Temperature compensation method for strapdown inertial navigation systems

• US 6,175,807 B1
• Filed: 06/09/1999
• Issued: 01/16/2001
• Est. Priority Date: 06/09/1999
• Status: Expired due to Term

• Current Assignee: Northrop Grumman Systems Corporation (Northrop Grumman Corporation)
• Original Assignee: Litton Systems Incorporated (Northrop Grumman Corporation)
• Inventors: Buchler, Robert J., Fann, Shaw-Wen, Moeller, Larry R., Tazartes, Daniel A., Mark, John G.
• Primary Examiner(s): Issing, Gregory C.
• Application Number:
  US09/329,094
• Time in Patent Office: 587 Days
• Field of Search: 701/220, 701/216, 342/357.13, 342/357.14
• US Class Current: 701/220
• CPC Class Codes: G01C 21/183 Compensation of inertial measurements, e.g. for temperature effects
• CPC Class Codes: G01C 25/005 initial alignment, calibration or starting-up of inertial devices

Abstract

The invention is a method continuing over a plurality of time periods for compensating for the output error in each of one or more navigation instruments in a system comprising a plurality of navigation instruments after the system is introduced into its operating environment. The practice of the method begins with determining the values of one or more of a set of coordinates that specify the position, velocity, and orientation of the system in space together with the error in a compensated output for each of the one or more navigation instruments. The method continues with determining a compensation model for each of the one or more navigation instruments. A compensation model specifies for a current time period an adjustment in amplitude of the output of a navigation instrument as a function of time and temperature. A compensation model is expressed as the sum of a first compensation model and a present second compensation model where the present second compensation model is a future second compensation model determined during the prior time period. The final steps of the method consist of measuring the time and the temperature of the navigation instruments and then obtaining a compensated output for each of the one or more navigation instruments by adjusting the output of a navigation instrument in accordance with its compensation model.

Claims

1. A method for compensating for the output error in each of one or more navigation instruments in a system comprising a plurality of navigation instruments, the method being practiced after the system is introduced into its operating environment, the practice of the method continuing for a plurality of time periods, a time period being started and ended by events independent of the timing of method operations, the method comprising the step:

compensating during a present time period for the output error in each of the one or more navigation instruments as a function of temperature utilizing a present second compensation model based on measurements obtained in one or more prior time periods, a future second compensation model for use in the next time period being determined during the present time period, the future second compensation model becoming the present second compensation model at the start of the next time period.

2. The method of claim 1 wherein the future second compensation model is determined from data obtained when the system is subjected to specified types of motion or is supplied with data by other navigation data sources.

3. The method of claim 1 comprising a plurality of steps performed repetitively during a time period, the method comprising the steps:

(a) determining the values of one or more of a set of coordinates that specify the position, velocity, and orientation of the system in space together with the error in the compensated output for each of the one or more navigation instruments utilizing the compensated outputs for the one or more navigation instruments obtained as a result of the prior execution of step (d);

(b) determining a compensation model for each of the one or more navigation instruments, a compensation model specifying for the current time period an adjustment in amplitude of the output of a navigation instrument as a function of time and temperature, a compensation model being the sum of the values of a first compensation model and a present second compensation model, the present second compensation model being the future second compensation model determined during the prior time period;

(c) measuring the time and the temperature of the navigation instruments;

(d) obtaining a compensated output for each of the one or more navigation instruments by adjusting the output of a navigation instrument in accordance with its compensation model.

4. The method of claim 3 wherein step (a) comprises the steps:

(a1) determining the error in the compensated output for each of the one or more navigation instruments during a time period utilizing the future second compensation model being determined during the same time period in step (b).

5. The method of claim 3 wherein the first compensation model is defined in terms of temperature by the product of a first observation matrix and a first model vector, one or more of the components of the first observation matrix being functions of temperature, zero or more of the components of the first model vector being functions of time.

6. The method of claim 5 wherein an operating temperature range is specified for the system, the first compensation model comprising a polynomial in temperature, the components of the first model vector comprising the coefficients of the polynomial.

7. The method of claim 6 wherein the operating temperature range is divided into temperature intervals, the first compensation model also comprising a polynomial in temperature defined for each temperature interval, the components of the first model vector also comprising the coefficients of each temperature interval polynomial.

8. The method of claim 7 wherein the first compensation model also comprises a minibias, the value of the minibias being determined as a result of performing the method.

