Compensation system

• US 6,285,954 B1
• Filed: 07/21/1999
• Issued: 09/04/2001
• Est. Priority Date: 07/21/1999
• 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): NGUYEN, TAN QUANG
• Application Number:
  US09/358,630
• Time in Patent Office: 776 Days
• Field of Search: 701/221, 701/224, 701/226, 701/220, 342/357.12, 342/357.14, 702/94.95
• US Class Current: 701/221
• CPC Class Codes: G05D 1/0825 using mathematical models

Abstract

The invention is a method and apparatus for obtaining an accurate value x_1c of a variable x₁ based on an estimate x_1e that is a function of K variables x₁, x₂, . . . , x_k, . . . , x_K. The method comprises the steps of (a) obtaining a plurality of estimates x_1e, x_2e, . . . , x_ke, . . . , x_Ke of the variables x₁, x₂, . . . , x_k, . . . , x_K over a method-execution time period, the values of the variables x₁, x₂, . . . , x_k, . . . , x_K changing or being changed during the method-execution time period; (b) obtaining from an external source the actual values x_1a of x₁ during the method-execution time period; (c) defining a compensation model δx₁ that is a function of one or more of the estimates x_1e, x_2e, . . . , x_ke, . . . x_Ke of the variables x₁, x₂, . . . , x_k, . . . , x_K, the compensation model being further defined by I unknown constants a₁, a₂, . . . , a_i, . . . , a_I; (d) applying an operator G to the values of x_1e−x_1a and δx₁; (e) determining the values of a₁, a₂, . . . , a_i, . . . , a_I; and (f) determining the value of x_1c.

Claims

1. A method for obtaining an accurate value x_1c of a variable x₁ based on an estimate x_1e that is a function of K variables x₁, x₂, . . . , x_k, . . . , x_K, the method comprising the steps:

(a) obtaining from a plurality of sensors a plurality of estimates x_1e, x_2e, . . . , x_ke, . . . , x_Ke of the variables x₁, x₂, . . . , x_k, . . . , x_K over a method-execution time period, the values of the variables x₁, x₂, . . . , x_k, . . . , x_K changing or being changed during the method-execution time period;

(b) obtaining from an external source the actual values x_1a of x₁ during the method-execution time period;

(c) defining a compensation model δ

x₁ that is a function of one or more of the estimates x_1e, x_2e, . . . , x_ke, . . . , x_Ke of the variables x₁, x₂, . . . , x_k, . . . , x_K, the compensation model being further defined by I unknown constants a₁, a₂, . . . , a_i, . . . , a_I;

(d) applying an operator G to the values of x_1e−

x_1a and δ

x₁;

(e) determining the values of a₁, a₂, . . . , a_i, . . . , a_I;

(f) determining the value of x_1c.

2. The method of claim 1 wherein in step (a) at least one of the variables is a time derivative of another variable.

3. The method of claim 1 wherein step (c) comprises the steps:

(c1) defining a set of I basis functions ƒ

_i(x_ie), the compensation model being the sum over i of a_iƒ

_i(x_ie), x_ie denoting a set of one or more of the estimates x_1e, x_2e, . . . , x_ke, . . . , x_Ke.

4. The method of claim 3 wherein one or more of the basis functions are polynomials.

5. The method of claim 1 wherein in step (d) the values of x_1e−

x_1a and δ

x₁ obtained prior to present time minus a specified time T contribute negligibly to present-time values of G(x_1e−

x_1a) and Gδ

x₁.

6. The method of claim 1 wherein in step (d) G(x_j+x_k) does not equal G(x_j)+G(x_k), j and k being integers less than or equal to K.

7. The method of claim 1 wherein step (e) comprises the step:

(e1) finding the values of a_i that minimize a statistical measure of the magnitude of G(x_1e−

x_1a)−

Gδ

x₁(x_ie) for the values of x_ie determined in step (a).

8. The method of claim 1 wherein step (e) comprises the step:

(e1) finding the values of a_i which minimize a statistical measure of the magnitude of $G<br><br>\left(x_{1<br><br>e}-x_{1<br><br>a}\right)-\underset{i}{\sum <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>a_i<br><br>G<br><br>\text{\hspace{1em}<br><br>}<br><br>f_i<br><br>\left(x_{\mathrm{ie}}\right)$

 

for the values of x_ie determined in step (a).

9. The method of claim 1 wherein in step (f) the value of x_1c is determined by subtracting δ

x₁(x_ie) from x_1e.

10. The method of claim 1 wherein x_1e is equal to x_1em minus δ

, x_1em being a measured value of x₁, δ

being a predetermined function of one or more of estimates x_1e, x_2e, . . . , x_ke, . . . , x_Ke of the variables x₁, x₂, . . . , x_k, . . . , x_K.

11. The method of claim 10 wherein in step (d) G is approximated by G*, G* being a linearized version of G.

12. The method of claim 10 wherein in step (f) the value of x_1c is determined by subtracting δ

+δ

x₁ from x_1e.

13. The method of claim 10 wherein δ

is the δ

x₁ resulting from a prior execution of the method of claim 1.

14. Apparatus for practicing the method of claim 1.

29. The apparatus of claim 17 wherein δ

is the δ

x₁ resulting from a prior execution of the method of claim 1.

