fast input speed (“Max”) from this group of input speeds. The slow reference speed may be slower than one or more other onboard-based input speeds, or that may be the slowest input speed of the onboard-based input speeds received by the filter module  302 . The fast input speed may be faster than one or more other onboard-based input speeds, or that may be the fastest input speed of the input speeds received by the filter module  302 . 
     In the illustrated embodiment, the filter module  302  communicates the fast and slow onboard-based input speeds to a reference speed processing module  304 . The reference speed processing module  304  selects one or more of these input speeds communicated from the filter module  302  for sending to the inverter controllers  204  (shown in  FIG. 2 ) associated with the axles. For example, the reference speed processing module  304  may select the fastest onboard-based input speed, the slowest onboard-based input speed, the average onboard-based input speed, the median onboard-based input speed, or another onboard-based input speed as a vehicle reference speed for the axles. The reference speed processing module  304  can communicate this onboard-based vehicle reference speed (“Ref Speed” in  FIG. 3 ) that may be selected from those onboard-based input speeds communicated from the filter module  302  to the inverter controllers  204 B-F that control the speeds at which the motors  208  rotate the axles that may be not associated with the off-board-based input speed (e.g., the axles or another set of axles). 
     To account for potential inaccuracies in the off-board-based input speed, the vehicle control system may determine an uncertainty parameter of the off-board-based input speed. The uncertainty parameter may be indicative of inaccuracy or potential inaccuracy of the actual speed of the vehicle system as represented by the off-board-based input speed. Larger uncertainty parameters can indicate that a difference between the off-board-based input speed and the actual speed of the vehicle may be larger than for smaller uncertainty parameters. An off-board-based input speed quality module  306  (“GPS Quality” in  FIG. 3 ) can determine this uncertainty parameter. In one aspect, the quality module  306  uses both the off-board-based input speed (“GPS Velocity” in  FIG. 3 ), or data signals from the position and/or velocity data receiver  118  (shown in  FIG. 1 ), and vehicle-based information to determine the uncertainty parameter. 
       FIG. 5  illustrates a schematic diagram of one example of the quality module  306  shown in  FIG. 3 . The quality module  306  receives input data from the position and/or velocity data receiver  118  (“GPS Receiver” in  FIG. 3 , although the position and/or velocity data receiver  118  may represent a device other than a GPS receiver) and from one or more of the inverters  206  of the vehicle  200  (shown in  FIG. 2 ). The input data that may be provided by and/or received from the position and/or velocity data receiver  118  includes a carrier signal to noise ratio (“Carrier signal/noise (1−n)” in  FIG. 5 ), one or more position measurements of the vehicle system (e.g., an azimuth measurement, an elevation measurement, a latitude measurement, a longitude measurement, or the like; shown as “Az/Elev (1−n)” and “Lat/Lon” in  FIG. 5 ), a number of off-board devices  116  from which input data signals may be received by the position and/or velocity data receiver  118  (“Num. of Sats Used” in  FIG. 5 ), a dilution of precision or geometric dilution of precision measurement (“DOP” in  FIG. 5 ), and the like. Optionally, the input data provided by and/or received from the position and/or velocity data receiver  118  may include less than this information, additional information, or different information. The input data that may be provided by and/or received from one or more of the inverters  206  includes speeds at which the axles may be rotated (shown as “Axle Speed (1−n)” in  FIG. 5 ). Optionally, this input data may be provided by and/or received from one or more of the inverter controllers  204 . 
     The quality module  306  can apply a quality function (shown as “GPS Quality function” in  FIG. 5 ) using some or all of the input data described above to determine an uncertainty parameter (shown as “Uncertainty” in  FIG. 5 ). In an embodiment, the quality function involves comparing the input data to a cascade of different thresholds to derive the uncertainty parameter and/or position and/or velocity data representative of the location of the position and/or velocity data receiver  118  (e.g., GPS or other coordinates, represented as “Valid (T/F)” in  FIG. 5 ). The uncertainty parameter and/or position and/or velocity data may be output by the quality module  306 , such as by communicating this information to the vehicle controller  202  (shown in  FIG. 2 ). 
     With continued reference to the quality module  306  illustrated in  FIG. 5 ,  FIG. 6  illustrates a schematic diagram of one example of application of the quality function used by the quality module  306  to determine the uncertainty parameter. The quality module  306  can examine a number of factors in determining the uncertainty parameter of location data. In an embodiment, one or more of these factors may be based on data or information provided by a source other than the position and/or velocity data receiver  118 . For example, input speeds representative of speeds at which the axles (shown in  FIG. 1 ) rotate may be used. The factors used by the quality module  306  to determine the uncertainty parameter can include, but may be not limited to or require the use of all of, a comparison of the magnitude of measured axle speeds (“Axle(s) Speed(s)” in  FIG. 5 ; also referred to as onboard-based input speeds) with a velocity based on position and/or velocity data received by the position and/or velocity data receiver  118  (“GPS Vel” in  FIG. 5 ; also referred to as an off-board-based input speed), a comparison of a rate of change in the onboard-based input speeds with a rate of change in the off-board-based input speeds, a mean or average signal-to-noise ratio of the carrier signal received by the position and/or velocity data receiver  118 , a magnitude of the carrier signal received by the position and/or velocity data receiver  118 , the existence or detection of any signals or other factors that may negatively impact the signals received by the position and/or velocity data receiver  118  (e.g., solar flares, wireless interference, buildings, trees, cloud coverage, and the like; shown as “Impulse Detection” in  FIG. 5 ), a stability or variance in the off-board-based input speed (e.g., a deviation, variance, or other statistical analysis of how much the off-board-based input speed changes or varies with respect to time due to variances or instability in the input data; shown as “GPS Calculated Velocity Signal Stability” in  FIG. 5 ), a number of off-board devices  116  (shown in  FIG. 1 ) from which signals used to determine the position and/or velocity data may be received, and the like. Additional or other factors may be used. 
     Application of the quality function to these factors involves comparing some of the factors with each other, comparing the factors (and/or a comparison of the factors) to one or more thresholds, and/or summing the results of these comparisons to derive the uncertainty signal. In an embodiment, a first comparison  604  that may be performed by the quality module  306  to determine the uncertainty parameter involves comparing an off-board-based input speed  600  and one or more onboard-based input speeds  602 . The quality module  306  compares these input speeds  600 ,  602  to determine a difference between the input speeds  600 ,  602 . This difference may be compared to one or more thresholds. In the illustrated example, the difference in input speeds  600 ,  602  may be compared to a plurality of thresholds. In the illustrated embodiment, there are three thresholds  606 ,  608 ,  610 . The third threshold  610  may be larger than the second threshold  608 , and the second threshold  608  may be larger than the first threshold  606 . If the difference between the input speeds  600 ,  602  exceeds one or more of these thresholds  606 ,  608 ,  610 , then a weighted influence  612  may be determined. This weighted influence  612  can be combined with one or more other weighted influences (described below) to calculate the uncertainty parameter that may be output by the quality module  306 . Different weighted influences may be determined based on which of the thresholds  606 ,  608 ,  610  may be exceeded by the difference in the input speeds  600 ,  602 . In the illustrated example, if the first threshold  606  may be exceeded by the difference between the input speeds  600 ,  602  and the second and third thresholds  608 ,  610  may be not exceeded by this difference, then the weighted influence  612  that may be determined may be assigned a smaller value (e.g., one or another value) than if this difference exceeded the second and/or third threshold  608 ,  610 . If the first and second thresholds  606 ,  608  may be exceeded by the difference between the input speeds  600 ,  602  but the third threshold  610  may be not exceeded by this difference, then the weighted influence  612  that may be determined may be assigned a larger value (e.g., three or another value) than if this difference exceeded the third threshold  610 . If the first, second, and third thresholds  606 ,  608 ,  610  may be exceeded by the difference between the input speeds  600 ,  602 , then the weighted influence  612  that may be determined may be assigned a larger value (e.g., nine or another value). In one aspect, the weighted influence  612  may have a smaller, smallest, or no value (e.g., value of zero) if the difference in the input speeds  600 ,  602  does not exceed any of the thresholds  606 ,  608 ,  610 . 
     A second comparison  614  that may be performed by the quality module  306  to determine the uncertainty parameter involves another comparison of the off-board-based input speed  600  and one or more onboard-based input speeds  602 . The quality module  306  compares these input speeds  600 ,  602  to determine a difference in the rate of changes in the input speeds  600 ,  602 . For example, the quality module  306  may determine a first rate of change in the off-board-based input speed  600  (shown as “GPS Dv/dt” in  FIG. 6 ) and determine a second rate of change in the onboard-based input speed  602  (shown as “Axle Dv/dt” in  FIG. 6 ). The quality module  306  may compare these rates of change with each other to determine a difference between the rates of change. This difference may be compared to one or more thresholds. In the illustrated example, the difference in the rates of change in the input speeds  600 ,  602  may be compared to three thresholds  616 ,  618 ,  620 . Optionally, a different number of thresholds may be used. The third threshold  620  may be larger than the second threshold  618 , and the second threshold  618  may be larger than the first threshold  616 . If the difference between the rates of change in the input speeds  600 ,  602  exceeds one or more of these thresholds  616 ,  618 ,  620 , then a weighted influence  622  may be determined. As described above, this weighted influence  622  can be combined with one or more other weighted influences to calculate the uncertainty parameter that may be output by the quality module  306 . Similar to as described above, different weighted influences may be determined based on which of the thresholds  616 ,  618 ,  620  may be exceeded by the difference in the rates of change in the input speeds  600 ,  602 . In the illustrated example (and similar to as described above), if the first threshold  616  may be exceeded, then the weighted influence  622  that may be determined may be assigned a smaller value (e.g., one or another value). If the first and second thresholds  616 ,  618  may be exceeded, then the weighted influence  622  that may be determined may be assigned a larger value (e.g., three or another value). If the first, second, and third thresholds  616 ,  618 ,  620  may be exceeded, then the weighted influence  622  that may be determined may be assigned a larger value (e.g., nine or another value). In one aspect, the weighted influence  622  may have a smaller, smallest, or no value (e.g., value of zero) if the difference does not exceed any of the thresholds  616 ,  618 ,  620 . 
     A third comparison  624  that may be performed by the quality module  306  to determine the uncertainty parameter involves a comparison of a carrier signal-to-noise ratio  626 , an azimuth measurement, and an elevation measurement (collectively referred to by  628  in  FIG. 6 ). C/N represents Carrier Signal/Noise ratio (similar to stated previously). And the Magnitude of C/N may be compared to thresholds. D/dt may be the C/N d/dt, or the change in C/N over time(Impulse). The C/N d/dt may be then compared to thresholds. The quality module  306  may compare the C/N to one or more thresholds and the d/dt to one or more thresholds. In the illustrated example, the C/N may be compared to three thresholds  630 ,  632 ,  634  and the d/dt may be compared to three threhsolds  648 ,  650 ,  652 . Optionally, a different number of thresholds may be used. 
     With respect to the thresholds  630 ,  632 ,  634 , the third threshold  634  may be larger than the second threshold  632 , and the second threshold  632  may be larger than the first threshold  630 . If the C/N exceeds one or more of these thresholds  630 ,  632 ,  634 , then a weighted influence  636  may be determined. As described above, this weighted influence  636  can be combined with one or more other weighted influences to calculate the uncertainty parameter that may be output by the quality module  306 . Similar to as described above, different weighted influences may be determined based on which of the thresholds  630 ,  632 ,  634  may be exceeded by the C/N, such as values of one, three, and nine. Alternatively, one or more other values may be used. In one aspect, the weighted influence  636  may have a smaller, smallest, or no value (e.g., value of zero) if the C/N does not exceed any of the thresholds  630 ,  632 ,  634 . 
     With respect to the thresholds  648 ,  650 ,  652 , the third threshold  652  may be larger than the second threshold  650 , and the second threshold  650  may be larger than the first threshold  648 . If the d/dt exceeds one or more of these thresholds  648 ,  650 ,  652 , then a weighted influence  654  may be determined. As described above, this weighted influence  654  can be combined with one or more other weighted influences to calculate the uncertainty parameter that may be output by the quality module  306 . Similar to as described above, different weighted influences may be determined based on which of the thresholds  648 ,  650 ,  652  may be exceeded by the d/dt, such as values of one, three, and nine, respectively. Alternatively, one or more other values may be used. In one aspect, the weighted influence  654  may have a smaller, smallest, or no value (e.g., value of zero) if the d/dt does not exceed any of the thresholds  648 ,  650 ,  652 . 