9. The method of claim 5 wherein step (a) is repeated at specified INS time intervals during a time period, the values of the first compensation model and the present second compensation model being determined for each INS time interval and added together to obtain the value of the compensation model.

10. The method of claim 9 wherein in step (a) the determination of the values for an INS time interval utilize the values determined for the previous INS time interval.

11. The method of claim 10 wherein step (a) corresponds to an iteration of a Kalman filter process called the INS Kalman filter process.

12. The method of claim 11 wherein the state variables for the INS Kalman filter process include the error in the compensated output for each of the one or more navigation instruments.

13. The method of claim 12 wherein step (a) comprises the following step performed upon the occurrence of one or more specified events:

(a1) saving the error in compensated output for each of the one or more navigation instruments, the associated temperature, and a flag identifying the type of update required at the beginning of the next time period.

14. The method of claim 13 wherein a specified event is included in the group (1) the completion of an initialization process at the beginning of a time period, (2) the completion of delayed updates resulting from extended alignment procedures, (3) the transition of the system from motion relative to earth to non-motion, (4) the passage of a specified long time interval since the occurrence of a specified event, and (5) the passage of a short time interval since the occurrence of a specified event.

15. The method of claim 3 wherein the future second compensation model is determined during a time period utilizing the error in the compensated output for each of the one or more navigation instruments determined during the same time period in step (a).

16. The method of claim 3 wherein a second compensation model is defined in terms of temperature by the product of a second observation matrix and a second model vector, one or more of the components of the second observation matrix being functions of temperature, zero or more of the components of the second model vector being fimctions of time, step (b) comprising the steps:

(b1) determining the values of the components of the future second model vector by utilizing the values of the components of the present second model vector and data resulting from the performance of step (a) if one or more criteria are satisfied.

17. The method of claim 16 wherein the second compensation model comprises a polynomial in temperature, the coefficients of the polynomial being approximated by polynomials in time, the components of the second model vector comprising the coefficients of the polynomials in time.

18. The method of claim 17 wherein the coefficient of the highest order term of the polynomial in time is a function of time.

19. The method of claim 17 wherein the operating temperature range is divided into temperature intervals, the second compensation model also comprising a polynomial in temperature for each temperature interval, the components of the second model vector also comprising the coefficients of the polynomials in temperature for each temperature interval.

20. The method of claim 19 wherein one or more of the coefficients of the temperature interval polynomial are functions of time.

21. The method of claim 19 wherein the second compensation model also comprises a minibias under certain specified conditions.

22. The method of claim 16 wherein the error in the compensated output of an instrument is utilized in updating the components of the second model vector to obtain the components of the future second model vector.

23. The method of claim 22 wherein step (a) is repeated at specified INS time intervals and step (b1) is repeated at specified TCS time intervals during a time period, a TCS time interval being equal to or greater than an INS time interval.

24. The method of claim 23 wherein the values of the components of the second model vector for a TCS time interval are used to determine the values of the components for the next TCS time interval.

25. The method of claim 24 wherein step (b1) corresponds to an iteration of a Kalman filter process called the TCS Kalman filter process, the error in the compensated output of an instrument being an observable for the TCS Kalman filter process.

26. The method of claim 25 wherein the state variables for the TCS Kalman filter process include the components of the future second model vector.

27. The method of claim 26 wherein the present second model vector and a corrections vector are separately saved for each TCS Kalman filter process iteration, the future second model vector being the sum of the present second model vector and the corrections vector.

28. The method of claim 27 wherein the future second model vector at the end of a time period becomes the present second model vector at the beginning of the next time period and the corrections vector becomes zero.

29. The method of claim 26 wherein the dynamics matrix for the TCS Kalman filter process is non-zero.

30. The method of claim 26 wherein step (bl) further comprises the following steps performed upon the occurrence of one or more specified events:

(b1a) saving the component values of the present second model vector;

(b1b) saving data from which the component values of the present second model vector for the next time period can be determined.

31. The method of claim 30 wherein the saved data of step (b1b) include the values of the TCS Kalman filter covariance matrix.

32. The method of claim 30 wherein a specified event is one of a group comprising (1) the completion of an initialization process at the beginning of a time period, (2) the completion of delayed updates resulting from extended alignment procedures, (3) the transition of the system from motion relative to earth to non-motion, and (4) the passage of a specified long time interval since the occurrence of a specified event.