15. A method for obtaining an accurate value x_1c of a navigation variable x₁ based on an estimate x_1e that is a function of K variables x₁, x₂, . . . , x_k, . . . , x_K, the method comprising the steps:

(a) obtaining a plurality of estimates x_1e, x_2e, . . . , x_ke, . . . , x_Ke of the variables x₁, x₂, . . . , x_k, . . . , x_K over a method-execution time period, the values of the variables x₁, x₂, . . . , x_k, . . . , x_K changing or being changed during the method-execution time period;

(b) obtaining from an external source the actual values x_1a of x₁ during the method-execution time period;

(c) defining a compensation model δ

x₁ that is a function of one or more of the estimates x_1e, x_2e, . . . , x_ke, . . . , x_Ke of the variables x₁, x₂, . . . , x_k, . . . , x_K, the compensation model being further defined by I unknown constants a₁, a₂, . . . , a_i, . . . , a_I;

(d) applying an operator G to the values of x_1e−

x_1a and δ

x₁;

(e) determining the values of a₁, a₂, . . . , a_i, . . . , a_I;

(f) determining the value of x_1c.

16. Apparatus for practicing the method of claim 15.

17. Apparatus for obtaining an accurate value x_1c of a variable x₁ based on an estimate x_1e that is a function of K variables x₁, x₂, . . . , x_k, . . . , x_K, the apparatus comprising:

a means for obtaining from a plurality of sensors a plurality of estimates x_1e, x_2e, . . . , x_ke, . . . , x_Ke of the variables x₁, x₂, . . . , x_k, . . . , x_K over a method-execution time period, the values of the variables x₁, x₂, . . . , x_k, . . . , x_K changing or being changed during the method-execution time period;

a means for obtaining from an external source the actual values x_1a of x₁ during the method-execution time period;

a means for applying an operator G to the values of x_1e−

x_1a and δ

x₁, δ

x₁ being a compensation model that is a function of one or more of the estimates x_1e, x_2e, . . . , x_ke, . . . , x_Ke of the variables x₁, x₂, . . . , x_k, . . . , x_K, the compensation model being further defined by I unknown constants a₁, a₂, . . . , a_i, . . . , a_I;

a means for determining the values of a₁, a₂, . . . , a_i, . . . , a_I;

a means for determining the value of x_1c.

18. The apparatus of claim 17 wherein at least one of the variables x₁, x₂, . . . , x_k, . . . , x_K is a time derivative of another variable.

19. The apparatus of claim 17 wherein the compensation model is the sum over i of a_iƒ

_i,(x_ie), ƒ

_i(x_ie) being a set of I basis functions, x_ie denoting a set of one or more estimates x_1e, x_2e, . . . , x_ke, . . . , x_Ke of the variables x₁, x₂, . . . , x_k, . . . , x_K.

20. The apparatus of claim 19 wherein one or more of the basis functions are polynomials.

21. The apparatus of claim 17 wherein the values of x_1e−

x_1a and δ

x₁ obtained prior to present time minus a specified time T contribute negligibly to present-time values of G(x_1e−

x_1a) and Gδ

x₁.

22. The apparatus of claim 17 wherein G(x_j+x_k) does not equal G(x_j)+G(x_k), j and k being integers less than or equal to K.

23. The apparatus of claim 17 wherein the values of a_i are determined by finding the values of a_i that minimize a statistical measure of the magnitude of G(x_1e−

x_1a)−

Gδ

x₁(x_ie).

24. The apparatus of claim 17 wherein the values of a_i are determined by finding the values of a_i that minimize a statistical measure of the magnitude of $G$

(x1

e-x1

a)-∑

i

 



ai

G

 



fi

(xie).

25. The apparatus of claim 17 wherein the value of x_1c is determined by subtracting δ

x₁(x_ie) from x_1e.

26. The apparatus of claim 17 wherein x_1e is equal to x_1em minus δ

, x_1em being a measured value of x₁, δ

being a predetermined function of one or more of the estimates x_1e, x_2e, . . . , x_ke, . . . , x_Ke of the variables x₁, x₂, . . . , x_k, . . . , x_K.

27. The apparatus of claim 26 wherein G is approximated by G*, G* being a linearized version of G.

28. The apparatus of claim 26 wherein the value of x_1c is determined by subtracting δ

+δ

x₁ from x_1e.

30. Apparatus for obtaining an accurate value x_1c of a navigation variable x₁ based on an estimate x_1e that is a function of K variables x₁, x₂, . . . , x_k, . . . , x_K, the apparatus comprising:

a plurality of sensors for obtaining a plurality of estimates x_1e, x_2e, . . . , x_ke, . . . , x_Ke of the variables x₁, x₂, . . . , x_k, . . . , x_K over a method-execution time period, x_1e being the output of a navigation sensor, the values of the variables x₁, x₂, . . . , x_k, . . . , x_K changing or being changed during the method-execution time period;

a means for obtaining from an external source the actual values x_1a of x₁ during the method-execution time period;

a means for applying an operator G to the values of x_1e−

x_1a and δ

x₁, δ

x₁ being a compensation model that is a function of one or more of the estimates x_1e, x_2e, . . . , x_ke, . . . , x_Ke of the variables x₁, x₂, . . . , x_k, . . . , x_K, the compensation model being further defined by I unknown constants a₁, a₂, . . . , a_i, . . . , a_I;

a means for determining the values of a₁, a₂, . . . , a_i, . . . , a_I;

a means for determining the value of x_1c.