     A fourth comparison  638  that may be performed by the quality module  306  to determine the uncertainty parameter involves an examination and comparison of the stability or variance  640  in the off-board-based input speed (e.g., a deviation, variance, or other statistical analysis of how much the off-board-based input speed changes or varies with respect to time due to variances or instability in the input data) with one or more thresholds  642 ,  644 ,  646 . A stability quantity can be calculated to represent this deviation, variance, or other statistical analysis. For example, for a vehicle, a potential or calculated acceleration of the vehicle can be calculated from a mass of the vehicle and potential or directed propulsion forces generated by the vehicle. This potential or calculated acceleration can be used to derive a velocity of the vehicle as an expected velocity. The stability quantity can represent how close or far the expected velocity and the off-board-based input speed are with each other. For example, if the expected velocity is much slower or faster than the off-board-based input speed, then the stability may be calculated as being a relatively small number. On the other hand, if the expected velocity is closer to the off-board-based input speed, then the stability may be calculated as a larger number. For a given vehicle, and based on the vehicle mass and potential propulsion forces (e.g., from traction motors or drive shafts), the control system calculates the possible acceleration that could occur at a moment in time. Knowing the possible/potential/expected value of Velocity, if GPS Velocity input changes such that do not follow the expected physics model outcome, then it may be detected that the GPS Velocity signal may be “unstable”. Standard Deviation may be just one way to estimate the expected, and then compare it to the change in Velocity (acceleration/deceleration). The quality module  306  may compare this stability to one or more thresholds. In the illustrated example, the stability may be compared to three thresholds  642 ,  644 ,  646 . Optionally, a different number of thresholds may be used. The third threshold  646  may be larger than the second threshold  644 , and the second threshold  644  may be larger than the first threshold  642 . If the stability exceeds one or more of these thresholds  642 ,  644 ,  646 , then a weighted influence  656  may be determined. As described above, this weighted influence  656  can be combined with one or more other weighted influences to calculate the uncertainty parameter that may be output by the quality module  306 . Similar to as described above, different weighted influences may be determined based on which of the thresholds  642 ,  644 ,  646  may be exceeded by the stability, such as values of one, three, and nine, respectively. Alternatively, one or more other values may be used. In one aspect, the weighted influence  656  may have a smaller, smallest, or no value (e.g., value of zero) if the stability does not exceed any of the thresholds  642 ,  644 ,  646 . 
     A fifth comparison  658  that may be performed by the quality module  306  to determine the uncertainty parameter involves a comparison of a number of off-board devices  116  from which data signals were received by the position and/or velocity data receiver  118  (shown as “Num. of Sats Used” in  FIG. 6  and referred to as “number  668 ” in  FIG. 6 ) with one or more thresholds  660 ,  662 ,  664 . In the illustrated example, this number  668  of off-board devices  116  may be compared to three thresholds  660 ,  662 ,  664 . Optionally, a different number of thresholds may be used. In contrast to the other sets of thresholds, the third threshold  664  may be smaller than the second threshold  662 , and the second threshold  662  may be smaller than the first threshold  660 . If the number  668  of off-board devices  116  from which data signals were received may be smaller or larger than one or more of these thresholds  660 ,  662 ,  664 , then a weighted influence  666  may be determined. For example, if this number  668  may be greater than the first threshold  660 , then a smaller value (e.g., a value of one or another value) may be output as the weighted influence  666 . If this number  668  may be less than the first threshold  660  but greater than the second threshold  662 , then a larger value (e.g., a value of three or another value) may be output as the weighted influence  666 . If this number  668  may be less than the second threshold  662  but larger than the third threshold  664 , then a larger value (e.g., a value of nine or another value) may be output as the weighted influence  666 . In one aspect, if this number  668  may be smaller than the third threshold  664 , then the weighted influence  666  may be output with an even larger value. 
     One or more, or all, of the weighted influences  612 ,  622 ,  636 ,  654 ,  656  may be used to determine the uncertainty parameter  668  that may be output from the quality module  306 . In an embodiment, the weighted influences  612 ,  622 ,  636 ,  654 ,  656  may be combined (e.g., by summing the influences  612 ,  622 ,  636 ,  654 ,  656 ). The combined influences  612 ,  622 ,  636 ,  654 ,  656  may be scaled, such as by multiplying the combined influences  612 ,  622 ,  636 ,  654 ,  656  by a number that may be less than or greater than one, to produce the uncertainty parameter  668 . The uncertainty parameter  668  that may be produced can represent a range of speeds above and/or below the off-board-based input speed. For example, if the off-board-based input speed may be 60 kilometers per hour and the uncertainty parameter  668  may be 3 kilometers per hour, then the uncertainty parameter  668  can indicate that the actual, true speed of the vehicle system may be between 57 and 63 kilometers per hour. 
     Returning to the description of the vehicle controller  300  shown in  FIG. 3 , the uncertainty parameter can be communicated from the quality module  306  to an off-board-based input speed processing module  308 , otherwise referred to as a GPS reference speed processing module (“GRS Processing” in  FIG. 3 ). The off-board-based input speed (or data signals received from the satellites  116  to enable the off-board-based input speed to be calculated) also may be communicated to another filter module  310 . The filter module  310  may filter out one or more of the off-board-based input speeds, such as by only communicating slower or the slowest off-board-based input speeds that may be received over a given time period. The filter module  310  can communicate the filtered off-board-based input speeds to the processing module  308 . The processing module  308  also may receive the tractive effort supplied by the propulsion subsystem  112 ,  210  (shown in  FIGS. 1 and 2 ) and/or that may be designated by the selected throttle setting received from the user input  122  (shown in  FIG. 1 ). The uncertainty parameter may be in units of velocity, such as kilometers or miles per hour. 
     The processing module  308  may examine the uncertainty parameter, the filtered off-board-based input speed(s), one or more onboard-based input speeds, and/or the tractive effort and calculate an estimated velocity of the vehicle. The estimated velocity may be first order estimate, or an estimate of a first magnitude of the actual speed of the vehicle. The estimated velocity can be based on recent acceleration of the vehicle and/or vehicle system (as determined from the filtered off-board-based input speeds), inertia of the vehicle system, and/or the tractive effort of the vehicle and/or vehicle system (e.g., where more than one propulsion-generating vehicle may be included in the vehicle system). 
     In one aspect, the processing module  308  determines if one or more of the speed sensors  120  (shown in  FIG. 1 ) provide onboard-based input speeds that fall within the range of speeds represented by the off-board-based input speed and the uncertainty parameter  668 . For example, if the off-board-based input speed and the uncertainty parameter  668  represent a range of speeds of 65 kilometers to 75 kilometers, then the processing module  308  can determine if any of the onboard-based input speeds may be within 65 to 75 kilometers per hour. Any such onboard-based input speeds may be identified and used to influence (e.g., modify) the off-board-based input speed. 
     As one example, if the off-board-based input speed and the uncertainty parameter  668  represent a range of speeds of 65 kilometers per hour to 75 kilometers per hour, and the off-board-based input speed indicates a speed of 70 kilometers per hour, then the processing module  308  may determine if any onboard-based input speeds may be within 65 kilometers per hour to 75 kilometers per hour. If one or more onboard-based input speeds may be within this range (e.g., 68 kilometers per hour), then the processing module  308  may modify (e.g., reduce) the off-board-based input speed and/or future off-board-based input speeds. The off-board-based input speeds may be modified such that the off-board-based input speeds may be closer or equivalent to the onboard-based input speeds that fall within the range of the uncertainty parameter  668 . 
     The processing module  308  can combine the estimated velocity with the uncertainty parameter to determine an upper limit on the speed of the vehicle (e.g., “GRS Speed Upper Limit” in  FIG. 3 ) and a lower limit on the speed of the vehicle (e.g., “GRS Speed Lower Limit” in  FIG. 3 ). For example, the upper limit may be calculated as a sum of the estimated velocity of the vehicle or vehicle system and the uncertainty parameter. The lower limit may be calculated as a difference between the estimated velocity and the uncertainty parameter, such as the uncertainty parameter subtracted from the estimated velocity. 
     An output module  312  receives the upper limit and the lower limit from the processing module  308  and receives the slow onboard-based input speed and the fast onboard-based input speed from the filter module  302 . For example, the output module  312  can receive the outer limits on the off-board-based input speed (as represented by the upper limit and lower limits on the off-board-based input speed received from the processing module  308 ) and receive the slower or slowest onboard-based input speed (“Slowest Axle Speed” in  FIG. 3 ) and the faster or fastest onboard-based input speed from the filter module  302  (“Fastest Axle Speed” in  FIG. 3 ). 
     The output module  312  can monitor the tractive and/or braking efforts provided by the propulsion subsystem  112 ,  210  to determine if the vehicle may be motoring or braking and to select the vehicle reference speed for the axle  110 A based on this determination. If the vehicle may be motoring, the output module  312  identifies a smaller speed or the smallest speed of the speeds in a group that includes the slow speed of the onboard-based input speeds received from the filter module  302  (e.g., the Slowest Axle Speed) and the upper limit on the off-board-based input speed received from the processing module  308  (e.g., the GRS Speed Upper Limit). The speed that may be identified (“GRS Speed” in  FIG. 3 ) can be used as a vehicle reference speed for the axle  110 A to control the speed at which the axle  110  associated with the off-board-based input speed may be rotated. For example, the identified speed can be used to control the speed of the axle  110 A during motoring. 
     If the vehicle may be braking, the output module  312  identifies a faster speed or the fastest speed of the speeds in a group that includes the fast speed of the onboard-based input speeds received from the filter module  302  (e.g., the Fastest Axle Speed) and the lower limit on the off-board-based input speed received from the processing module  308  (e.g., the GRS Speed Lower Limit). The speed that may be identified (“GRS Speed” in  FIG. 3 ) can be used as a vehicle reference speed for the axle  110 A to control the speed at which the axle  110  associated with the off-board-based input speed may be rotated. For example, the identified speed can be used to control the speed of the axle  110 A during braking. 
     The vehicle reference speed that may be identified for the axle  110 A may be communicated to the inverter controller  204 A that controls operations of the inverter  206 A to control the speed at which the axle  110 A may be rotated. The inverter controller  204 A determines the speed at which to rotate the axle  110 A using the received vehicle reference speed and the inverter  206 A may be controlled to rotate the axle  110 A accordingly, as described above. The vehicle reference speed that may be determined for the other axles by the reference speed processing module  304  may be communicated to the inverter controllers  204 B-F that control operations of the respective inverters  206 B-F to control the speed at which the axles may be rotated. The inverter controllers  204 B-F determine the speeds at which to rotate the axles using the received vehicle reference speed and the inverters  206 B-F may be controlled to rotate the axles accordingly, as described above. 
       FIG. 4  is a flowchart of a method  400  for controlling axles of a vehicle system. The method  400  may be used in conjunction with the vehicle system shown in  FIG. 1 , such as to allow for the control of movement of the vehicle system using the vehicle control systems  102 ,  200  (shown in  FIGS. 1 and 2 ) described herein. The operations that may be described in connection with the method  400  need not necessarily be performed concurrently, simultaneously, or sequentially in the orders shown in  FIG. 4 . 
     At  402 , an off-board-based input speed (“SIS” in  FIG. 4 ) may be obtained. For example, a GPS-based velocity of the vehicle (shown in  FIG. 1 ) and/or the vehicle system may be determined as the vehicle system moves along the route  108  (shown in  FIG. 1 ). This off-board-based input speed may be associated with one or more axles (shown in  FIG. 1 ) of the vehicle (shown in  FIG. 1 ), such as the axle  110 A or another axle  110 B-F. 
     At  404 , one or more onboard-based input speeds (“NSIS” in  FIG. 4 ) may be obtained. For example, wheel speeds for the wheels  114  (shown in  FIG. 1 ) connected to the axles may be measured as the onboard-based input speeds. The wheel speeds may be measured for one or more of the wheels  114  that may be not connected to the axle  110  associated with the off-board-based input speed (e.g., the axle  110 A). Alternatively, the wheel speeds may be measured for the one or more of the wheels  114  connected with this axle  110 . 
     At  406 , an uncertainty parameter of the off-board-based input speed may be determined. As described above, the uncertainty parameter may represent potential inaccuracies in the off-board-based input speed, such as those caused by only receiving data signals  124  (shown in  FIG. 1 ) from a relatively small number of off-board devices  116  (shown in  FIG. 1 ), low signal-to-noise ratios of the data signals  124 , or the like. 
     At  408 , an estimated velocity of the vehicle (and/or vehicle system) may be determined. This estimated velocity may be calculated using the uncertainty parameter, the filtered off-board-based input speed(s), and/or the tractive effort, as described above. At  410 , upper and lower limits on the estimated velocity may be determined. These limits may be calculated using the uncertainty parameter to determine a range of velocities above and below this estimated velocity of the vehicle, as described above. 
