Methods and systems for determining vehicle position in an automatic vehicle identification system

1. A method of estimating vehicle location in a roadway using an automatic vehicle identification system, the system including an antenna defining a coverage area for communicating with a transponder mounted to a vehicle in the roadway, the method comprising:

receiving a set of response signals from the transponder at points in time and determining a range rate of the transponder relative to the antenna at each point in time to obtain a plurality of range rates;

identifying a minima in the magnitude of the plurality of range rates;

estimating a first position of the transponder at a first time corresponding to the occurrence of the minima;

estimating a velocity of the vehicle based upon one or more of the plurality of range rates; and

estimating a second position of the transponder based upon the first position and the velocity.

2. The method claimed in claim 1 , wherein a range rate of the plurality of range rates of the transponder relative to the antenna comprises the rate of change of a distance between the transponder and the antenna, and wherein the antenna is elevated above the roadway.

3. The method claimed in claim 1 , wherein determining the range rate of the transponder relative to the antenna at each point in time comprises measuring the Doppler shift in the response signal at each point in time.

4. The method claimed in claim 1 , wherein identifying a minima in the magnitude of the plurality of range rates comprises finding a best fit curve using the plurality of range rates.

5. The method of claim 4 , wherein finding the best fit curve includes using least squared error to select the best fit curve, and wherein identifying the minima in the magnitude includes finding a zero-crossing point of the best fit curve.

6. The method claimed in claim 1 , wherein estimating the velocity comprises selecting a bounded set of velocities and selecting the velocity within the bounded set that corresponds to the plurality of range rates determined to have occurred.

7. The method claimed in claim 6 , wherein selecting the bounded set of velocities includes determining the time during which the transponder was in communication with the antenna, determining a bounded range of possible lengths for the coverage area, and determining the bounded set of velocities based upon the bounded range of possible lengths and the time during which the transponder was in communication with the antenna.

8. The method claimed in claim 1 , wherein estimating the second position is further based upon a bounded range of cross-track offsets, wherein the cross-track offset is a distance, in a plane parallel to the roadway, between a trajectory of the transponder and a center of the antenna, wherein the distance is orthogonal to the trajectory.

9. The method claimed in claim 1 , wherein estimating the second position is further based upon a bounded range of possible angles of a trajectory of the transponder to a centerline of the roadway.

10. The method claimed in claim 1 , wherein estimating the velocity comprises estimating the velocity at a second point in time, and wherein the method further comprises estimating a second velocity of the vehicle at another time based upon one or more of the plurality of range rates, and estimating a third position of the transponder based upon the first position and the second velocity.

11. The method claimed in claim 1 , further comprising determining a likely position of the transponder at a selected time based upon the estimates for the velocity, the first position and the second position.

12. The method claimed in claim 11 , wherein the likely position of the transponder is outside the coverage area.

13. The method claimed in claim 1 , further comprising determining a time and a location at which the transponder likely passed a vehicle detection line across the roadway, based upon the estimates for the velocity, the first position and the second position.

14. An automatic vehicle identification system for identifying the position in a roadway of a vehicle, the system comprising:

an antenna for communicating with a transponder mounted to the vehicle in the roadway;

a transceiver for broadcasting a continuous wave signal over the antenna and for receiving response signals from the transponder;

a memory storing vehicle position locating instructions; and

a processor, which when executing the vehicle position locating instructions, is configured to:

determine a plurality of range rates of the transponder relative to the antenna based upon response signals received at points in time,

identify a minima in the magnitude of the plurality of range rates,

estimate a first position of the transponder at a first time corresponding to the occurrence of the minima,

estimate a velocity of the vehicle based upon one or more of the plurality of range rates, and

estimate a second position of the transponder based upon the first position and the velocity.

15. The system claimed in claim 14 , wherein a range rate of the plurality of range rates of the transponder relative to the antenna comprises the rate of change of a distance between the transponder and the antenna, and wherein the antenna is elevated above the roadway.

16. The system claimed in claim 14 , wherein the processor is configured to determine the range rate of the transponder relative to the antenna at each point in time by measuring the Doppler shift in the response signal at each point in time.

17. The system claimed in claim 14 , wherein the processor is configured to identify a minima in the magnitude of the plurality of range rates by finding a best fit curve using the plurality of range rates.

18. The system claimed in claim 17 , wherein finding the best fit curve includes using least squared error to select the best fit curve, and wherein the processor identifies the minima in the magnitude by finding a zero-crossing point of the best fit curve.

19. The system claimed in claim 14 , wherein the processor is configured to estimate the velocity by selecting a bounded set of velocities and selecting the velocity within the bounded set that corresponds to the plurality of range rates determined to have occurred.

20. The system claimed in claim 19 , wherein selecting the bounded set of velocities includes determining the time during which the transponder was in communication with the antenna, determining a bounded range of possible lengths for the coverage area, and determining the bounded set of velocities based upon the bounded range of possible lengths and the time during which the transponder was in communication with the antenna.

21. The system claimed in claim 14 , wherein the processor is configured to estimate the second position further based upon a bounded range of cross-track offsets, wherein the cross-track offset is a distance, in a plane parallel to the roadway, between a trajectory of the transponder and a center of the antenna, and wherein the distance is orthogonal to the trajectory.

22. The system claimed in claim 14 , wherein the processor is configured to estimate the second position further based upon a bounded range of possible angles of a trajectory of the transponder to a centerline of the roadway.

23. The system claimed in claim 14 , wherein the processor is configured to estimate the velocity by estimating the velocity at a second point in time, and wherein the processor is further configured to estimate a second velocity of the vehicle at another time based upon one or more of the plurality of range rates, and to estimate a third position of the transponder based upon the first position and the second velocity.

24. The system claimed in claim 14 , wherein the processor is further configured to determine a likely position of the transponder at a selected time based upon the estimates for the velocity, the first position and the second position.

25. The system claimed in claim 24 , wherein the likely position of the transponder is outside the coverage area.

26. The system claimed in claim 14 , wherein the processor is further configured to determine a time and a location at which the transponder likely passed a vehicle detection line across the roadway, based upon the estimates for the velocity, the first position and the second position.

27. A non-transitory computer-readable medium storing processor-executable instructions which, when executed, cause a processor to carry out the method claimed in claim 1 .