Technique for determining closest point of approach

1. A method of estimating the closest point of approach of an object, comprising:

tracking in a first tracker a range rate of the object based on Doppler measurements of the object obtained at sequential measurement times;

computing for each measurement time a first closest point of approach estimate based on the tracked range rate;

tracking in a second tracker separate from and independent of the first tracker a position of the object based on position measurements of the object obtained at the sequential measurement times;

computing for each measurement time a second closest point of approach estimate based on the tracked position;

computing in a processor a fused closest point of approach estimate based on the first and second closest point of approach estimates; and

reporting, via a user interface, an output closest point of approach estimate based on the fused closest point of approach estimate.

2. The method of claim 1 , further comprising:

tracking in a third tracker the fused closest point of approach estimate, wherein the output closest point of approach estimate is generated as an output of the third tracker.

3. The method of claim 2 , further comprising:

tracking in the third tracker a closest point of approach velocity based on the fused closest point of approach estimate; and

reporting the closest point of approach velocity via the user interface.

4. The method of claim 1 , further comprising:

computing an accuracy of first closest point of approach estimate; and

computing an accuracy of the second closest point of approach estimate,

wherein the fused closest point of approach estimate is computed based on the accuracies of the first and second closest point of approach estimates.

5. The method of claim 1 , further comprising:

computing for each measurement time a first time to closest point of approach estimate based on the tracked range rate;

computing for each measurement time a second time to closest point of approach estimate based on the tracked position; and

computing a fused time to closest point of approach estimate based on the first and second time to closest point of approach estimates.

6. The method of claim 5 , further comprising:

computing an accuracy of the first time to closest point of approach estimate; and

computing an accuracy of the second time to closest point of approach estimate,

wherein the fused time to closest point of approach estimate is computed based on the accuracies of the first and second time to closest point of approach estimates.

7. The method of claim 6 , further comprising:

tracking in a third tracker the fused time to closest point of approach estimate.

8. The method of claim 1 , wherein:

the first tracker is implemented with a first Kalman filter; and

the second tracker is implemented with a second Kalman filter that is independent of the first Kalman filter.

9. The method of claim 1 , wherein tracking the position of the object comprises:

tracking separately each coordinate of the position of the object in a coordinate system by which the position of the object is identified.

10. The method of claim 9 , wherein tracking each coordinate of the position of the object comprises:

tracking separately x, y and z coordinates of the position of the object in the Cartesian coordinate system.

11. An apparatus for estimating the closest point of approach of an object, comprising:

a sensor system configured to generate Doppler and position measurements of an object at each of sequential measurement times;

a processor configured to: track a range rate of the object based on the Doppler measurements; track a position of the object based on the position measurements independently of the range rate tracking; compute for each measurement time first and second closest point of approach estimates respectively based on the tracked range rate and position; and compute a fused closest point of approach estimate based on the first and second closest point of approach estimates; and

a user interface configured to report an output closest point of approach estimate based on the fused closest point of approach estimate.

12. The apparatus of claim 11 , wherein the processor is further configured to track the fused closest point of approach estimate to generate the output closest point of approach estimate.

13. The apparatus of claim 12 , wherein the processor is further configured to track a closest point of approach velocity based on the fused closest point of approach estimate, and wherein the user interface is configured to report the closest point of approach velocity.

14. The apparatus of claim 11 , wherein the processor is further configured to:

compute an accuracy of the first closest point of approach estimate and an accuracy of the second closest point of approach estimate; and

compute the fused closest point of approach estimate based on the accuracies of the first and second closest point of approach estimates.

15. The apparatus of claim 11 , wherein the processor is further configured to:

compute for each measurement time a first time to closest point of approach estimate based on the tracked range rate;

compute for each measurement time a second time to closest point of approach estimate based on the tracked position; and

compute a fused time to closest point of approach estimate based on the first and second time to closest point of approach estimates.

16. The apparatus of claim 15 , wherein the processor is further configured to:

compute an accuracy of the first time to closest point of approach estimate;

compute an accuracy of the second time to closest point of approach estimate; and

compute the fused time to closest point of approach estimate based on the accuracies of the first and second time to closest point of approach estimates.