     At  412 , a determination may be made as to whether the vehicle may be motoring or braking. For example, a decision may be made as to whether the vehicle may be generating tractive effort to propel the vehicle or if the vehicle may be generating braking effort to slow or stop movement of the vehicle. If the vehicle may be motoring, then the speeds that may be used to determine the vehicle reference speed for the axle  110  or axles associated with the off-board-based input speed may need to be slower speeds to avoid using faster speeds that may be indicative of wheel slip as a vehicle reference speed for those axle(s)  110 . As a result, flow of the method  400  may proceed to  414 . 
     On the other hand, if the vehicle may be braking, then the speeds that may be used to determine the vehicle reference speed for the axle  110  or axles associated with the off-board-based input speed may need to be faster speeds to avoid using slower speeds that may be indicative of wheel slip (e.g., where a wheel  114  may be not rolling along the route  108 ) as a vehicle reference speed for those axle(s)  110 . As a result, flow of the method  400  may proceed to  416 . 
     At  414 , a vehicle reference speed (e.g., “second vehicle reference speed” in  FIG. 4 ) for the axle  110  or axles associated with the off-board-based input speed may be determined. This vehicle reference speed may be determined from the slower of the onboard-based input speeds for the other axles (that may be not associated with the off-board-based input speed) and the upper limit on the estimated velocity of the vehicle. 
     At  416 , a vehicle reference speed (e.g., “second vehicle reference speed” in  FIG. 4 ) for the axle  110  or axles associated with the off-board-based input speed may be determined. This vehicle reference speed may be determined from the faster of the onboard-based input speeds for the other axles (that may be not associated with the off-board-based input speed) and the lower limit on the estimated velocity of the vehicle. 
     With respect to the axles associated with the onboard-based input speeds, at  418 , a vehicle reference speed (e.g., “first vehicle reference speed” in  FIG. 4 ) may be determined for these axles. This vehicle reference speed may be an average, median, maximum, minimum, or some other value derived from the onboard-based input speeds, as described above. 
     At  420  and  422 , the vehicle reference speeds may be used to control the speeds at which the various axles may be individually rotated to propel the vehicle according to the power output associated with the selected throttle setting. For example, at  420 , the axle  110  or axles associated with the off-board-based input speed may be rotated to a speed within a range of speeds that may be based on the second vehicle reference speed. At  422 , the axle  110  or axles that may be not associated with the off-board-based input speed may be rotated to a speed within a range of speeds that may be based on the first vehicle reference speed. 
     The off-board-based input speeds and/or the onboard-based input speeds may be used by the control system to determine or measure one or more other operating characteristics of the vehicle. In one aspect, the control system compares onboard-based input speeds with off-board-based input speeds to calculate a creep value for one or more wheels  114  of the vehicle. The control system may calculate a difference between the onboard-based input speed associated with an axle  110  and the off-board-based input speed. This difference may represent an amount of creep for the wheels  114  connected to that axle  110 . The amount of creep can represent slippage between the wheels  114  and the route  108 . In some cases, a certain amount of creep (e.g., one to three percent or another value of difference between the input speeds) may be desired for increased efficiency in translating work of the engine disposed onboard the vehicle to tractive effort applied to the route  108 . Too much creep, however, can result in the wheels  114  losing adhesion with the route  108  and result in reduced efficiency in translating this work. As used herein, wheel creep includes other related terminology, such as wheel slip and slip ratio, as well as other terms for loss of adhesion or traction. 
     The control system can compare the off-board and onboard-based input speeds for one or more of the axles to monitor the amount of creep associated with the wheels of the various axles. If the amount of creep may be too small (e.g., no greater than a designated threshold, such as no more than one percent, three percent, or another percentage), then the control system can direct the motors coupled to the axles to increase the amount of torque applied to the axles. If the amount of creep may be too large (e.g., greater than a designated threshold, such as greater than one percent, three percent, or another percentage), then the control system can direct the motors coupled to the axles to reduce the amount of torque applied to the axles. 
     In one aspect, the off-board-based input speeds may be based on data that may be obtained from and/or provided by the off-board devices  116  periodically, as opposed to continuously. For example, the vehicle system may receive positional and/or velocity data from the devices  116  at discrete points in time, with no positional and/or velocity data being received during the time periods that extend between these discrete points in time. During the time periods between when the position and/or velocity data may be received and/or the off-board-based input speeds may be determined, the control system may determine one or more estimated references speeds to use in controlling the torques applied by the motors. As described herein, the torques that may be applied by the motors to the axles and the speeds at which the motors rotate the axles to propel the vehicle system may be determined from a selected throttle setting of the vehicle system and a vehicle reference speed. The vehicle reference speed that may be used during the time periods between when the position data may be received and/or the off-board-based input speeds may be determined may be an estimated reference speed. 
     The estimated reference speed may be derived by extrapolating from previously used tractive efforts and resistive forces exerted on the vehicle system. For example, the control system may examine the tractive efforts applied by the motors of the vehicle system during a previous time period and/or the resistive forces exerted on the vehicle system during this time period to determine what estimated reference speed can be used to control the torques applied by the motors and/or rotational speeds of the motors. The estimated reference speed can be calculated so as to avoid abrupt changes in these torques or rotational speeds during the time periods between when the position and/or velocity data may be received and/or the off-board-based input speeds may be determined. 
     The control system may use the off-board-based input speeds and/or the onboard-based input speeds to estimate a size (e.g., mass and/or weight) of the vehicle system and/or resistive forces (e.g., drag) being experienced by the vehicle system. For example, using these input speeds, the control system may calculate acceleration of the vehicle system. The control system may know the amount of tractive effort (e.g., tractive or propulsive force) being applied by the vehicle system based on command signals used by the control system to control this tractive effort. Because the mass of the vehicle system may be proportional to the forces applied on the vehicle system and the inversely proportional to the acceleration of the vehicle system (e.g., F=ma, where F represents tractive efforts and a represents accelerations), the control system may estimate the mass of the vehicle system from the input speeds and tractive effort. For example, for larger tractive efforts and/or smaller accelerations, the control system may estimate heavier weights (e.g., masses) for the vehicle system. Conversely, for smaller tractive efforts and/or larger accelerations, the control system may estimate lighter weights (e.g., masses) for the vehicle system. 
     Once the size (e.g., weight or mass) of the vehicle system may be known or estimated (such as by being input into the control system by an operator using a manifest), then the control system may estimate resistive forces (e.g., drag, friction between the wheels  114  and the route  108 , and the like) being experienced by the vehicle system. For example, the off-board-based and/or onboard-based input speeds may be used to calculate an acceleration of the vehicle system. The tractive efforts being applied by the vehicle system may be known, as described above. The mass and acceleration of the vehicle system may be used to estimate a total amount of force exerted on the vehicle system (e.g., F=ma, where F represents the total forces exerted on the vehicle system). If the tractive efforts may be known, the control system may estimate the resistive forces exerted on the vehicle system by removing the tractive effort component from the calculated total amount of force exerted on the vehicle system. The remaining amount of force may be an estimate of the resistive forces exerted on the vehicle system. 
     These resistive forces and previously applied tractive efforts can be used to estimate what tractive efforts should be applied by the motors so as to avoid abrupt changes in the torques applied by the motors and/or in the rotational speeds of the motors during the time periods between when the position and/or velocity data may be received and/or the off-board-based input speeds may be determined may be an estimated reference speed. For example, the control system may use the resistive forces and previously applied tractive efforts to calculate tractive efforts to be applied by the motors that do not significantly deviate from the previously applied tractive efforts or cause a significant change in the total forces applied to the vehicle system (e.g., where the tractive efforts and the resistive forces represent the total forces applied to the vehicle system). Based on these calculated tractive efforts, the control system determines the reference speeds to be communicated to the inverters of the motors so that the motors generate the calculated tractive efforts. 
     In accordance with one or more embodiments described herein, systems and methods provide for the real-time measurement of curvature in a route being traveled by a vehicle system (e.g., a single propulsion-generating vehicle or a group of one or more propulsion-generating vehicles and/or one or more non-propulsion generating vehicles mechanically coupled with each other). The term “real-time” means that the curvature of a route being traveled (referred to as “route curvature”) can be measured by components disposed onboard the vehicle system as the vehicle system travels along the curvature in the route, as opposed to the vehicle system obtaining data during travel along the curvature in the route and later calculating the route curvature when the vehicle system may be no longer traveling and/or may be no longer traveling on the route curvature. As used herein, the term “curvature” or “route curvature” refers to a segment or subset of a route that may be curved (e.g., not linear). The curvature of a route may be represented by a radius of a circle or portion of another curved shape that matches or corresponds to the curvature of the route being measured. 
     The curvature of the route may be calculated by mathematically calculating the curvature of a rail or rails being traveled by a rail vehicle using measured speeds and/or heading of the rail vehicle. The curvature may not be determined with reference to a route database, such as a map or other memory structure that includes the curvature or layout of the route. For example, the curvature of the route may be measured without knowing the layout or position of the route. The measured curvature may be used to automatically control operations of the vehicle, as described below. 
     In one aspect, the systems and methods described herein may measure route curvature without reference to or obtaining information from a route database that has previously measured or input information about the curvature of the route being traveled along. For example, the systems and methods described herein may determine the curvature of a route without obtaining previously calculated estimates of the curvature that may be stored in an onboard or off-board database (or other memory device or structure). Additionally or alternatively, systems and methods described herein may use the onboard measurement of the route curvature to validate and/or replace curvature data that was previously determined and stored in the database. For example, if the route curvature that may be measured during travel over a segment of a route does not correspond or match (e.g., may be not within a designated numerical range) of a previously measured curvature of the segment of the route that may be stored in a database or other memory structure, then the route curvature that may be currently measured may be stored in the database to replace or otherwise supplant the previously measured curvature. 
     Measuring the route curvature during travel along a route can provide for improved performance and control of the vehicle system. For example, measuring the route curvature can allow the operator or automatic control of the vehicle system to modify tractive efforts and/or braking efforts of one or more of the vehicles in the vehicle system to ensure that forces exerted on mechanical couplers (that link the vehicles with each other) stay within prescribed limits. Curved segments of the route can impact these forces, and measuring the curvatures during travel on the curved segments can allow for the vehicle system to be manually and/or automatically controlled to ensure that any changes to these coupler forces caused by the curvature may be modified by control of tractive efforts and/or braking efforts to ensure that the coupler forces do not become too positive (e.g., as tensile forces that could cause the couplers to break) or too negative (e.g., as compressive forces that could cause the vehicles in the same vehicle system to collide). 
     As another example, the vehicle system may be traveling along the route according to a trip plan that designates operational settings of the vehicle system as a function of time and/or distance along the route. The measured curvatures of the route that may be measured during travel of the vehicle system along the route may be used to create and/or modify the trip plan during travel of the vehicle system. For example, the operational settings designated by the trip plan may include the speed of the vehicle system, acceleration of the vehicle system, tractive efforts produced by the vehicle system, braking efforts produced by the vehicle system, throttle settings of the vehicle system, and the like. The operational settings may be used to direct manual control of the vehicle system (e.g., by coaching or directing an operator to manually control the vehicle system according to the trip plan) and/or to automatically control operations of the vehicle system. Traveling according to the trip plan can result in improved performance of the vehicle system in that the designated operational settings of the trip plan can reduce fuel consumption and/or emissions generation of the vehicle system (relative to the same vehicle system traveling over the same route(s) for the same trip, but using manual control without a trip plan or using a trip plan that designates different operational settings). 
