Coning compensation in strapdown inertial navigation systems

• US 5,828,980 A
• Filed: 07/01/1997
• Issued: 10/27/1998
• Est. Priority Date: 03/18/1996
• Status: Expired due to Term

• Current Assignee: Northrop Grumman Systems Corporation (Northrop Grumman Corporation)
• Original Assignee: Litton Systems Incorporated
• Inventors: Tazartes, Daniel A., Mark, John G.
• Primary Examiner(s): ZANELLI, MICHAEL J
• Application Number:
  US08/937,251
• Time in Patent Office: 483 Days
• Field of Search: 701/221, 701/220, 701/207, 702/93
• US Class Current: 701/220
• CPC Class Codes: G01C 21/188 for accumulated errors, e.g. by coupling inertial systems with absolute positioning systems

Abstract

The invention is a method for compensating for coning in a strapdown inertial navigation system which utilizes groups of five successive incremental angles of rotation of a body-fixed coordinate system as measured by orthogonally-mounted gyros at regular measurement intervals, each group of five measurements being obtained during a group interval equal to five measurement intervals. The coning-compensated angular displacement of the body-fixed coordinate system about a fixed axis in space during a p'"'"'th group interval is obtained by summing the five measured incremental angles and a coning compensation term. The coning compensation term consists of the sum of: (1) one-half the cross-product of a first and a second vector sum, the second vector sum being the sum of the five incremental angles of rotation in a group and the first vector sum being the sum of the second vector sum over p groups; and (2) the weighted sum of three vector cross-products, the multiplier and the multiplicand of each vector cross-product being a weighted sum of five measured incremental angles. The coning-compensated angular displacement can be summed over p to obtain an accurate estimate of the vector angle of rotation over a plurality of group intervals.

Claims

1. A coning compensation method for use in a strapdown inertial navigation system, the method utilizing the incremental angles of rotation of a coordinate system expressed as a vector Δ

Θ

(k,n,m) and measured in successive time periods to obtain an estimate of the coning compensation for NK successive time periods, the vector Δ

Θ

(k,n,m) corresponding to the vector angle of rotation for the (mNK+nK+k)'"'"'th data sampling interval of duration T as provided by orthogonally mounted gyros in a body-fixed coordinate system, k taking on integer values from 1 to K, n taking on integer values from 1 to N, m taking on integer values, N and K being predetermined integers, the method comprising the steps;

calculating R(h,m) for K equal to 5 and h equal to 1, 2, and 3, R(h,m) being the vector cross-product of the sum of U(h,k)Δ

Θ

(k,n,m) and the sum of V(h,k)Δ

Θ

(k,n,m), the sums being taken over all values of k and all values of n, U(h,k) and V(h,k) being predetermined numbers for all values of h and k;

calculating R(m), R(m) being the sum of W(h)R(h,m) over all values of h, W(h) being a predetermined number for each value of h where h takes on the values 1, 2, and 3, the estimate of the coning compensation comprising R(m).

2. The coning compensation method of claim 1 further comprising the steps:

calculating Θ

(p,m), Θ

(p,m) being the sum of Δ

Θ

(k,n,m) over k and n, k taking on integer values from 1 to K and n taking on integer values from 1 to p;

calculating R(0,m) for K equal to 5, R(0,m) being the sum over n of the vector cross-product of Θ

(n,m) and the sum over k of Δ

Θ

(k,n,m), the estimate of the coning compensation further comprising 1/2 R(0,m).

3. The coning compensation method of claim 1 wherein W(1) is greater than W(2) and W(3), W(2) being equal to W(3).

4. The coning compensation method of claim 1 wherein either U(1,k)=-U(1,K+1-k) or V(1,k)=-V(1,K+1-k).

5. The coning compensation method of claim 1 wherein either U(1,k)=U(1,K+1-k) or V(1,k)=V(1,K+1-k).

6. The coning compensation method of claim 1 wherein either U(2,k)=V(2,K+1-k) or U(2,k)=V(3,K+1-k).

7. The coning compensation method of claim 1 wherein either U(3,k)=V(2,K+1-k) or U(3,k)=V(3,K+1-k).

8. The coning compensation method of claim 1 wherein either U(2,k)=0 or V(2,k)=0 and either U(3,k)=0 or V(3,k)=0 for all but one value of k.

9. The coning compensation method of claim 1 wherein U(h,k) and U(h,k+1) are opposite in sign for k equal to 2, 3, and 4 and h equal to either 2 or 3 and V(h,k) and V(h,k+1) are opposite in sign for k equal to 1, 2, and 3 and h equal to either 2 or 3.

10. The coning compensation method of claim 1 wherein U(h,k) and V(h,k) are equal to integers for all values of h and for all values of k.

