GPS accumulated delta range processing for navigation applications

• US 7,490,008 B2
• Filed: 05/16/2005
• Issued: 02/10/2009
• Est. Priority Date: 09/17/2004
• Status: Active Grant

• Current Assignee: Harris Corporation (L3Harris Technologies, Inc.)
• Original Assignee: ITT Manufacturing Enterprises, Inc. (ITT, Inc.)
• Inventors: Draganov, Alexander
• Primary Examiner(s): NGUYEN, TAN QUANG
• Application Number:
  US11/129,423
• Publication Number:
  US 20060195262A1
• Time in Patent Office: 1,366 Days
• Field of Search: 701/213, 701/214, 701/200, 701/216, 701/3, 701/13, 701/215, 342/357.02, 342/357.12, 342/357.14, 455/456.01, 714/800
• US Class Current: 701/214
• CPC Class Codes: G01S 19/43 using carrier phase measurements, e.g. kinematic positioning; using long or short baseline interferometry
• CPC Class Codes: G01S 19/47 the supplementary measurement being an inertial measurement, e.g. tightly coupled inertial

Abstract

Techniques for GPS navigation used to determine the position and velocity of a moving object. Pseudorange (PR) measurements and accumulated delta range (ADR) measurements are made at the object from received GPS signals. Differences are computed between ADR measurements that are separated by a time interval that is greater than a time interval between consecutive ADR measurements. Navigational parameters (e.g., position, velocity and clock) are estimated from the PR measurements and the ADR differences. The ADR measurement equations set for herein are formulated in a much more accurate way so that the time interval between the ADR measurements used to compute an ADR difference can be much larger than that used for current ADR differencing techniques in GPS navigation applications. Consequently, the ADR differences are more accurate, which translates into a much more accurate navigation solution. In addition, the ADR differencing technique contributes to shorten convergence times of the Kalman filter processing, and thereby improve the accuracy of spacecraft navigation. Techniques are also provided to extend these highly accurate ADR processing algorithms to integrated GPS/IMU navigation applications, where IMU data is used as an accurate propagation model to propagate the state vector.

Claims

1. A method of determining navigational parameters of a moving object, comprising:

making pseudorange (PR) measurements at the object from signals received from ranging signal sources;

making accumulated delta range (ADR) measurements at the object from signals received from the ranging signal sources;

computing ADR differences between ADR measurements separated by a time interval that is greater than a time interval between consecutive ADR measurements;

determining an optimal time interval between ADR measurements to be used for computing the ADR differences; and

estimating at least one navigation parameter of the moving object from the PR measurements and the ADR differences.

2. The method of claim 1, wherein determining the optimal time interval between ADR measurements comprises computing a minimum of a variance of a velocity estimate error for two ADR measurements.

3. The method of claim 2, wherein determining the optimal time interval is dependent on an accuracy of the propagation model, such that the optimal time interval can be longer when a more accurate propagation model is used.

4. The method of claim 1, wherein estimating comprises computing partial derivatives of the ADR differences with respect to at least a velocity component of a state vector that represents position and velocity of the object to derive instantaneous velocity estimates of the object.

5. The method of claim 1, wherein (a) making comprises making PR measurements at the object from signals received from global positioning satellites (GPS).

6. The method of claim 1, wherein the time interval between consecutive ADR measurements is on the order of 100 seconds.

7. The method of claim 1, wherein estimating comprises applying a mathematical formulation that maps the ADR differences to a current state vector of the object, wherein the state vector comprises at least position and velocity of the object.

8. A method of determining navigational parameters of a moving object, comprising:

making pseudorange (PR) measurements at the object from signals received from ranging signal sources;

making accumulated delta range (ADR) measurements at the object from signals received from the ranging signal sources;

computing ADR differences between ADR measurements separated by a time interval that is greater than a time interval between consecutive ADR measurements;

estimating at least one navigation parameter of the moving object from the PR measurements and the ADR differences, wherein estimating comprises computing partial derivatives of the ADR differences with respect to at least a velocity component of a state vector that represents position and velocity of the object to derive instantaneous velocity estimates of the object and propagating the state vector with propagation equations that compute the state vector for the object at time N based on the state vector at time N−

1.

9. The method of claim 8, wherein computing partial derivatives comprising computing partial derivatives of the ADR differences with respect to position and velocity of the state vector;

computing partial derivatives of the ADR differences with respect to a clock and a clock drift of the object; and

computing instantaneous velocity estimates of the object by using these partial derivatives in a Kalman filter to process ADR differences.

10. The method of claim 9, wherein estimating the position of the moving object comprises computing position and velocity components of the state vector using the PR measurements and the estimated instantaneous velocity measurements.

11. The method of claim 10, wherein computing partial derivatives of the ADR differences comprises computing derivatives of the object position at a past epoch with respect to a state vector at a current epoch, wherein the state vector comprises components for at least position and velocity of the object at an epoch.

12. The method of claim 11, wherein computing derivatives of the object position at a past epoch with respect to the state vector at a current epoch comprises computing a higher-order approximation with respect to a time difference between consecutive epochs.