     For one or more reasons, the designated operational settings of the trip plan may result in the vehicle system consuming more fuel, generating more emissions, producing larger coupler forces, or the like, than may be desired (e.g., by exceeding one or more previously designated thresholds). This may occur when the trip plan may be created using erroneous or outdated information, such as incorrect curvatures of the route. During travel of the vehicle system along a route according to the trip plan, the vehicle system can measure the route curvature in one or more segments of the route as the vehicle system travels over the one or more segments and compare the measured route curvatures with the route curvatures on which the trip plan may be based. If these curvatures do not match (e.g., may be not within a previously designated numerical range of each other), then performance of the vehicle system may suffer relative to if the route curvatures were closer to each other. For example, actual adhesion of the wheels in the vehicle system to the route may be less than desirable and result in increased fuel consumption, increased emission generation, increased coupler forces, and the like, relative to the adhesion of the wheels that was expected or planned for when creating the trip plan. One or more components of the vehicle system may modify the trip plan to account for the differences in expected and actual curvatures. For example, if the vehicle system determines that the actual curvature has a smaller radius than the expected curvature used to create the trip plan, the vehicle system may modify the trip plan to modify unexpected coupler forces, slower travel, or the like, that was not anticipated or planned for when the trip plan was created. The vehicle system may then continue along in the trip using the modified trip plan. 
     One or more embodiments described herein also may provide for the control of one or more adhesion-modifying devices based on a route curvature that may be measured by a vehicle system traveling along a curved segment of the route. During travel on a segment of the route that has relatively significant curvature (e.g., a relatively small radius of curvature), a lubricant may be applied to the route to reduce adhesion between the wheels of the vehicle system and the route so that the vehicle system may more easily travel through the curved segment of the route. In one aspect, the curvature of the route can be measured onboard the vehicle system and, if the curvature may be significant enough (e.g., the radius of curvature may be smaller than a designated threshold), then an adhesion-modifying device disposed onboard the vehicle system may apply lubricant to the route in response to this measurement. Additionally or alternatively, a command message may be communicated from the vehicle system to one or more off-board devices (e.g., wayside devices) disposed alongside the route in response to this measurement. This command message may direct these devices to apply lubricant to the route. 
     One or more embodiments described herein also may provide for detection of an intersection or a switch at an intersection between two or more routes. For example, onboard detection of the vehicle system following a curved path may indicate that the vehicle system has passed through and/or turned in an intersection between routes, and/or has traveled over or through a switch, such as a switch between two tracks traveled upon by rail vehicles. 
       FIG. 7  is a schematic diagram of a vehicle  700  having an embodiment of a vehicle control system  702 . The vehicle in  FIG. 7  is similar to the vehicle shown in  FIG. 1 . For example, the vehicles may differ according to details of the components onboard the vehicle as described below. Optionally, the control system  702  may be disposed onboard another vehicle, such as the vehicle  106  shown in  FIG. 1 . 
     A propulsion subsystem  712  of the vehicle  700  generates tractive effort to propel the vehicle  700  along a route  708 , similar to the propulsion subsystem  112  (shown in  FIG. 1 ). A user input and/or output device  722  (“User Input/Output” in  FIG. 7 ) represents one or more devices that can be manually actuated to control one or more components of the vehicle  700  that may be shown in  FIG. 7  and/or provide information to an operator of the vehicle  700 . The device  722  can represent the user input  122  shown in  FIG. 1 . The device  722  can include one or more throttles, brake controls, buttons, switches, levers, touchscreens, keyboards, microphones, display screens, and the like. 
     An onboard energy management subsystem  726  represents one or more hardware components (e.g., one or more processors that operate based on instructions, such as software, stored on a computer readable, tangible, and/or non-transitory component, such as a computer memory  728 ) obtains a trip plan for controlling the vehicle  700  and/or a vehicle system that includes the vehicle  700 . Optionally, the energy management subsystem  726  may be disposed off-board the vehicle  700  and/or the vehicle system that includes the vehicle  700 . 
     The energy management subsystem  726  may obtain the trip plan by receiving the trip plan from an off-board location (e.g., a dispatch center or other location) or by creating the trip plan. The trip plan designates operational settings of the vehicle  700  and/or a vehicle system that includes the vehicle  700  (e.g., the vehicle system) to improve one or more operational variables of the vehicle  700  and/or the vehicle system, subject to one or more operating constraints of the vehicle  700  and/or vehicle system. The operational settings may include throttle settings, brake settings, speeds, accelerations, power outputs, motor rotational speeds, electric current generated by onboard generators and/or alternators, forces exerted on couplers disposed between vehicles in the vehicle system, segments of routes to be traveled on to reach a location, and/or the like. The operational settings may be designated by the trip plan as a function of time and/or distance along a trip  708  to one or more locations. For example, for a trip of the vehicle  700  or vehicle system, a trip plan may dictate different throttle settings and/or different speeds for different locations along the route  708 . 
     The operational variables that may be improved by the trip plan can include fuel consumption, emission generation, travel time to one or more locations, and the like. The term “improve” means that the variable being referred to may be increased or decreased relative to some designated objective value. Controlling the vehicle  700  and/or vehicle system according to a trip plan that seeks to improve fuel efficiency may result in the vehicle  700  consuming less fuel, producing fewer emissions, and/or reaching a destination location in less time relative to some objective benchmark. The objective benchmark can be designated or set by an owner or operator of the vehicle  700  and/or vehicle system, a governmental body, a previous trip of the vehicle  700  and/or vehicle system along the same route  708  to the same location. For example, following the trip plan can cause the vehicle  700  and/or vehicle system consume less fuel (e.g., at least 1 to 3 percent, or another value), produce fewer emissions, and/or reach a location in less time than the previous trip of the vehicle  700  and/or vehicle system to the same location along the same route  708  where the vehicle  700  and/or vehicle system was manually controlled or not controlled according to the trip plan. In one aspect, controlling the vehicle system according to a trip plan can cause the vehicle system to consume less fuel, produce fewer emissions, and/or reach a location in less time than the same vehicle system traveling over the same routes and route segments but using one or more operational settings (e.g., throttle settings, speeds, power outputs, brake applications, or the like) that differ from the operational settings designated by the trip plan at one or more locations along the trip. 
     The operating constraints to which the trip plan may be subject may include speed limits, slow orders, weather conditions, upper limits on working hours of an onboard crew, a schedule for the vehicle system, and the like. These operating constraints may prevent the trip plan from directing the vehicle system to travel too slow, apply the brakes too many times, and the like, so that the constraints may be satisfied (e.g., not violated). 
     The energy management subsystem  726  can create and/or modify the trip plan onboard the vehicle  700 , and/or can receive the trip plan from an off-board location, such as a dispatch center or other location not on board the vehicle system that includes the vehicle  700 . A communication apparatus  730  includes communication hardware and associated circuitry and software (where applicable) for communicating information between the vehicle  700  and one or more other vehicles of the same vehicle system, one or more other vehicles in another vehicle system, or an off-board location. For example, the communication apparatus  730  can include transceiver circuitry, an antenna  732  for wireless communication, one or more routers, modems, and the like for communicating via a wired connection  734  (e.g., a conductive pathway extending between vehicles in the vehicle system, such as a multiple unit line, train line, electronically controlled pneumatic brake line, or the like). The communication apparatus  730  can receive information used by the energy management subsystem  726  to create and/or modify a trip plan, can receive a trip plan, and/or can communicate a trip plan with one or more other vehicles, vehicle systems, and/or off-board locations. 
     The vehicle  700  includes an adhesion modifying device  704  that may be controlled to change adhesion of wheels  710  of the vehicle  700  to the route  708 . For example, the device  704  may include a blower or fan that directs air (e.g., cold air, hot air, or room temperature air) onto the route  708  to clear the route  708  of debris (and thereby increase adhesion between the wheels and the route  708 ). As another example, the device  704  may dispense a substance onto the route  708 , such as sand, gravel, an adhesive, or the like, to change adhesion between the wheels and the route  708 . The device  704  can apply a lubricant, such as an oil, onto the route  708  to reduce adhesion and assist with movement of the vehicle system. For example, when traveling over curved segments of the route  708 , a lubricant can be applied to the route  708  to allow the wheels of the vehicle system to more easily move along the route  708 . The device  704  may be manually and/or automatically controlled by the control system  702 . Optionally, the adhesion modifying device  704  may be disposed off-board of the vehicle  700  but may be controlled using signals communicated from the vehicle  700 . 
     The vehicle  700  includes a position and/or velocity data receiver  718  that may be similar or identical to the position and/or velocity data receiver  118  shown in  FIG. 1 . Using position and/or velocity data (e.g., position and/or velocity data signals) acquired by the position and/or velocity data receiver  718 , the vehicle  700  (e.g., the vehicle control system  702 ) can measure curvatures of the route  708  being traveled by the vehicle  700 . The position and/or velocity data can be received from off-board devices, such as the devices  116  shown in  FIG. 1 . 
     With continued reference to the vehicle  700  shown in  FIG. 7 ,  FIG. 8  illustrates a schematic diagram of one example of the vehicle  700  traveling along a segment  800  of the route  708 . The vehicle  700  may be included in a larger vehicle system that may be not shown in  FIG. 8 . During travel along the route  708 , the position and/or velocity data receiver  718  obtains position and/or velocity data signals from the off-board devices  116  to determine headings of the vehicle  700 . As used herein, the heading of the vehicle  700  refers to the course or direction of travel of the vehicle  700 . For example, the vehicle  700  may have a heading of 90° when the vehicle  700  travels east, a heading of 180° when the vehicle  700  travels south, a heading of 270° when the vehicle  700  travels west, a heading of 0° when the vehicle  700  travels north, and so on. The heading may be communicated to the position and/or velocity data receiver  718  in the signals received from the off-board devices  116 . Optionally, the heading may be derived from position and/or velocity data received from the off-board devices  116 . For example, if the position and/or velocity data signals indicate the geographic location (e.g., longitude, latitude, and/or elevation) of the vehicle  700 , then position and/or velocity data signals for two or more different locations may be used to calculate the heading of the vehicle  700 . 
     In one aspect, only headings of the vehicle  700  are used to determine curvatures of routes being traveled upon. For example, the systems and methods described herein may calculate or estimate curvatures of a curved route segment using GPS headings, and not using any geographic locations or coordinates, such as GPS coordinates. 
     The position and/or velocity data signals may be acquired and/or the headings of the vehicle  700  may be determined periodically, upon manual prompt by the operator of the vehicle  700  (e.g., using user input/output  722 ), in response to one or more events, or the like. The events that may cause the acquisition of data signals and/or determining the heading may include the heading of the vehicle  700  deviating from a designated heading (e.g., as acquired from the memory  728 ) by at least a designated amount (and thereby indicating that the designated curvature of the route  708  may not match or correspond with the actual curvature). Optionally, actual operations of the vehicle  700  deviating from the operations designated by a trip plan (e.g., actual speed does not match the designated speed) may cause the heading of the vehicle  700  to be determined. 
     In the illustrated example, the headings of the vehicle  700  may be determined from the signals received from the off-board devices  116  for locations  802 ,  804 ,  806 ,  808 ,  810 ,  812  of the vehicle  700 . The radius of curvature (e.g., the curvature of the route segment  800 ) may be determined from these headings. For example, the radius of curvature of the route segment  800  may be calculated from one or more of the following relations: 
     