11. The coning compensation method of claim 1 wherein U(1,1)=1, U(1,2)=1, U(1,3)=0, U(1,4)=-1, U(1,5)=-1, U(2,1)=1, U(2,2)=0, U(2,3)=0, U(2,4)=0, U(2,5)=0, U(3,1)=1, U(3,2)=3, U(3,3)=-10, U(3,4)=28, U(3,5)=-22, V(1,1)=1, V(1,2)=1, V(1,3)=3, V(1,4)=1, V(1,5)=1, V(2,1)=-22, V(2,2)=28, V(2,3)=-10, V(2,4)=3, V(2,5)=1, V(3,1)=0, V(3,2)=0, V(3,3)=0, V(3,4)=0, V(3,5)=1.

12. The coning compensation method of claim 1 wherein W(1)=225/1008, W(2)=225/9072, and W(3)=225/9072.

13. A digital processor for use in a strapdown inertial navigation system, the digital processor receiving as inputs the incremental angles of rotation of a coordinate system expressed as a vector Δ

Θ

(k,n,m) and measured in successive time periods to obtain an estimate of the coning compensation for NK successive time periods, the vector Δ

Θ

(k,n,m) corresponding to the vector angle of rotation for the (mNK+nK+k)'"'"'th data sampling interval of duration T as provided by orthogonally mounted gyros in a body-fixed coordinate system, k taking on integer values from 1 to K, n taking on integer values from 1 to N, m taking on integer values, N and K being predetermined integers, the functions performed by the digital processor comprising;

calculating R(h,m) for K equal to 5 and h equal to 1, 2, and 3,R(h,m) being the vector cross-product of the sum of U(h,k)Δ

Θ

(k,n,m) and the sum of V(h,k)Δ

Θ

(k,n,m) the sums being taken over all values of k and all values of n, U(h,k) and V(h,k) being predetermined numbers for all values of h and k;

calculating R(m), R(m) being the sum of W(h)R(h,m) over all values of h, W(h) being a predetermined number for each value of h where h takes on the values 1, 2, and 3, the estimate of the coning compensation comprising R(m).

14. The digital processor of claim 13 wherein W(1)=225/1008, W(2)=225/9072, and W(3)=225/9072.

15. The digital processor of claim 13 wherein the functions performed by the digital processor further comprise:

calculating Θ

(p,m), Θ

(p,m) being the sum of Δ

Θ

(k,n,m) over k and n, k taking on integer values from 1 to K and n taking on integer values from 1 to p;

calculating R(0,m) for K equal to 5, R(0,m) being the sum over n of the vector cross-product of Θ

(n,m) and the sum over k of Δ

Θ

(k,n,m), the estimate of the coning compensation further comprising 1/2 R(0,m).

16. The digital processor of claim 13 wherein W(1) is greater than W(2) and W(3), W(2) being equal to W(3).

17. The digital processor of claim 13 wherein either U(1,k)=-U(1,K+1-k) or V(1,k)=-V(1,K+1-k).

18. The digital processor of claim 13 wherein either U(1,k)=U(1,K+1-k) or V(1,k)=V(1,K+1-k).

19. The digital processor of claim 13 wherein either U(2,k)=V(2,K+1-k) or U(2,k)=V(3,K+1-k).

20. The digital processor of claim 13 wherein either U(3,k)=V(2,K+1-k) or U(3,k)=V(3,K+1-k).

21. The digital processor of claim 13 wherein either U(2,k)=0 or V(2,k)=0 and either U(3,k)=0 or V(3,k)=0 for all but one value of k.

22. The digital processor of claim 13 wherein U(h,k) and U(h,k+1) are opposite in sign for k equal to 2, 3, and 4 and h equal to either 2 or 3 and V(h,k) and V(h,k+1) are opposite in sign for k equal to 1, 2, and 3 and h equal to either 2 or 3.

23. The digital processor of claim 13 wherein U(h,k) and V(h,k) are equal to integers for all values of h and for all values of k.

24. The digital processor of claim 13 wherein U(1,1)=1, U(1,2)=1, U(1,3)=0, U(1,4)=-1, U(1,5)=-1, U(2,1)=1, U(2,2)=0, U(2,3)=0, U(2,4)=0, U(2,5)=0, U(3,1)=1, U(3,2)=3, U(3,3)=-10, U(3,4)=28, U(3,5)=-22, V(1,1)=1, V(1,2)=1, V(1,3)=3, V(1,4)=1, V(1,5)=1, V(2,1)=-22, V(2,2)=28, V(2,3)=-10, V(2,4)=3, V(2,5)=1, V(3,1)=0, V(3,2)=0, V(3,3)=0, V(3,4)=0, V(3,5)=1.