33. The method of claim 16 wherein the criteria of step (b″

) comprise one or more of a group including (1) navigation data obtained from other navigation sources having a quality better than a specified level, (2) navigation data obtained as a result of the system being subjected to specified types of motion having a quality better than a specified level, (3) first motion of the system after the beginning of a time period having occurred, (4) a specified time interval having elapsed after the beginning of a time period, (5) no delayed updates pending, (6) azimuth error being less than a specified value, and (7) errors in the data resulting from the performance of step (a) and utilized in step (b1) being less than specified values.

34. The method of claim 3 wherein step (b) comprises the step:

saving navigation data at end of a time period, the navigation data being data needed to re-establish execution of the method at the beginning of the next time period as a continuation of the method as it was being executed at the end of the time period.

35. The method of claim 3 wherein a second compensation model is defined by the product of a second observation matrix and a second model vector, step (a) being repeated at specified INS time intervals and step (b) being repeated at specified TCS time intervals during a time period, a TCS time interval being equal to or greater than an INS time interval, step (a) corresponding to an iteration of a Kalman filter process called the INS Kalman filter process, step (b) corresponding to an iteration of a Kalman filter process called the TCS Kalman filter process, the error in the compensated output of each of the one or more instruments being a state variable of the INS Kalman filter process and an observable for the TCS Kalman filter process, the state variables for the TCS Kalman filter being the components of the future second model vector, the values of the TCS Kalman filter state variables being saved upon the occurrence of one or more specified events and the values of the INS Kalman filter compensated output error state variables being saved at specified short time intervals.

36. The method of claim 35 wherein step (b) comprises the following steps performed at the end of a time period:

(b1) saving information about any saving steps occurring at the end of the time period;

(b2) saving the number of instances that the INS Kalman filter compensated-output-error state variables were saved after the last save of the TCS Kalman filter state variables.

37. The method of claim 35 wherein step (b) comprises the following steps performed at the end of a time period:

(b1) saving data from which can be derived (1) the component values of the present second model vector and the future second model vector, (2) the TCS Kalman filter covariance matrix element values, (3) the INS Kalman filter compensated-output-error values, and (4) the instrument temperature, the data being saved at time intervals no greater than specified long time intervals during a time period;

(b2) saving data from which can be derived INS Kalman filter compensated-output-error values and instrument temperature value at specified short time intervals following the data saving of step (b1);

(b3) determining the values of the TCS Kalman filter state variables and covariance matrix elements corresponding to the beginning of the next time period utilizing the data saved in steps (b1) and (b2).

38. The method of claim 35 wherein step (b) comprises the following steps:

(b1) saving the value of the INS compensated output error for each of the one or more navigation instruments, the associated temperature, and the associated time beginning after a specified initial delay from the beginning of a time period at short time intervals, offsets being introduced in the compensated output values by uncertainties in the values of one or more INS Kalman filter state variables;

(b2) determining the offsets in the saved compensated-output-error values when the uncertainties in the values of the one or more INS Kalman filter state variables have been reduced to a specified level;

(b3) correcting the saved compensated-output-error values for the offsets of step (b2);

(b4) performing delayed updates of the TCS Kalman filter state variables from the beginning of the time period utilizing the corrected saved compensated-output-error values of step (b3).

39. The method of claim 38 wherein delayed updates of the TCS Kalman filter state variables are executed before current updates may begin, a current update utilizing observable values acquired during the current TCS time interval, a delayed update utilizing observable values acquired prior to the current TCS time interval.

40. The method of claim 38 wherein steps (b1) through (b4) are executed only if one or more conditions are satisfied.

41. The method of claim 35 wherein step (b) comprises the following steps:

(b1) saving the value of the INS compensated output error for each of the one or more navigation instruments, the associated temperature, and the associated time beginning after a specified initial delay from the beginning of a time period at short time intervals, offsets being introduced in the compensated output values by uncertainties in the values of one or more INS Kalman filter state variables;

(b2) adding a fraction of the most recent value of the compensated output error for each of the one or more navigation instruments saved in step (b1) to the present second compensation model at the beginning of a time period if the values of the compensated output errors saved in step (b1) were not used in the prior time period.

42. The method of claim 35 wherein short time intervals are the same as TCS time intervals.

43. The method of claim 3 wherein the plurality of navigation instruments consists of the x-axis gyro and the y-axis gyro, the x axis and the y axis being the nominally level instrument frame axes.

44. The method of claim 3 wherein a time period begins with power-on and ends with power-off of the system.

45. The method of claim 3 wherein time is a measure of the time that a system is in a power-on state.