       
         
           
             
               
                 
                   r 
                   = 
                   
                     
                       2 
                        
                       π 
                        
                       
                           
                       
                        
                       C 
                     
                     
                       360 
                        
                       
                           
                       
                        
                       D 
                     
                   
                 
               
               
                 
                   ( 
                   
                     Equation 
                      
                     
                         
                     
                      
                     #1 
                   
                   ) 
                 
               
             
           
         
       
     
     where r represents the radius of curvature of the route segment  800 , C represents a chord length, and D represents a degree of curvature of the route segment  800 . The chord length C may be a straight-line distance between two of the locations  802 ,  804 ,  806 ,  808 ,  810 ,  812  where the heading may be determined. For example, chord lengths  814 ,  816 ,  818 ,  820 ,  822  may be used. Optionally, chord lengths may be measured between two or more other locations  802 ,  804 ,  806 ,  808 ,  810 ,  812 , such as locations  802  and  806 ,  804  and  812 , or the like. The chord length C may be a designated distance, such as 100 feet (e.g., 30.48 meters). Or, the chord length C may change based on the time period between when the headings may be measured and how fast the vehicle  700  may be traveling. For example, the chord length C will increase if the time period between determining the headings and/or the speed increases. 
     The degree of curvature D of the route segment  800  may represent a deflection angle (measured in degrees, for example) that may be subtended (e.g., bounded by) the chord length C. In the examples shown in  FIG. 8 , the chord length  802  may be associated with a degree of curvature  824 , the chord length  804  may be associated with a degree of curvature  826 , and so on. The degree of curvature D for a chord length C can be determined from the following relation: 
     
       
         
           
             
               
                 
                   D 
                   = 
                   
                     
                       
                         d 
                          
                         
                             
                         
                          
                         
                           
                             ( 
                             heading 
                             ) 
                           
