Object velocity vector estimation by multiple radars with different observation angles

1. A method of estimating operating a vehicle, comprising:

obtaining a plurality of velocity hypotheses based on a coarse estimate of a velocity of an object with respect to the vehicle;

determining a likelihood map for each of the plurality of velocity hypotheses;

determining a likelihood score for each of the plurality of velocity hypotheses from the likelihood maps, the likelihood score of a velocity hypothesis being a difference between an entropy term of the likelihood map and a sum of probabilities for the likelihood map;

selecting, as an estimate of the velocity of the object, the velocity hypothesis having an extremum likelihood score from the plurality of velocity hypotheses; and

operating the vehicle to navigate with respect to the object based on the selected velocity hypothesis.

2. The method of claim 1 , wherein the plurality of velocity hypotheses are within an ellipse having eigenvectors of a covariance matrix of the coarse estimate as axes.

3. The method of claim 1 , wherein the sum of probabilities is a sum of a square of probabilities for each pixel of the likelihood map.

4. The method of claim 1 , further comprising selecting the velocity hypothesis for which the likelihood score is a lowest of the likelihood scores.

5. The method of claim 1 , further comprising:

obtaining a measurement of Doppler frequency for the object at each of a plurality of spaced apart radars; and

determining the coarse estimate of the velocity of the object from the Doppler frequencies.

6. The method of claim 5 , further comprising determining the coarse estimate of velocity from the Doppler frequencies and angular locations of the object with respect to each of the plurality of spaced-apart radars.

7. The method of claim 1 , further comprising generating a search grid from the coarse estimate and selecting the velocity hypotheses from an area within the search grid.

8. A system for operating a vehicle, comprising:

a plurality of radars associated with the vehicle for providing a coarse estimate of a velocity of an object with respect to the vehicle;

a processor configured to:

obtain a plurality of velocity hypotheses based on the coarse estimate of the velocity of the object;

determine a likelihood map for each of the plurality of velocity hypotheses;

determine a likelihood score for each of the plurality of velocity hypotheses from the likelihood maps, the likelihood score of a velocity hypothesis being a difference between an entropy term of the likelihood map and a sum of probabilities for the likelihood map;

select, as an estimate of the velocity of the object, the velocity hypothesis having an extremum likelihood score from the plurality of velocity hypotheses; and

operate the vehicle to navigate with respect to the object based on the selected velocity hypothesis.

9. The system of claim 8 , wherein the processor obtains the plurality of velocity hypotheses from within an ellipse having eigenvectors of a covariance matrix of the coarse estimate as axes.

10. The system of claim 8 , wherein the sum of probabilities is a sum of a square of probabilities for each pixel of the likelihood map.

11. The system of claim 8 , wherein the processor further chooses the velocity hypothesis for which the likelihood score is a lowest of the likelihood scores.

12. The system of claim 8 , wherein the plurality of radars obtain measurements of Doppler frequency for the object, and the processor is configured to determine the coarse estimate of the velocity of the object from the Doppler frequencies.

13. The system of claim 12 , wherein processor is further configured to determine the coarse estimate of velocity from the Doppler frequencies and angular locations of the object with respect to each of the plurality of spaced-apart radars.

14. The system of claim 8 , wherein the processor is configured to generate a search grid from the coarse estimate and select the velocity hypotheses from an area within the search grid.

15. A vehicle, comprising:

a plurality of radars associated with the vehicle for providing a coarse estimate of a velocity of an object with respect to the vehicle; and

a processor configured to:

generate a search grid based on the coarse estimate;

generate a plurality of velocity hypotheses within the search grid based on the coarse estimate;

determine a likelihood map for each of the plurality of velocity hypotheses;

determine a likelihood score for each of the plurality of velocity hypotheses from the likelihood maps, the likelihood score of a velocity hypothesis being a difference between an entropy term of the likelihood map and a sum of probabilities for the likelihood map;

select, as an estimate of the velocity of the object, the velocity hypothesis having an extremum likelihood score from the plurality of velocity hypotheses; and

operate the vehicle to navigate with respect to the object based on the selected velocity hypothesis.

16. The vehicle of claim 15 , wherein the processor is further configured to generate the plurality of velocity hypotheses within an ellipse on the search grid, the ellipse having eigenvectors of a covariance matrix of the coarse estimate as axes.

17. The vehicle of claim 15 , wherein the sum of probabilities is a sum of a square of probabilities for each pixel of the likelihood map.

18. The vehicle of claim 15 , wherein the plurality of radars obtain measurements of Doppler frequency for the object, and the processor is configured to determine the coarse estimate of the velocity of the object from the Doppler frequencies.

19. The vehicle of claim 16 , wherein processor is further configured to determine the coarse estimate of velocity from the Doppler frequencies and angular locations of the object with respect to each of the plurality of spaced-apart radars.

20. The vehicle of claim 15 , wherein the processor is configured to generate a search grid from the coarse estimate and select the velocity hypotheses from an area within the search grid.