Method and apparatus for determining a satellite attitude using crosslink reference signals

1. A method of determining the attitude of a first satellite, comprising the steps of:

receiving a crosslink signal from a second satellite;

computing a measured vector {circumflex over (r)} Body between the first satellite and the second satellite from the crosslink signal;

computing a predicted vector {tilde over (r)} Body between the first satellite and the second satellite;

computing crosslink measurement residuals Δr as a difference between the computed predicted vector between the first satellite and the second satellite and the computed measured vector between the first satellite and the second satellite {circumflex over (r)} Body −{tilde over (r)} Body ;

computing estimated attitude errors from a current estimated attitude, the crosslink measurement residuals, and position sensor measurement residuals, wherein the position sensor measurement residuals are computed from the current estimated attitude the attitude position sensor error parameters and the crosslink measurement residuals Δr; and

correcting and propagating the current estimated satellite attitude using the computed estimated attitude errors.

2. The method of claim 1 , wherein the first satellite and the second satellite are in the same satellite constellation.

3. The method of claim 1 , wherein the first satellite and the second satellite are in different satellite constellations.

4. The method of claim 1 , wherein the measured vector between the first satellite and the second satellite is computed according to {circumflex over (r)} Body =[Ĉ Body — GB ]{circumflex over (r)} GB , wherein [Ĉ Body — GB ] is a 3×3 direction cosine matrix representing a known attitude between a reference frame of a device receiving the crosslink signal and a satellite body reference frame of the satellite and {circumflex over (r)} GB is a vector from between the antenna and the second satellite.

5. The method of claim 4 , wherein the predicted vector {tilde over (r)} Body between the first satellite and the second satellite is computed from a current first spacecraft position vector, the second satellite position vector and the satellite attitude.

6. The method of claim 5 , wherein the predicted vector between the first satellite and the second satellite is computed according to,

[

C

^

Body_ECI

]

⁢

R

~

2

ECI

-

R

~

1

ECI



R

~

2

ECI

-

R

~

1

ECI



wherein {tilde over (R)} 1 ECI is the current first spacecraft position vector, {tilde over (R)} 2 ECI is the current second satellite position vector, and [{tilde over (C)} Body — ECI ] is a 3×3 direction cosine matrix representing the bus inertial attitude.

7. The method of claim 6 , wherein the computed estimated attitude errors are computed using a Kalman filter.

8. An apparatus for determining the attitude of a first satellite, comprising:

a receiver, disposed on a first satellite, the receiver for receiving a crosslink signal from a second satellite;

a processor, having a plurality of modules, including:

a first module for computing a measured vector {circumflex over (r)} Body between the first satellite and the second satellite from the crosslink signal;

a second module for computing a predicted vector {tilde over (r)} Body between the first satellite and the second satellite;

a third module for computing crosslink measurement residuals Δr as a difference between the computed predicted vector between the first satellite and the second satellite and the computed measured vector between the first satellite and the second satellite {circumflex over (r)} Body −{tilde over (r)} Body ;

a third module for computing estimated attitude errors from a current estimated attitude, the crosslink measurement residuals, and position sensor measurement residuals, wherein the position sensor measurement residuals are computed from the current estimated attitude the position sensor error parameters and the crosslink measurement residuals Δr; and

a fourth module for correcting and propagating the current estimated satellite attitude using the computed estimated attitude errors.

9. The apparatus of claim 8 , wherein the first satellite and the second satellite are in the same satellite constellation.

10. The apparatus of claim 8 , wherein the first satellite and the second satellite are in different satellite constellations.

11. The apparatus of claim 8 , wherein the measured vector between the first satellite and the second satellite is computed according to {circumflex over (r)} Body =[Ĉ Body — GB ]{circumflex over (r)} GB , wherein [Ĉ Body — GB ] is a 3×3 direction cosine matrix representing a known attitude between a reference frame of an antenna receiving the crosslink signal and a satellite body reference frame of the satellite and {circumflex over (r)} GB is a vector between the antenna and the second satellite.

12. The apparatus of claim 11 , wherein the predicted vector {tilde over (r)} Body between the first satellite and the second satellite is computed from a current first spacecraft position vector, the second satellite position vector and the satellite attitude.

13. The apparatus of claim 12 , wherein the predicted vector between the first satellite and the second satellite is computed according to

[

C

^

Body_ECI

]

⁢

R

~

2

ECI

-

R

~

1

ECI



R

~

2

ECI

-

R

~

1

ECI



,

wherein {tilde over (R)} 1 ECI is the current first spacecraft position vector, {tilde over (R)} 2 ECI is the current second satellite position vector, and [{tilde over (C)} Body — ECI ] is a 3×3 direction cosine matrix representing the bus inertial attitude.

14. The apparatus of claim 13 , wherein the computed estimated attitude errors are computed using a Kalman filter.

15. An apparatus of determining the attitude of a first satellite, comprising:

means capable of receiving a crosslink signal from a second satellite;

means capable of computing a measured vector {circumflex over (r)} Body between the first satellite and the second satellite from the crosslink signal;

means capable of computing a predicted vector {tilde over (r)} Body between the first satellite and the second satellite;

means capable of computing crosslink measurement residuals Δr as a difference between the computed predicted vector between the first satellite and the second satellite and the computed measured vector between the first satellite and the second satellite {circumflex over (r)} Body −{tilde over (r)} Body ;

means capable of computing estimated attitude errors from a current estimated attitude, the crosslink measurement residuals, and position sensor measurement residuals, wherein the position sensor measurement residuals are computed from the current estimated attitude the position sensor error parameters and the crosslink measurement residuals Δr; and

means capable of correcting and propagating the current estimated satellite attitude using the computed estimated attitude errors.

16. The apparatus of claim 15 , wherein the first satellite and the second satellite are in the same satellite constellation.

17. The apparatus of claim 15 , wherein the first satellite and the second satellite are in different satellite constellations.

18. The apparatus of claim 15 , wherein the measured vector between the first satellite and the second satellite is computed according to {circumflex over (r)} Body =[Ĉ Body — GB ]{circumflex over (r)} GB , wherein [Ĉ Body — GB ] is a 3×3 direction cosine matrix representing a known attitude between a reference frame of the means capable of receiving the crosslink signal and a satellite body reference frame of the satellite and {circumflex over (r)} GB is a vector from between the antenna and the second satellite.

19. The apparatus of claim 18 , wherein the predicted vector {tilde over (r)} Body between the first satellite and the second satellite is computed from a current first spacecraft position vector, the second satellite position vector and the satellite attitude.

20. The apparatus of claim 19 , wherein the predicted vector between the first satellite and the second satellite is computed according to

[

C

^

Body_ECI

]

⁢

R

~

2

ECI

-

R

~

1

ECI



R

~

2

ECI

-

R

~

1

ECI



,

wherein {tilde over (R)} 1 ECI is the current first spacecraft position vector, {tilde over (R)} 2 ECI is the current second satellite position vector, and [{tilde over (C)} Body — ECI ] is a 3×3 direction cosine matrix representing the bus inertial attitude.

21. The apparatus of claim 20 , wherein the computed estimated attitude errors are computed using a Kalman filter.

22. The apparatus of claim 15 , wherein the receiver is gimbaled, and wherein the measured vector between the first satellite and the second satellite is computed from the angle of the gimbal.