                           / 
                           dt 
                         
                       
                       
                         d 
                          
                         
                             
                         
                          
                         
                           
                             ( 
                             distance 
                             ) 
                           
                           / 
                           dt 
                         
                       
                     
                     = 
                     
                       
                         d 
                          
                         
                             
                         
                          
                         
                           
                             ( 
                             heading 
                             ) 
                           
                           / 
                           dt 
                         
                       
                       v 
                     
                   
                 
               
               
                 
                   ( 
                   
                     Equation 
                      
                     
                         
                     
                      
                     #2 
                   
                   ) 
                 
               
             
           
         
       
     
     where d(heading)/dt represents the change in the heading of the vehicle  700  with respect to time, and both d(heading)/dt and v represent the moving speed of the vehicle  700 . 
     In one aspect, the control system  702  may use “rollover protection” to prevent relatively small changes in the heading of the vehicle  700  across the magnetic north direction from being confused with more significant changes in headings. For example, if a heading along magnetic north may be referred to by an angle of zero degrees, then a heading that changes from slightly east of north (e.g., 2 degrees) to slightly west of north (e.g., 357 degrees) may be treated by the control system  702  as a change of 5 degrees (e.g., moving from 2 degrees to 357 degrees across magnetic north) as opposed to a change of 355 degrees (e.g., moving from 2 degrees to 357 degrees without crossing magnetic north). The control system  702  may use this rollover protection if the change in headings may be larger than a designated threshold. This threshold may change or be based on the rate at which the headings may be obtained. For example, the heading threshold may increase when the headings may be measured less frequently (and, as a result, a larger change in heading may be more realistically possible). Conversely, the heading threshold may decrease when the headings may be measured more frequency (and, as a result, a larger change in heading may be less realistically possible). 
     The control system  702  may filter the rate of heading change (e.g., d(heading)/dt) based on the speed of the vehicle  700 . For example, the control system  702  can apply a spatial low pass filter that filters more of the rates of heading change when the vehicle speed increases and that filters less of the rates of heading change when the vehicle speed decreases. For example, the control system  702  may remove some of the rates of heading change from the calculation of the radius of curvature. The rates of heading change that may be removed or not used in the calculation of the radius of curvature can be based on the speed of the vehicle  700 . As the speed of the vehicle  700  increases, more of the rates of heading change may be eliminated or not used to calculate the radius of curvature. As the speed of the vehicle  700  decreases, less of the rates of heading change may be eliminated or not used to calculate the radius of curvature. 
     In one aspect, the heading of the vehicle  700  that may be monitored by the control system  702  may be reset responsive to one or more events. The heading may be reset by changing or setting the value of the heading to a designated amount, such as zero or another direction. The events that may cause the resetting of the heading may include the uncertainty parameter (described above) becoming too large, such as larger than a first designated threshold. Another event may be the signal-to-noise ratio  626  of the signals  124  received from the off-board devices  116  falling below a second designated threshold. Another event may be the number of off-board devices  116  from which the signals  124  may be received by position and/or velocity data receiver  118  being less than a third designated threshold, or no greater than a fourth designated threshold. 
     The radius of curvature R of the route  708  may be measured one or more times during travel of the vehicle  700  over the segment  800  and compared to a previously designated or measured curvature of the segment  800 . For example, the currently measured curvature may be compared to the curvature stored in the memory  728  of the vehicle  700  and/or the curvature used to create or modify the trip plan. If the measured curvature may be different from the curvature stored in the memory  728  and/or used to create or modify the trip plan (e.g., by at least a designated amount), then the stored curvature may be replaced or updated with the measured curvature and/or the trip plan may be modified with the updated curvature. 
     The control system  702  may estimate forces exerted on the couplers that mechanically couple the vehicles in the vehicle system with each other. For example, the control system  702  may estimate these forces based on the curvature of the route segment being traveled upon by the vehicle system. For smaller radii of curvature, the control system  702  may estimate greater forces (e.g., larger compressive forces or larger tensile forces) relative to larger radii of curvature. The control system  702  may warn an operator when the estimated coupler forces may be growing too large (e.g., using the user input/output  722 ) and/or automatically modify control of the vehicle system. For example, the control system  702  may direct the operator to manually slow movement of the vehicle system and/or automatically slow movement of the vehicle system when the estimated coupler forces grow too large. 
     The control system  702  may modify the adhesion of the wheels to the route  708  based on the curvature of the route  708  that may be measured. In response to measuring the curvature of the route  708  being traveled on (e.g., when the radius of curvature may be smaller than a designated radius), the control system  702  may direct the operator to manually control the adhesion modifying device  704  and/or may automatically control the device  704  to change one or more characteristics of the route  708  as the vehicle  700  travels over the route  708  to modify adhesion of the wheels  710  of the vehicle  700  on the route  708 . By way of example, the adhesion modifying device  704  may apply one or more friction-modifying substances to the route  708  that change the coefficient of friction between the wheels  710  and the route  708  (e.g., sand, lubricant, or the like). Optionally, the adhesion modifying device  704  may direct the flow of a fluid (e.g., gas such as air, liquid, or the like) toward the route  708  to clean the route  708 . In another example, the adhesion modifying device  704  may physically or mechanically engage the route  708  to clean the route  708 . Optionally, the adhesion modifying device  704  may engage the route  708  to remove a portion of the route  708 , such as by sanding the route  708 . 
     The adhesion modifying device  704  may include two or more applicator devices  706  through which friction-modifying substances (e.g., air, sand, lubricant, and the like) may be applied to the route  708  and/or the device  704  engages the route  708 . With respect to rail vehicles, the device  704  may include an applicator device  706  over each one of the rails being traveled along. The applicator devices  706  can include nozzles that direct friction-modifying substances toward the route  708 , brushes that clean the route  708 , or the like. 
     Additionally or alternatively, one or more of the applicator devices  706  can represent a sanding device that removes part of the route  708 . For example, such a sanding device can engage the route  708  and sand down (e.g., smoothen) the top surface of the route  708  that may be engaged by the sanding device. With respect to rail vehicles, the top sides of the rails can become damaged. Sanding these top sides of the rails can remove the damage and prolong the life of the rails by preventing the damage (e.g., cracks and microcracks) from spreading. 
     In one aspect, the control system  702  and/or the adhesion modifying device  704  can control how much friction modifying substances may be applied to the route  708  based on the curvature of the route  708  that may be measured. For example, the control system  702  and/or the adhesion modifying device  704  may apply greater amounts of lubricant to the route  708  for segments of the route  708  having smaller radii of curvature relative to segments of the route  708  having larger radii of curvature. The increased amount of lubricant may assist the vehicle  700  in more easily traveling over the smaller radii of curvature, where the wheels  710  may otherwise have more friction with the route  708  relative to larger radii of curvature. 
     The control system  702  and/or the adhesion modifying device  704  can control the what type of friction modifying substances may be applied to the route  708  based on the curvature of the route  708  that may be measured. For example, the control system  702  and/or the adhesion modifying device  704  may apply substances (e.g., lubricant) that reduce the coefficient of friction between the wheels  710  and the route  708  for radii of curvature in the route  708  that may be smaller than a threshold radius and apply substances (e.g., sand) that increase this coefficient of friction for larger radii of curvature. 
     The control system  702  and/or the adhesion modifying device  704  can control the rate at which the friction modifying substances may be applied to the route  708  based on the curvature of the route  708  that may be measured. For example, the control system  702  and/or the adhesion modifying device  704  may friction modifying substances at a larger rate of flow for segments of the route  708  having smaller radii of curvature relative to segments of the route  708  having larger radii of curvature. The increased rate of substances may assist the vehicle  700  in more easily traveling over the smaller radii of curvature by applying more of the substance. 
     The control system  702  may use the radius of curvature that may be measured and the heading of the vehicle  700  to determine whether to deactivate the device  704  and/or one or more of the applicator devices  706 . Optionally, the control system  702  may use the radius of curvature that may be measured to change a position of one or more of the applicator devices  706 . 
       FIG. 10  illustrates a top view of the vehicle  700  traveling over a curved segment of the route  708 . As shown, the curvature of the route  708  causes the applicator devices  706  of the adhesion modifying device  704  to not be located over the route  708 . For example, a distance  1000  between the wheels  710  of the vehicle  700  and the applicator devices  706  may be sufficiently long and the curvature of the route  708  may be sufficiently small to cause the applicator devices  706  to be located between tracks that form the route  708  and/or be disposed outside of the route  708 , as shown in  FIG. 10 . 
     The control system  702  may deactivate those applicator devices  706  that may be pointed away from the route  708  (e.g., tracks) when the measured curvature of the route  708  may be smaller than a designated threshold. For example, when the vehicle  700  may be traveling over a relatively tight curve in the route  708 , the applicator devices  706  may be positioned such that any friction-modifying substances will not be applied to the route  708  and/or the applicator devices  706  do not engage the route  708 . The control system  702  may compare the measured radius of curvature to the designated threshold to determine if the applicator devices  706  may be disposed over and/or may be engaging or positioned to engage the route  708 . If the measured radius may be at least as large as the threshold, then the applicator devices  706  may be directed toward the route  708  such that the friction-modifying substances delivered from the devices  706  will be applied to the route  708  and/or such that the devices  706  engage or may be positioned to engage the route  708 . As a result, the control system  702  may activate or keep the devices  704 ,  706  active to apply the friction-modifying substances to the route  708  and/or engage the route  708 . 
     If the measured radius may be not as large as the threshold, then the applicator devices  706  may not be directed toward the route  708  such that the friction-modifying substances delivered from the devices  706  will not be applied to the route  708  and/or such that the devices  706  do not engage or may be not positioned to engage the route  708 . Allowing such applicator devices  706  to apply the friction-modifying substances may actually result in the substances being applied to the ground between or outside of the rails, which can waste the supply of the substances and/or stir up dirt, debris, and the like, and further negatively impact adhesion of the wheels to the route  708 . As a result, the control system  702  may deactivate or otherwise prevent the devices  704 ,  706  from applying the friction-modifying substances to the route  708  and/or from engaging the route  708 . 
       FIG. 11  is a front view of an embodiment of a vehicle  1100 . The vehicle  1100  may represent one or more of the vehicles  104 ,  106 ,  700  shown in  FIGS. 1 and 7 , or another vehicle. The vehicle  1100  includes a control system  1110  (such as the control system  702 ) and an adhesion modifying device  1102  (such as the device  704 ). The adhesion modifying device  1102  controls applicator devices  1104 , similar to the actuator devices  706 , to apply friction-modifying substances to a route  1106  that may be being traveled by the vehicle  1100 , to clean the route  1106 , to sand the route  1106 , and the like. Although the route  1106  may be shown as being parallel tracks being traveled upon by wheels  1108  of a rail vehicle, the route  1106  may optionally be a road or other surface. 
     The applicator devices  1104  may be connected to actuators  1112  that may be controlled by the adhesion modifying device  1102  to move the applicator devices  1104 . The actuators  1112  may include or represent one or more motors (e.g., servo motors, pneumatic motor, electric motor, or the like), gears, pinions, screws, wheels, axles, or the like, that may be controlled by the adhesion modifying device  1102  to change an orientation of the applicator devices  1104 . As shown in  FIG. 11 , the actuators  1112  may move the applicator devices  1104  by turning the applicator devices  1104  inward (e.g., to the right in the view of  FIG. 11  and as shown in dashed lines) and/or outward (e.g., to the left in the view of  FIG. 11 ). The actuators  1112  may be controlled to move the applicator devices  1104  to point inward or outward and, as a result, direct friction-modifying substances inward or outward relative to the vehicle  1100 , engage the route  1108  at an angle, or the like. 
     The control system  1110  may use the measured curvature of the route  1106  to direct the adhesion modifying device  1102  to control the orientation of the applicator devices  1104 . For example, as described above in connection with  FIG. 10 , the curvature of the route  1106  may be sufficiently small that the applicator devices  1104  may be located outside of the route  1106  (e.g., such that an applicator device  1104  may be outside of the curved segment of the route  1106 ) and/or inside of the route  1106  (e.g., such that an applicator device  1104  may be inside the curved segment of the route  1106  or disposed above a location that may be between the tracks of the route  1106 ). In such a situation, the control system  1110  may direct the adhesion modifying device  1102  to control the actuators  1112  to change the orientation of the applicator devices  1104 . The actuator  1112  connected to the applicator device  1104  that may be outside of the curved segment of route  1106  may bias (e.g. move) the applicator device  1104  inward, so that the applicator device  1104  may be directed more toward the route  1106  than the applicator device  1104  would be without biasing the device  1104 . The actuator  1112  connected to the applicator device  1104  that may be inside of the curved segment of route  1106  may bias (e.g. move) the applicator device  1104  outward, so that the applicator device  1104  may be directed more toward the route  1106  than the applicator device  1104  would be without biasing the device  1104 . 
     The control system  1110  may decide when to bias the applicator devices  1104  by comparing the measured curvature of the route  1106  to one or more designated thresholds. These thresholds may represent different curvatures of the route  1106  and may be separately associated with different amounts of biasing (e.g., movement) of the applicator devices  1104 . Depending on which of the thresholds may be exceeded and/or not exceeded by the measured curvature of the route  1106 , the control system  1110  may direct the adhesion modifying device  1102  to control the actuators  1112  and change the orientations of the applicator devices  1104  by different amounts. For example, for smaller radii of curvature in the route  1106 , the actuators  1112  may move the applicator devices  1104  by greater amounts relative to larger radii of curvature in the route  1106 . 
