Sculling compensation in strapdown inertial navigation systems

• US 5,890,093 A
• Filed: 11/01/1996
• Issued: 03/30/1999
• Est. Priority Date: 11/01/1996
• Status: Expired due to Term

• Current Assignee: Litton Systems Incorporated (Northrop Grumman Corporation), Northrop Grumman Systems Corporation (Northrop Grumman Corporation)
• Original Assignee: Litton Systems Incorporated (Northrop Grumman Corporation)
• Inventors: Tazartes, Daniel A., Mark, John G.
• Primary Examiner(s): ZANELLI, MICHAEL J
• Application Number:
  US08/742,384
• Time in Patent Office: 879 Days
• Field of Search: 701/220, 701/221, 702/94, 702/95, 702/141, 702/151, 702/152
• 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 and apparatus for compensating for sculling in a strapdown inertial navigation system. The method operates on a sequence of inputs ΔV_B (n) derived at times nΔt from the outputs of one or more accelerometers. Separately compensated quantities ΔV_Bc (m,p) calculated at times (pJ+1/2)Δt for M values of m are obtained by summing A(m,k)ΔV_B (pJ-j-k) over k from 0 to K-1 and over j from 0 to J-1 where the constants A(m,k) are chosen to minimize sculling error in the individual ΔV_Nc (m,p) quantities where ΔV_Nc (m,p) is the representation of ΔV_Bc (m,p) in the navigation frame of reference. The final compensated quantity ΔV_Bc (p) is obtained by summing B(m)ΔV_Bc (m,p) over m where the constants B(m) are chosen to minimize sculling error in ΔV_Nc (p) where ΔV_Nc (p) is the representation of ΔV_Bc (p) in the navigation frame of reference.

Claims

1. A method for compensating for sculling in a strapdown inertial navigation system, a sequence of inputs Δ

V_B (n) being derived at times nΔ

t from the outputs of one or more accelerometers, n being an integer and Δ

t being a time interval, the inputs Δ

V_B (n) being compensated for sculling, the compensated outputs being obtained at times (pJ+1/2)Δ

t and being denoted by Δ

V_Bc (m,p), the method comprising the steps;

selecting values for the set A (m,k) in the equation ##EQU32## k taking on values from 0 to K-1, m being equal to 1,j taking on values from 1 to J, J being equal to or greater than 2, p being an integer;

determining the value of Δ

V_Bc (m,p) for each value of p.

2. The method of claim 1 wherein Δ

V_Bc (m,p) is transformed from body to navigation frame by the direction cosine matrix C_B^N evaluated at time pJ-(J+K-2)/2!Δ

t, the navigation frame expression of Δ

V_Bc (m,p) being Δ

V_Nc (m,p).

3. The method of claim 2 wherein the values selected for the set A(m,k) result in the average error in Δ

V_Nc (m,p)/Δ

t caused by inphase sculling being approximately proportional to (ω

Δ

t)^q for values of ω

Δ

t in a range of values less than 1, ω

being the angular frequency of the sculling motion, q being equal to or greater than 4.

4. The method of claim 1 wherein m takes on values from 1 to M, the method further comprising the steps:

selecting values for the set A(m,k) for values of m from 2 to M;

selecting values for the set B(m) for all values of m in the equation ##EQU33## determining the value of Δ

V_Bc (p) for each value of p.

5. The method of claim 4 wherein Δ

V_Bc (p) is transformed from body to navigation frame by the direction cosine matrix C_B^N evaluated at time pJ-(J+K-2)/2!Δ

t, the navigation frame expression of Δ

V_Bc (p) being Δ

V_Nc (p).

6. The method of claim 5 wherein the values selected for the set A(m,k) result in the average error in Δ

V_Nc (m,p)/Δ

t caused by inphase sculling being approximately proportional to (ω

Δ

t)^q for values of ω

Δ

t in a range of values less than 1, ω

being the angular frequency of the sculling motion, q being equal to or greater than 4.

7. The method of claim 6 wherein the values selected for the set B(m) result in the average error in Δ

V_Nc (p)/Δ

t caused by inphase sculling being proportional to (ω

Δ

t)^q for values of ω

Δ

t in a range of values less than 1, ω

being the angular frequency of the sculling motion, q being equal to or greater than 6.