17. The apparatus of claim 16 , wherein the processor is further configured to track the fused time to closest point of approach estimate.

18. The apparatus of claim 11 , wherein the processor is further configured to:

implement a first Kalman filter to track the range rate of the object; and

implement a second Kalman filter to track the position of the object.

19. A non-transitory processor readable medium storing instructions that, when executed by a processor, cause the processor to:

track a range rate of the object based on Doppler measurements of the object obtained at sequential measurement times;

compute for each measurement time a first closest point of approach estimate based on the tracked range rate; track, independently of the range rate tracking, a position of the object based on position measurements of the object obtained at the sequential measurement times;

compute for each measurement time a second closest point of approach estimate based on the tracked position; and

compute a fused closest point of approach estimate based on the first and second closest point of approach estimates.

20. The processor readable medium of claim 19 , storing further instructions that, when executed by the processor, further cause the processor to:

track the fused closest point of approach estimate.

21. The processor readable medium of claim 20 , storing further instructions that, when executed by the processor, further cause the processor to:

track a closest point of approach velocity based on the fused closest point of approach estimate.

22. The processor readable medium of claim 19 , storing further instructions that, when executed by the processor, further cause the processor to:

compute an accuracy of the first closest point of approach estimate;

compute an accuracy of the second closest point of approach estimate; and

compute the fused closest point of approach estimate based on the accuracies of the first and second estimates.

23. The processor readable medium of claim 19 , storing further instructions that, when executed by the processor, further cause the processor to:

compute for each of the measurement times a first time to closest point of approach estimate based on the tracked range rate;

compute for each of the measurement times a second time to closest point of approach estimate based on the tracked position; and

compute a fused time to closest point of approach estimate based on the first and second time to closest point of approach estimates.

24. A method of estimating the closest point of approach between a sensor platform and an object, comprising:

tracking in a tracker a time derivative of range R to the object as range rate {dot over (R)} and a time derivative of range rate {umlaut over (R)} of the object based on Doppler measurements of the object;

computing in a processor a closest point of approach estimate CPA based on the tracked range rate {dot over (R)}, the tracked time derivative of range rate {umlaut over (R)}, and the range R to the object according to the expression:

CPA

=

R

3

⁢

R

¨

R

.

2

+

R

⁢

R

¨

;

⁢

and

reporting, via a user interface, an output closest point of approach estimate based on the closest point of approach estimate CPA.

25. The method of claim 24 , further comprising:

computing in the processor a time to closest point of approach estimate TCPA according to the expression:

TCPA

Truth

=

R

R

.

⁢

(

1

-

CPA

2

R

2

)

.

26. A method of estimating the closest point of approach between a sensor platform and an object, comprising:

tracking in a tracker a position and velocity of the object based on position measurements of the object, wherein the position and velocity of the object are tracked along x, y, and z axes of a coordinate system;

computing in a processor a time to closest point of approach between the sensor platform and the object;

computing in the processor a closest point of approach estimate CPA according to the expression:

CPA=((Δ x+Δ{dot over (x)} *TCPA) 2 +(Δ y+Δ{dot over (y)} *TCPA) 2 +(Δ z+Δż *TCPA) 2 ) ½

where Δx and Δ{dot over (x)} are the position and velocity differences, respectively, between the sensor platform and the object along the x axis, Δy and Δ{dot over (y)} are the position and velocity differences, respectively, between the sensor platform and the object along the y axis, Δz and Δż are the position and velocity differences, respectively, between the sensor platform and the object along the z axis, and TCPA is the computed time to closest point of approach; and

reporting, via a user interface, an output closest point of approach estimate based on the closest point of approach estimate CPA.

27. The method of claim 26 , wherein the time to closest point of approach TCPA is computed by the expression:

TCPA

=

-

Δ

⁢

⁢

x

⁢

⁢

Δ

⁢

⁢

x

.

+

Δ

⁢

⁢

y

⁢

⁢

Δ

⁢

⁢

y

.

+

Δ

⁢

⁢

z

⁢

⁢

Δ

⁢

⁢

z

.

Δ

⁢

⁢

x

.

2

+

Δ

⁢

⁢

y

.

2

+

Δ

⁢

⁢

z

.

2

.