     With renewed reference to the vehicle  700  shown in  FIG. 7 ,  FIG. 9  illustrates one example of the vehicle traveling toward a switch  900  along the route  708 . The switch  900  represents a mechanism that can be actuated to direct which of two or more route segments  902 ,  904 ,  906  of the route that the vehicle travels on when the vehicle travels through or over the switch  900 . For example, in a first state or position, the switch  900  may direct the vehicle  700  to travel from the route segment  902  to the route segment  904 . In a different, second state or position, the switch  900  may direct the vehicle  700  to travel from the route segment  902  to the route segment  906 . 
     The control system  702  can detect which route segment  902 ,  904  may be being traveled upon when the vehicle  700  travels over the switch  900  and/or detect the state of the switch  900  based on the route curvature that may be measured. For example, as the vehicle  700  travels over the switch  900 , the control system  702  can measure the route curvature as described above. The relative locations of the route segments  902 ,  904 , and/or  906  may be known (e.g., stored in the memory  728 ). Based on the route curvature that may be measured, the control system  702  can determine if the vehicle  700  traveled from the route segment  902  to the route segment  904  or from the route segment  902  to the route segment  906 . For example, a larger radius of curvature that may be measured by the control system  702  may indicate that the vehicle  700  traveled from the route segment  902  to the route segment  906 . A smaller radius of curvature may indicate that the vehicle  700  traveled from the route segment  902  to the route segment  904 . 
     The control system  702  can use the identification of which route segment  904 ,  906  may be being traveled upon to ensure that the vehicle  700  may be not entering into a restricted area, such as a section of the route  708  that may be currently occupied by another vehicle system, that may be being repaired by a maintenance crew, that may be not along the path that the vehicle system may be to take to reach a destination, and the like. The energy management system  726  can use the identification of which route segment  904 ,  906  may be being traveled upon to ensure that the vehicle  700  may be traveling according to the trip plan. For example, the trip plan may dictate which route segments  902 ,  904 ,  906  that the vehicle  700  may be to travel along. Upon traveling through or across the switch  900 , the control system  702  may determine that the vehicle  700  may be not traveling on a segment of the route  708  that may be designated by the trip plan. For example, the trip plan may direct the vehicle  700  to travel from the segment  902  to the segment  904 , or from the segment  902  to the segment  906 . If the control system  702  determines that the vehicle  700  may be not traveling on the segments designated by the trip plan (such as when the switch  900  malfunctions, may be modified to an incorrect state, or the like), then the control system  702  may notify the energy management system  726 . The energy management system  726  may then modify or revise the trip plan (e.g., into a modified trip plan) to account for and include the vehicle  700  traveling on the segment of the route  708  that the vehicle  700  may be currently traveling on, but that was not included in the previous trip plan. 
       FIGS. 12 and 13  illustrate top views of an embodiment of a vehicle  1200 . The vehicle  1200  may represent the vehicle,  106 ,  700 , and/or  1100  shown in  FIGS. 1, 7, and 11 . For example, the vehicle  1200  may be a propulsion-generating vehicle that may be capable of generating tractive effort to propel itself, such as a locomotive, or may be a non-propulsion-generating vehicle that may be incapable of generating tractive effort to propel itself, such as a railcar. 
     The vehicle  1200  includes a control system  1202 , such as the control system,  702 , or  1110 . The control system  1202  may be communicatively coupled (e.g., by one or more wired and/or wireless connections) with one or more steering systems  1204  (e.g., systems  1204 A,  1204 B) of the vehicle  1200 . The steering systems  1204  may be connected with wheels  1206  of the vehicle  1200  and can turn the wheels  1206  as shown in  FIG. 13 . The steering system  1204 A steers the wheels  1206  of a first set  1210  of the wheels  1206  while the steering system  1204 B steers the wheels  1206  of a second set  1212  of the wheels  1206 . 
     The steering systems  1204  can turn the wheels  1206  to allow the vehicle  1200  to more easily travel over curved segments of a route, such as the route  108 ,  708  (shown in  FIGS. 1 and 7 ). For example, without being able to turn the wheels  1206 , more force may be required to move the wheels  1206  and the vehicle  1200  along curved segments of the route due to the fact that the wheels  1206  may be rigidly oriented along a linear direction during travel over a curved route. 
     The steering systems  1204  can include or represent gears, pinions, axles, actuators, motors, or the like, for turning the wheels  1206  left or right relative to a direction of travel  1208  of the vehicle  1200 . The steering systems  1204  may include or be coupled with axles  1214  that may be joined with the wheels  1206 . In one aspect, one or more of the steering systems  1204  may include or represent a propulsion-generating device, such as a motor. The propulsion-generating device may be directly or indirectly coupled with one or more of the wheels  1206  or axles  1214  to rotate the wheels  1206  and/or axles  1214  and generate tractive effort to propel the vehicle  1200  along the route. 
     The steering system  1204 A turns the wheels  1206  of the set  1210  to the left relative to the direction of travel  1208  and the steering system  1204 B turns the wheels  1206  of the set  1212  to the right relative to the direction of travel  1208 . The steering systems  1204  may turn the wheels  1206  in this manner when the vehicle  1200  may be traveling over a segment of the route that may be curved to the left relative to the direction of travel  1208 . The steering system  1204 A may turn the wheels  1206  of the set  1210  to the right relative to the direction of travel  1208  and the steering system  1204 B may turn the wheels  1206  of the set  1212  to the left relative to the direction of travel  1208  when the vehicle  1200  may be traveling over a segment of the route that may be curved to the right relative to the direction of travel  1208 . Optionally, the vehicle  1200  may include only one of the steering systems  1204  that turns the wheels  1206  of only a single set  1210  or  1212 , or that turns the wheels  1206  of multiple sets  1210 ,  1212 . While only four wheels  1206  and two sets  1210 ,  1212  may be shown, the vehicle  1200  may include a different number of wheels  1206  and/or sets  1210 ,  1212 . 
     The control system  1202  may measure the curvature of a route being traveled upon (as described above) and control one or more of the steering systems  1204  to turn the wheels  1206  along the measured curvature of the route. The control system  1202  may control how far each or both of the steering systems  1204  turn the wheels  1206  based on the measured route curvature. For example, for smaller measured radii of curvature in the route, the control system  1202  may direct the steering systems  1204  to turn the wheels  1206  more than for larger measured radii of curvature in the route. 
     As described above, one or more of the steering systems  1204  may include a propulsion-generating device to propel the vehicle  1200 . For example, the steering system  1204 A and/or the steering system  1204 B may include one or more traction motors that may be powered to rotate the corresponding axle  1214  and rotate the wheels  1206  connected to the axle  1214 . The torques applied to the axles  1214  by the steering systems  1204  may be controlled using the curvature of a route segment being traveled on to control the shifting of weight between the axles  1214 . For example, if the vehicle  1200  may be traveling on a curved segment of the route in the direction of travel  1208 , the control system  1202  may measure the radius of curvature (as described above) and use this radius to change the torque applied by the steering system  1204 A and/or the torque applied by the steering system  1204 B to the respective axles  1214  to propel the vehicle  1200 . 
     In one aspect, the control system  1202  may reduce the torque applied by the “rear” steering system  1204 B (e.g., the steering system  1204  that follows one or more other steering systems  1204  on the same vehicle  1200  along the direction of travel  1208 ) and/or increase the torque applied by the “leading” steering system  1204 A (e.g., the steering system  1204  that may be ahead of one or more other steering systems  1204  on the same vehicle  1200  along the direction of travel  1208 . If the vehicle  1200  includes more than two steering systems  1204 , then one or more of the steering systems  1204  may be both a rear steering system  1204  relative to at least one other steering system  1204  and a leading steering system  1204  relative to at least one other, different steering system  1204 . 
     By “reduce the torque,” it may be meant that the control system  1202  may reduce the torque applied by the steering system  1204 B on the axle  1214  connected to the system  1204 B relative to the torque applied by the steering system  1204 B on the axle  1214  when the vehicle  1200  may be traveling along a straight segment of the route. In one aspect, the control system  1202  directs the rear steering system  1204 B to stop applying torque to the axle  1214  (e.g., the rear steering system  1204 B applies no torque to the axle  1214 ). 
     Optionally, the control system  1202  may reduce the torque applied by the steering system  1204 B relative to the torque applied by the other steering system  1204 A. For example, for a designated speed of the vehicle  1200  obtained from a trip plan, a manually selected throttle setting of the vehicle  1200 , or another input into the control system  1202  that dictates a power output or speed of the vehicle  1200 , the control system  1202  may command the traction motors of the steering systems  1204  to apply a certain amount of torque. The amount of torque applied by the steering systems  1204  on a straight segment of the route may be the same or approximately the same (e.g., with any differences due to noise in measurements of the torque, communication delays, or manufacturing variances). In one aspect of the inventive subject matter, the control system  1202  may reduce the torque applied by the rear steering system  1204  but increase the torque applied by the leading steering system  1204  responsive to and/or proportional to the measured radius of curvature of the route being traveled upon. The decrease in torque applied by one or more steering systems  1204  of the vehicle  1200  may be equivalent to or substantially equivalent to the increase in torque applied by one or more other steering systems  1204  of the same vehicle  1200  such that the total torque applied by the steering systems  1204  of the vehicle  1200  remains the same or substantially the same. Optionally, the torques applied by the steering systems  1204  may change such that the total torque applied by the steering systems  1204  does not remain the same. 
     The torque may be decreased and/or increased by the steering systems  1204  in intervals. For example, instead of dropping the torque applied by a steering system  1204  from a current value to a reduced value, the control system  1202  may incrementally decrease the torque applied by the steering system  1204  from a current value to a final reduced value. The control system  1202  may reduce the torque by a first amount for a first non-zero time period, then an additional amount for an additional non-zero time period, and so on, until the torque may be at the final reduced value. 
     The torque may be decreased for the rear steering system  1204  to shift the weight of the vehicle  1200  between the axles  1214  while traveling on the curved segment of the route. Decreasing the torque applied by the rear steering system  1204  causes at least some of the weight borne by the rear steering system  1204  to be transferred to one or more other steering systems  1204  (e.g., the leading steering system  1204  or a steering system  1204  that does not reduce torque). Shifting this weight between the axles  1214  can allow a larger portion of the weight of the vehicle  1200  to be borne by the axles  1214  that lead other axles  1214  along the direction of travel  1208  and make it easier for the vehicle  1200  to maintain speed through the curved segment of the route. Once the weight has been shifted between the axles  1214 , the control system  1202  can increase the torque applied by the rear steering system  1204  and/or decrease the torque applied by the leading steering system  1204 . 
       FIG. 14  is a top view of an embodiment of a vehicle  1400 . The vehicle  1400  may represent one or more of the other vehicles described herein, or another vehicle. The vehicle  1400  includes a vehicle control system  1402  (such as one or more of the vehicle control systems described herein) and a lighting control system  1404 . As described above, the vehicle control system  1402  control operations of the vehicle  1400 , including the determination or measurement of a curvature of the route being traveled by the vehicle  1400 . The lighting control system  1404  controls operations of a lighting device  1406  that generates light to illuminate the area in front of the vehicle  1400  along a direction of travel of the vehicle  1400 . For example, the lighting control system  1404  may automatically or manually control the lighting device  1406  to emit light when ambient light may be relatively low or dark. 
     The lighting control system  1404  controls one or more actuators  1408  that may be coupled with the lighting device  1406 . The actuators  1408  may be similar to the actuators  1112  (shown in  FIG. 11 ) in that the actuators  1408  may be controlled by the lighting control system  1404  to change an orientation of the lighting device  1406 . As shown in  FIG. 14 , the actuators  1408  may move (e.g., turn, pivot, rotate, or the like) the lighting device  1406  by turning the lighting device  1406  left or right relative to a direction of travel of the vehicle  1400 . The lighting device  1406  may be shown in  FIG. 14  in dashed line in two example positions where the lighting device  1406  may be turned toward. 
     The control system  1402  may use the measured curvature of the route to direct the lighting control system  1404  to control the orientation of the lighting device  1406  so that the lighting device  1406  may be directed toward the route when the vehicle  1400  may be traveling on a curved segment of the route. For example, the control system  1402  may measure the curvature of the route (as described above) and report this curvature to the lighting control system  1404 . The lighting control system  1404  may then determine how far to pivot or turn the lighting device  1406  to ensure that the lighting device  1406  may be oriented more toward the route (e.g., toward the center of the route) than away from the route in the curved segment of the route. For smaller radii of curvature in the route, the lighting control system  1404  may determine that the lighting device  1406  needs to be turned more to be oriented toward the route than for larger radii of the route. The lighting control system  1404  may then direct the actuators  1408  to turn the lighting device  1406  accordingly such that the lighting device  1406  may be oriented in the same direction of travel as the vehicle  1400  along the curved segment of the route. 
     In accordance with one or more embodiments described herein, the off-board-based input speed and the onboard-based input speeds can be used to measure wheel sizes (e.g., diameters) of the wheels of a vehicle. For example, these input speeds can be used to estimate or measure the diameters of wheels of a rail vehicle, wheels of an automobile, or wheels of another vehicle. With respect to solid wheels (e.g., the wheels of a rail vehicle), the wheel sizes can be measured to monitor wear of the track or wheels and/or to calibrate the onboard-based input speeds (e.g., due to changes or errors in an input wheel size that may be used to determine the onboard-based input speeds). With respect to non-solid (e.g., inflatable) wheels (e.g., tires of an automobile), the wheel sizes can be indicative of wear of the tires and/or air pressure of the tires. The wheel sizes can be monitored and, if a decrease may be identified, then an operator of the automobile may be warned of decreasing tire pressure, an impending flat tire, and/or a flat tire. 
     In one embodiment, a current wheel size may be calculated using a scale factor that may be applied to a static reference wheel size (such as the wheel size of a new wheel). Speed calculations can then use current wheel size and the wheel rotation counter or tachometer values. The current wheel size can be either placed in non-volatile memory for retrieval, as needed, and updating as available; or, can be generated and use dynamically and in near real time to avoid having to store the wheel size value and then update the stored wheel size value. 
     Due to errors in the measurement of the reference wheel, wear on the reference wheel during a trip, or other factors, the measured diameter of the reference wheel may initially be inaccurate and/or may become inaccurate during a trip. As a result, the onboard-based input speed that may be calculated using the diameter of the reference wheel may be or become inaccurate. 
     Returning to the description of the vehicle system shown in  FIG. 1 , in one aspect, the control system uses the off-board-based input speeds determined from data signals received from off-board devices  116  to calculate a reference wheel diameter for one or more wheels  114  of the vehicle  100 . The control system also obtains the wheel speeds at which the one or more wheels  114  of the vehicle  100  rotate. As described above, these wheel speeds may be measured by the speed sensors  120 . The wheels speeds may be represented in terms of revolutions per unit time of the wheels  114 . 
     The control system may calculate the reference wheel diameter using a relationship between the off-board-based input speed and the wheel speed of one or more of the wheels  114 . For example, the control system may determine a reference wheel diameter using the following: 
     