8. The method of claim 4 wherein J=2, K=5, and M=2, the values of A(m,k) being approximately as follows:

A(1,0)=-1/24, A(1,1)=0, A(1,2)=13/12, A(1,3)=0, A(1,4)=-1/24, A(2,0)=0, A(2,1)=-1/6, A(2,2)=4/3, A(2,3)=-1/6, and A(2,4)=0, B(1) being approximately equal to -4/5 and B(2) being approximately equal to 9/5.

9. The method of claim 4 wherein J=4, K=5, and M=2, the values of A(m,k) being approximately as follows:

A(1,0)=-1/6, A(1,1)=0, A(1,2)=4/3, A(1,3)=0, A(1,4)=-1/6, A(2,0)=0, A(2,1)=-2/3, A(2,2)=7/3, A(2,3)=-2/3, and A(2,4)=0, B(1) being approximately equal to -11/5 and B(2) being approximately equal to 16/5.

10. The method of claim 1 wherein J=2, K=5, and m=1, the values of A(1,k) being approximately as follows:

A(1,0)=0, A(1,1)=-1/6, A(1,2)=4/3, A(1,3)=-1/6, and A(1,4)=0.

11. The method of claim 1 wherein J=2, K=5, and m=1, the values of A(1,k) being approximately as follows:

A(1,0)=1/30, A(1,1)=-3/10, A(1,2)=38/15, A(1,3)=-3/10, and A(1,4)=1/30.

12. The method of claim 1 wherein J=4, K=3, and m=1, the values of A(1,k) being approximately as follows:

A(1,0)=-2/3, A(1,1)=7/3, and A(1,2)=-2/3.

13. The method of claim 1 wherein J=4, K=5, and m=1, the values of A(1,k) being approximately as follows:

A(1,0)=11/30, A(1,1)=-32/15, A(1,2)=83/15, A(1,3)=-32/15, and A(1,4)=11/30.

14. The method of claim 1 wherein J=2, K=5, and m=1, the values of A(1,k) being approximately as follows:

A(1,0)=-1/24, A(1,1)=0, A(1,2)=13/12, A(1,3)=0, A(1,4)=-1/24.

15. The method of claim 1 wherein J=4, K=5, and m=1, the values of A(1,k) being approximately as follows:

A(1,0)=-1/6, A(1,1)=0, A(1,2)=4/3, A(1,3)=0, and A(1,4)=-1/6.

16. The method of claim 1 wherein J=4, K=5, and m=1, the values of A(1,k) being approximately as follows:

A(1,0)=0, A(1,1)=-2/3, A(1,2)=7/3, A(1,3)=-2/3, and A(1,4)=0.

17. The method of claim 1 wherein J=2, K=3, and m=1, the values of A(1,k) being approximately as follows:

A(1,0)=-1/6, A(1,1)=4/3, and A(1,2)=-1/6.

18. A digital processor including a memory for use in a strapdown inertial navigation system, the digital processor deriving a sequence of inputs Δ

V_B (n) at times (n+1/2)Δ

t from the outputs of one or more accelerometers, n being an integer and Δ

t being a time interval, the digital processor compensating the inputs Δ

V(n) for sculling, the compensated outputs being obtained at times (pJ+1/2)Δ

t and being denoted by Δ

V_Bc (m,p), the operations of the digital processor being specified by a program stored in memory, the program comprising the following program segments;

a first program segment which causes values for the set A(m,k) to be retrieved from memory, the selected values to be used in the equation ##EQU34## k taking on values from 0 to K-1, m being equal to 1,j taking on values from 1 to J, J being equal to or greater than 2, p being an integer;

a second program segment which causes the value of Δ

V_Bc (m,p) to be calculated for each value of p.

19. The digital processor of claim 18 wherein Δ

V_Bc (p) is transformed from body to navigation frame by the direction cosine matrix C_B^N evaluated at time pJ-(J+K-2)/2!Δ

t, the navigation frame expression of Δ

V_Bc (p) being Δ

V_Nc (p).

20. The digital processor of claim 19 wherein the values selected for the set A(m,k) result in the average error in Δ

V_Nc (m,p)/Δ

t caused by inphase sculling being approximately proportional to (ω

Δ

t)^q for values of ω

Δ

t in a range of values less than 1, ω

being the angular frequency of the sculling motion, q being equal to or greater than 4.