       
         
           
             
               
                 
                   d 
                   = 
                   
                     
                       
                         v 
                         OB 
                       
                       * 
                       
                         r 
                         G 
                       
                       * 
                       C 
                     
                     rpm 
                   
                 
               
               
                 
                   ( 
                   
                     Equation 
                      
                     
                         
                     
                      
                     #3 
                   
                   ) 
                 
               
             
           
         
       
     
     where d represents the reference wheel diameter, V OB  represents the off-board-based input speed, rpm represents the speed at which the reference wheel rotates (e.g., revolutions of the wheel per minute, obtained from the speed sensors  120 ), and r G  and C represent one or more variables and/or constant values based on one or more characteristics of the vehicle system. For example, r G  may represent a gear ratio for gears used to couple a motor to the axle  110  connected to the reference wheel  114  and C may represent a factor having a designated value, such as 336.13. Optionally, C may have another value. 
     The control system may calculate the reference wheel diameter for several, or all, of the wheels  114  in the vehicle. The reference wheel diameters may then be used to calculate or calibrate the onboard-based input speeds of the wheels  114 . In one aspect, the diameters of the wheels  114  may be individually calibrated (e.g., modified) to match or be closer to the reference wheel diameter that may be calculated using the off-board-based input speed and the rotational speed of the respective wheel  114 . Optionally, the diameters of a group of two or more wheels  114  may be calibrated to match or be closer to the reference wheel diameter that may be calculated using the off-board-based input speed and the rotational speed of the respective wheel  114 . 
     The reference wheel diameters may be periodically determined during a trip of the vehicle system using the off-board-based input speeds to re-calibrate the onboard-based input speeds. These onboard-based input speeds that may be re-calibrated may be used in connection with controlling the vehicle system according to a trip plan. For example, the control system may control operations of the vehicle system (or direct an operator to control the operations) so that the speed of the vehicle system (as determined from the onboard-based input speeds) matches or corresponds with the designated speeds of a trip plan for the vehicle system. 
     In one aspect of the inventive subject matter, the control system may compare the off-board-based input speed with the onboard-based input speed measured for a reference wheel  114  or a reference axle  110 . The reference wheel  114  may represent the wheel  114  for which an operator manually measured and/or input the size of the wheel  114  into the control system for determining the onboard-based input speed. The reference axle  110  may represent the axle  110  to which the reference wheel  114  may be joined. 
     If the off-board-based input speed differs from the onboard-based input speed for the reference wheel  114  or reference axle  110  (e.g., by at least a designated, non-zero threshold), then the control system may determine that this difference constitutes a relatively large error. The control system may then notify the operator of the vehicle, such as by activating one or more lights and/or speakers, displaying a warning on an output device, or the like. In response, the operator may obtain another manual measurement of the size of the reference wheel  114 . For example, the operator may stop movement of the vehicle system, disembark from the vehicle system, manually measure or re-measure the size of the reference wheel  114 , and input the size into the control system. 
     Optionally, the control system may scale or otherwise modify an input speed based on a difference between input speeds. If the off-board-based input speed differs from the onboard-based input speed, then the control system may scale the off-board-based input speeds (e.g., multiply the off-board-based input speeds by a correlation factor) to be closer to the onboard-based input speeds. For example, if the off-board-based input speeds may be 10% faster than the onboard-based input speeds, then the control system may divide future off-board-based input speeds by a factor of 1.1 (e.g., 110%) or multiply future off-board based input speeds by a factor of 0.9 (e.g., 90%). Or, if the off-board-based input speed differs from the onboard-based input speed, then the control system may scale the onboard-based input speeds to be closer to the off-board-based input speeds. 
     Calculation of the reference wheel diameter using the off-board-based input speeds may be used to check or monitor inflation of a tire on an automobile. The vehicle may represent an automobile and the wheels  114  may represent inflated tires of the automobile. The control system may represent an onboard computer system (e.g., having one or more processors) that compares reference wheel diameters calculated for the tires  114  using off-board-based input speeds, such as speeds derived from GPS data or other positional data. The control system may associate different reference wheel diameters with different amounts of inflation of the tires  114 . When the off-board-based input speeds indicate that the diameter of a tire  114  has changed, such as due to a loss in air pressure, then the control system may notify a driver of the automobile  104 . Optionally, the control system may monitor changes in the diameter of the tires  114  (as determined from the off-board-based input speeds) and notify the driver of the automobile  104  of significant changes in the diameter, such as those changes that may indicate a leak in the tire, a flat tire, or the like. In one aspect, the control system may automatically contact an off-board location, such as a repair facility or tow truck, responsive to determining that the tire pressure in one or more tires  114  has reduced and/or indicates a flat or impending flat tire. 
     In one aspect of the subject matter described herein, the use of positional data (e.g., geographic locations, headings, and the like) that is obtained from an off-board source may be limited to the use of only headings and/or velocities. For example, the curvature of a route segment may be determined using only headings of the vehicle system obtained from an off-board source, and not the coordinates of the vehicle system. As another example, the wheel diameter of a vehicle system may be determined using only the speed of the vehicle system, and not the headings of the vehicle system, that is obtained from an off-board source. 
     The systems and methods described herein may use the positional data regardless of how fast or slow the vehicle system is traveling. For example, the systems and methods described herein may not place a lower limit on the speed of the vehicle system, where travel at speeds below this limit prevent the calculation of reference speeds, wheel diameters, route curvatures, and the like. Similarly, the systems and methods described herein may not place an upper limit on the speed of the vehicle system, where travel at speeds faster than this limit prevent the calculation of reference speeds, wheel diameters, route curvatures, and the like. While one or more filters or adjustments may be made to the positional data, reference speeds, wheel diameters, route curvatures, and the like, may be made based on the moving speed of the vehicle system, the systems and methods described herein may continue to obtain positional data and calculate the reference speeds, wheel diameters, route curvatures, and the like, using that data, regardless of how fast or slow the vehicle system is moving when the positional data is acquired. 
     Additionally, the systems and methods described herein may use the positional data regardless of how fast or slow the vehicle system is accelerating. For example, the systems and methods described herein may not place a lower limit and/or an upper limit on the acceleration of the vehicle system, where changes in speeds below and/or above these limits, as appropriate, prevent the calculation of reference speeds, wheel diameters, route curvatures, and the like. The systems and methods described herein may continue to obtain positional data and calculate the reference speeds, wheel diameters, route curvatures, and the like, using that data, regardless of fast or slow the vehicle system is changing speeds (e.g., accelerating or decelerating) when the positional data is acquired. 
     In an embodiment, a method (e.g., for controlling a vehicle system) includes determining a vehicle reference speed of the vehicle system traveling along a route using an off-board-based input speed and an onboard-based input speed. The off-board-based input speed may be representative of a moving speed of the vehicle system and may be determined from data received from an off-board device. The onboard-based input speed may be representative of the moving speed of the vehicle system and may be determined from data obtained from an onboard device. The method may include, based at least in part on the vehicle reference speed, at least one of determining wheel creep for one or more wheels of the vehicle system or controlling at least one of torques applied by or rotational speeds of one or more motors of the vehicle system. The wheel creep may be determined by measuring the wheel creep, estimating the wheel creep, calculating the wheel creep, and the like. 
     In one aspect, the method may include controlling a speed of rotation of one or more axles of the vehicle system based at least in part on the vehicle reference speed. In one aspect, the wheel creep may be calculated using the vehicle reference speed and the speed of rotation of the one or more axles of the vehicle system. In one aspect, the method may include determining an uncertainty parameter of the off-board-based input speed. The uncertainty parameter may be representative of a potential inaccuracy of the off-board-based input speed and of a range of potential actual speeds of the vehicle system. The uncertainty parameter may be derived from the data received from the off-board-based input device. In one aspect, the method may include modifying the off-board-based input speed using the onboard-based input speed responsive to determining that the onboard-based input speed may be within the range of potential actual speeds that may be represented by the uncertainty parameter. 
     In one aspect, the method may include determining an estimated reference speed during time periods between when the off-board-based input speed is obtained or calculated and controlling the at least one of torques applied by or rotational speeds of the one or more motors using the estimated reference speed during the time periods between when the off-board-based input speed is obtained or calculated. In one aspect, the estimated reference speed is determined using a mass of the vehicle system and a resistive force exerted on the vehicle system. In one aspect, the estimated reference speed is determined by extrapolating from previously determined vehicle reference speeds and using at least one of the mass of the vehicle system, the resistive force exerted on the vehicle system, or previous tractive efforts applied by the one or more motors. 
     In an embodiment, a vehicle control system includes a vehicle controller configured to obtain an off-board-based input speed and an onboard-based input speed of a vehicle system traveling along a route. The off-board-based input speed is representative of a moving speed of the vehicle system and is determined from data received from an off-board device. The onboard-based input speed is representative of the moving speed of the vehicle system and is determined from data obtained from an onboard device. The vehicle controller also is configured to at least one of determine wheel creep for one or more wheels of the vehicle system based on the vehicle reference speed or control at least one of torques applied by or rotational speeds of one or more motors of the vehicle system based on the vehicle reference speed. 
     In one aspect, the vehicle controller is configured to control a speed of rotation of one or more axles of the vehicle system based at least in part on the vehicle reference speed. In one aspect, the vehicle controller is configured to calculate the wheel creep using the vehicle reference speed and the speed of rotation of the one or more axles of the vehicle system. In one aspect, the vehicle controller is configured to determine an uncertainty parameter of the off-board-based input speed that is representative of a potential inaccuracy of the off-board-based input speed and of a range of potential actual speeds of the vehicle system. The uncertainty parameter is derived from the data received from the off-board-based input device. 
     In one aspect, the vehicle controller is configured to modify the off-board-based input speed using the onboard-based input speed responsive to determining that the onboard-based input speed is within the range of potential actual speeds that is represented by the uncertainty parameter. In one aspect, the vehicle controller is configured to determine an estimated reference speed during time periods between when the off-board-based input speed is obtained or calculated. The vehicle controller also may be configured to control the at least one of torques applied by or rotational speeds of the one or more motors using the estimated reference speed during the time periods between when the off-board-based input speed is obtained or calculated. 
     In one aspect, the vehicle controller is configured to determine the estimated reference speed using a mass of the vehicle system and a resistive force exerted on the vehicle system. In one aspect, the vehicle controller is configured to determine the estimated reference speed by extrapolating from previously determined vehicle reference speeds and using at least one of the mass of the vehicle system, the resistive force exerted on the vehicle system, or previous tractive efforts applied by the one or more motors. 
     In an embodiment, a method (e.g., for controlling a vehicle system) includes controlling a rotational speed at which a first axle of a vehicle system is rotated by a first motor based on a throttle setting of the vehicle system and a first vehicle reference speed. The first vehicle reference speed is determined from a group of input speeds that includes an onboard-based input speed and an off-board-based input speed. The method may include controlling a rotational speed at which at least a second axle of the vehicle system is rotated by a second motor based on the throttle setting and a second vehicle reference speed. The second vehicle reference speed is determined from the onboard-based input speed. The rotational speeds of the first axle and the at least a second axle are controlled based on the respective first and second vehicle reference speeds. In one aspect, the method may include determining the first vehicle reference speed by identifying, based on whether the vehicle system is motoring or braking, a selected input speed of the group of input speeds for use as the first vehicle reference speed. In one aspect, the selected input speed is identified as the input speed in the group that is faster than one or more other input speeds in the group when the vehicle system is braking. In one aspect, the selected input speed is identified as the input speed in the group that is slower than one or more other input speeds in the group when the vehicle system is motoring. 
     In an embodiment, a method includes obtaining an off-board-based input speed of a vehicle system as the vehicle system travels along a route. The off-board-based input speed is obtained from signals received from one or more off-board devices and is representative of a speed of the vehicle system traveling along the route. The method may include measuring one or more non-satellite-based input speeds of the vehicle system as the vehicle system travels along the route. The one or more non-satellite-based input speeds are representative of speeds at which one or more wheels of the vehicle system rotate as the vehicle system travels along the route. The method further includes determining a first vehicle reference speed from a group of input speeds that includes at least one of the non-satellite-based input speeds and an estimated velocity of the vehicle system that is derived from the satellite-based input speed. The method includes determining a second vehicle reference speed from the one or more non-satellite-based input speeds and controlling a speed at which a first axle of the vehicle system is rotated by a first motor based on a throttle setting of the vehicle system and the first vehicle reference speed. The method further includes controlling a speed at which at least a second axle of the vehicle system is rotated by a second motor based on the throttle setting and the second vehicle reference speed. The speeds of the first axle and the at least a second axle are concurrently controlled based on the respective first and second vehicle reference speeds. 
     In one aspect, determining the first vehicle reference speed includes identifying a selected input speed of the group of input speeds for use as the first vehicle reference speed based on whether the vehicle system is motoring or braking. In one aspect, the selected input speed is identified as the input speed in the group that is faster than one or more other input speeds in the group when the vehicle system is braking. In one aspect, the selected input speed is identified as the input speed in the group that is slower than one or more other input speeds in the group when the vehicle system is motoring. In one aspect, obtaining the satellite-based input speed includes receiving position and/or velocity data signals from one or more global positioning system (GPS) satellites and determining the satellite-based input speed from the position and/or velocity data signals. 
     In one aspect, the method determines an uncertainty parameter of the satellite-based input speed that is indicative of a potential difference between the satellite-based input speed and the actual speed of the vehicle system and calculating the estimated velocity of the vehicle system using the uncertainty parameter and a tractive effort generated by the vehicle system. In one aspect, the vehicle system may be a rail vehicle in consist. In one aspect, at least one of obtaining the satellite-based input speed, determining the first vehicle reference speed, determining the second vehicle reference speed, controlling the speed at which the first axle is rotated, or controlling the speed at which the second axle is rotated is performed by one or more processors. 
     In an embodiment, a vehicle control system includes a vehicle controller, one or more speed sensors, and one or more inverter controllers. The vehicle controller is configured to obtain a satellite-based input speed of a vehicle system as the vehicle system travels along a route. The satellite-based input speed is obtained from signals received from one or more satellites and representative of a speed of the vehicle system traveling along the route. The one or more speed sensors are configured to measure one or more non-satellite-based input speeds of the vehicle system as the vehicle system travels along the route. The one or more non-satellite-based input speeds are representative of speeds at which one or more wheels of the vehicle system rotate as the vehicle system travels along the route. The one or more inverter controllers are configured to control speeds at which at least first and second axles of the vehicle system are rotated by at least first and second respective motors. The vehicle controller also is configured to determine a first vehicle reference speed and a second vehicle reference speed. The first vehicle reference speed is selected from a group of input speeds that includes at least one of the non-satellite-based input speeds and an estimated velocity of the vehicle system that is derived from the satellite-based input speed. The second vehicle reference speed is selected from the one or more non-satellite-based input speeds. The one or more inverter controllers also are configured to concurrently control the speed at which the first axle is rotated by the first motor based on a throttle setting of the vehicle system and the first vehicle reference speed and to control the speed at which at least the second axle of the vehicle system is rotated by the second motor based on the throttle setting and the second vehicle reference speed. 
     In one aspect, the vehicle controller is configured to determine the first vehicle reference speed by identifying a selected input speed of the group of input speeds for use as the first vehicle reference speed based on whether the vehicle system is motoring or braking. In one aspect, the selected input speed is identified by the vehicle controller as the input speed in the group that is faster than one or more other input speeds in the group when the vehicle system is braking. In one aspect, the selected input speed is identified by the vehicle controller as the input speed in the group that is slower than one or more other input speeds in the group when the vehicle system is motoring. In one aspect, the vehicle controller obtains the satellite-based input speed by receiving position data signals from one or more global positioning system (GPS) satellites and determining the satellite-based input speed from the position and/or velocity data signals. 
     In one aspect, the vehicle controller is configured to determine an uncertainty parameter of the satellite-based input speed that is indicative of a potential difference between the satellite-based input speed and the actual speed of the vehicle system and to calculate the estimated velocity of the vehicle system using the uncertainty parameter and a tractive effort generated by the vehicle system. In an embodiment, a method includes deriving a first input speed of a vehicle having at least first and second axles and traveling along a route from position data obtained by a global positioning system (GPS) receiver, deriving at least a second input speed of the vehicle from a wheel speed of one or more wheels joined to the second axle of the vehicle as the vehicle travels along the route, and controlling a first speed at which the first axle of the vehicle is rotated to propel the vehicle using a first vehicle reference speed. The first vehicle reference speed is selected from a first group of input speeds that includes the first input speed and the at least a second input speed. The method may include controlling a second speed at which the second axle of the vehicle is concurrently rotated to propel the vehicle using a second vehicle reference speed. The second vehicle reference speed is obtained from a second group of input speeds that excludes the first input speed. 
     In one aspect, the first input speed represents an estimated velocity of the vehicle that is calculated from at least a tractive effort generated by the vehicle to propel the vehicle and an uncertainty parameter of the position and/or velocity data. The uncertainty parameter is representative of a potential error between the estimated velocity and an actual speed at which the vehicle is moving along the route. In one aspect, the first vehicle reference speed is selected as the input speed that is slower than one or more other input speeds in the first group of input speeds when the vehicle is generating the tractive effort to propel the vehicle. In one aspect, the first vehicle reference speed is selected as the input speed that is faster than one or more other input speeds in the first group of input speeds when the vehicle is generating braking effort to slow or stop movement of the vehicle. In one aspect, the first input speed represents an upper limit on an estimated velocity of the vehicle as calculated from the position data. The first vehicle reference speed is selected as the input speed in the first group of input speeds that is slower of the upper limit on the estimated velocity and the at least a second input speed when the vehicle is motoring. In one aspect, the first input speed represents a lower limit on an estimated velocity of the vehicle as calculated from the position data. The first vehicle reference speed is selected as the input speed in the first group of input speeds that is faster of the lower limit on the estimated velocity and the at least a second input speed when the vehicle is braking. In one aspect, at least one of the deriving the first input speed, deriving the at least a second speed, controlling the first speed, or controlling the second speed is performed by one or more processors. 
     In one aspect, the controller may provide to a display device one or more of a location of the vehicle system along a route; a determined speed limit for the vehicle system for at least a segment of the route; an optimal speed of the vehicle system based on fuel consumption, equipment wear, arrival time, or an engine emission rate; the reference speed of the vehicle system; a scale factor that determines a current wheel size when applied to a static reference wheel size based at least in part on differential values of the off-board-based input speed and the onboard-based input speed; a current wheel size for one or more wheels of the vehicle system; a wheel creep for one or more wheels of the vehicle system; a torque value as applied by one or more motors of the vehicle system; or a rotational speed of one or more motors or axles of the vehicle system. 
     As used herein, an element or step recited in the singular and proceeded with the word “a” or “an” should be understood as not excluding plural of said elements or steps, unless such exclusion is explicitly stated. Furthermore, references to “one embodiment” of the present inventive subject matter are not intended to be interpreted as excluding the existence of additional embodiments that also incorporate the recited features. Moreover, unless explicitly stated to the contrary, embodiments “comprising,” “including,” or “having” an element or a plurality of elements having a particular property may include additional such elements not having that property. 
     It is to be understood that the above description is intended to be illustrative, and not restrictive. For example, the above-described embodiments (and/or aspects thereof) may be used in combination with each other. In addition, many modifications may be made to adapt a particular situation or material to the teachings of the inventive subject matter without departing from its scope. While the dimensions and types of materials described herein are intended to define the parameters of the inventive subject matter, they are by no means limiting and are exemplary embodiments. Many other embodiments will be apparent to one of ordinary skill in the art upon reviewing the above description. The scope of the inventive subject matter should, therefore, be determined with reference to the appended claims, along with the full scope of equivalents to which such claims are entitled. In the appended claims, the terms “including” and “in which” are used as the plain-English equivalents of the respective terms “comprising” and “wherein.” Moreover, in the following claims, the terms “first,” “second,” and “third,” etc. are used merely as labels, and are not intended to impose numerical requirements on their objects. Further, the limitations of the following claims are not written in means-plus-function format and are not intended to be interpreted based on 35 U.S.C. §112, sixth paragraph, unless and until such claim limitations expressly use the phrase “means for” followed by a statement of function void of further structure. 
     The foregoing description of certain embodiments of the present inventive subject matter will be better understood when read in conjunction with the appended drawings. To the extent that the figures illustrate diagrams of the functional blocks of various embodiments, the functional blocks are not necessarily indicative of the division between hardware circuitry. Thus, for example, one or more of the functional blocks (for example, processors or memories) may be implemented in a single piece of hardware (for example, a general purpose signal processor, microcontroller, random access memory, hard disk, and the like). Similarly, the programs may be standalone programs, may be incorporated as subroutines in an operating system, may be functions in an installed software package, and the like. The various embodiments are not limited to the arrangements and instrumentality shown in the drawings. 
     This written description uses examples to disclose several embodiments of the inventive subject matter and also to enable one of ordinary skill in the art to practice the embodiments of inventive subject matter, including making and using any devices or systems and performing any incorporated methods. The patentable scope of the inventive subject matter is defined by the claims, and may include other examples that occur to one of ordinary skill in the art. Such other examples are intended to be within the scope of the claims if they have structural elements that do not differ from the literal language of the claims, or if they include equivalent structural elements with insubstantial differences from the literal languages of the claims.