21. The digital processor of claim 18 wherein m takes on values from 1 to M, the program further comprising the program segments:

a third program segment which causes values for the set A (m,k) for values of m from 2 to M to be retrieved from memory;

a fourth program segment causing values for the set B(m) for all values of m in the equation ##EQU35## to be retrieved from memory;

a fifth program segment which causes the value of Δ

V_Bc (p) to be calculated for each value of p.

22. The digital processor of claim 21 wherein Δ

V_Bc (p) is transformed from body to navigation frame by the direction cosine matrix C_B^N evaluated at time pJ-(J+K-2)/2!Δ

t, the navigation frame expression of Δ

V_Bc (p) being Δ

V_Nc (p).

23. The digital processor of claim 22 wherein the values selected for the set A (m,k) result in the average error in Δ

V_Nc (m,p)Δ

t caused by inphase sculling being approximately proportional to (ω

Δ

t)^q for values of ω

Δ

t in a range of values less than 1, ω

being the angular frequency of the sculling motion, q being equal to or greater than 4.

24. The digital processor of claim 23 wherein the values selected for the set B(m) result in the average error in Δ

V_Nc (p)/Δ

t caused by inphase sculling being proportional to (ω

Δ

t)^q for values of ω

Δ

t in a range of values less than 1, ω

being the angular frequency of the sculling motion, q being equal to or greater than 6.

25. The digital processor of claim 21 wherein J=2, K=5, and M=2, the values of A(m,k) being approximately as follows:

A(1,0)=-1/24, A(1,1)=0, A(1,2)=13/12, A(1,3)=0, A(1,4)=-1/24, A(2,0)=0, A(2,1)=-1/6, A(2,2)=4/3, A(2,3)=-1/6, and A(2,4)=0, B(1) being approximately equal to -4/5 and B(2) being approximately equal to 9/5.

26. The digital processor of claim 21 wherein J=4, K=5, and M=2, the values of A(m,k) being approximately as follows:

A(1,0)=-1/6, A(1,1)=0, A(1,2)=4/3, A(1,3)=0, A(1,4)=-1/6, A(2,0)=0, A(2,1)=-2/3, A(2,2)=7/3, A(2,3)=-2/3, and A(2,4)=0, B(1) being approximately equal to -11/5 and B(2) being approximately equal to 16/5.

27. The digital processor of claim 18 wherein J=2, K=5, and m=1, the values of A(1,k) being approximately as follows:

A(1,0)=-1/24, A(1,1)=0, A(1,2)=13/12, A(1,3)=0, A(1,4)=-1/24.

28. The digital processor of claim 18 wherein J=2, K=3, and m=1, the values of A(1,k) being approximately as follows:

A(1,0)=-1/6, A(1,1)=4/3, and A(1,2)=-1/6.

29. The digital processor of claim 18 wherein J=2, K=5, and m=1, the values of A(1,k) being approximately as follows:

A(1,0)=0, A(1,1)=-1/6, A(1,2)=4/3, A(1,3)=-1/6, and A(1,4)=0.

30. The digital processor of claim 18 wherein J=2, K=5, and m=1, the values of A(1,k) being approximately as follows:

A(1,0)=1/30, A(1,1)=-3/10, A(1,2)=38/15, A(1,3)=-3/10, and A(1,4)=1/30.

31. The digital processor of claim 18 wherein J=4, K=3, and m=1, the values of A(1,k) being approximately as follows:

A(1,0)=-2/3, A(1,1)=7/3, and A(1,2)=-2/3.

32. The digital processor of claim 18 wherein J=4, K=5, and m=1, the values of A(1,k) being approximately as follows:

A(1,0)=11/30, A(1,1)=-32/15, A(1,2)=83/15, A(1,3)=-32/15, and A(1,4)=11/30.

33. The digital processor of claim 18 wherein J=4, K=5, and m=1, the values of A(1,k) being approximately as follows:

A(1,0)=0, A(1,1)=-2/3, A(1,2)=7/3, A(1,3)=-2/3, and A(1,4)=0.

34. The digital processor of claim 18 wherein J=4, K=5, and m=1, the values of A(1,k) being approximately as follows:

A(1,0)=-1/6, A(1,1)=0, A(1,2)=4/3, A(1,3)=0, and A(1,4)=-1/6.