13. The method of claim 12, wherein computing a higher-order approximation comprises propagating the state vector backwards over a time interval separating ADR measurements using a propagation routine having multiple substeps;

for each of the substeps of the propagation routine, computing a φ

matrix that corresponds to an element of a Λ

matrix;

computing the Λ

matrix from each of the φ

matrices;

using the Λ

matrix, computing partials of the object position at a past epoch with respect to position and velocity of the state vector.

14. The method of claim 13, and further comprising propagating the state vector using a force model and an integration routine, and propagating a covariance matrix by computing a partial derivative of the state vector at the next epoch with respect to the state vector at the current epoch.

15. The method of claim 14, wherein the state vector has partitions for position, velocity, clock and clock drift of the object, wherein propagating the state vector comprises computing a matrix having partitions for derivatives of positions with respect to velocity, derivatives of position with respect to clock, derivatives of position with respect to clock drift, derivatives of velocity with respect to position, derivatives of velocity with respect to clock and derivatives of velocity with respect to clock drift.

16. A method of determining navigational parameters of a moving object, comprising:

making pseudorange (PR) measurements at the object from signals received from ranging signal sources;

making accumulated delta range (ADR) measurements at the object from signals received from the ranging signal sources;

computing ADR differences between ADR measurements at two epochs separated by a time interval which is greater than a time period between consecutive epochs at which ADR measurements are made;

estimating at least one navigation parameter of the moving object from the PR measurements and the ADR differences.

17. The method of claim 16, wherein (c) computing comprises computing ADR differences between ADR measurements at two epochs separated by said time interval which is several orders of magnitude greater than the time period between consecutive epochs at which ADR measurements are made.

18. A method of determining navigational parameters of a moving object, comprising:

making pseudorange (PR) measurements at the object from signals received from ranging signal sources;

making accumulated delta range (ADR) measurements at the object from signals received from the ranging signal sources;

computing ADR differences between ADR measurements separated by a time interval that is greater than a time interval between consecutive ADR measurements;

estimating at least one navigation parameter of the moving object from the PR measurements and the ADR differences, wherein estimating further comprises propagating a state vector based on inertial measurement data produced by an inertial measurement unit (IMU) associated with said object.

19. The method of claim 18, wherein propagating comprises computing an observation matrix comprising partial derivatives of the ADR differences with respect to a state vector for the object, wherein the state vector comprises an estimate of the position, velocity, attitude and error states of inertial measurement data produced by the IMU associated with said object.

20. The method of claim 19, wherein computing the observation matrix comprises computing a rotation matrix that transforms a vector representing gyro sensor data in body axes of the IMU to an earth centered inertial (ECI) coordinate system and propagating the rotation matrix over an epoch in order to propagate the attitude component of the state vector.

21. The method of claim 20, wherein computing the observation matrix comprises propagating the position and velocity components of the state vector.

22. The method of claim 21, and further comprising computing a misalignment vector that characterizes misalignment parameters of the gyro sensor in the IMU, including the misalignment vector in the Kalman filter state vector.

23. The method of claim 22, and further comprising computing partial derivatives of the state vector at the end of each epoch with respect to the state vector at the start of the epoch to produce a forward propagation matrix, wherein at each epoch the attitude partition of the state vector is represented by Euler angles with respect to a current estimate of the attitude.

24. The method of claim 23, and further comprising computing a backward propagation matrix over multiple epochs.

25. The method of claim 24, and further comprising backward propagating the state vector with the backward propagation matrix using a recursive algorithm.

26. A method for determining the position and velocity of a moving object, comprising:

making pseudorange (PR) measurements at the object from signals received from ranging signal sources;

making accumulated delta range (ADR) measurements at the object from signals received from the ranging signal sources;

computing ADR differences between ADR measurements separated by a time interval that is greater than a time interval between consecutive ADR measurements; and

estimating components of a state vector comprising at least position and velocity of the object at a current state from the PR measurements and the ADR differences and the state vector at a prior state, wherein estimating comprises computing partial derivatives of the ADR differences with respect to at least a velocity component of the state vector to derive instantaneous velocity estimates of the object.

27. The method of claim 26, wherein computing comprises computing ADR differences for ADR measurements separated by said time interval, wherein said time interval is determined by computing a minimum of a variance of a velocity estimate error for two ADR measurements.

28. The method of claim 26, wherein computing partial derivatives of the ADR differences comprises computing derivatives of the object position at a past epoch with respect to the state vector at a current epoch.

29. The method of claim 28, wherein computing derivatives of the object position at a past epoch with respect to the state vector at a current epoch comprises computing a higher-order approximation with respect to a time difference between consecutive epochs.

30. The method of claim 29, wherein computing a higher-order approximation comprises propagating the state vector backwards over a time interval separating ADR measurements using a propagation routine having multiple substeps;

for each of the substeps of the propagation routine, computing a φ

matrix that corresponds to an element of a Λ

matrix;

computing the Λ

matrix from each of the φ

matrices;

using the Λ

matrix, computing partials of the object position at a past epoch with respect to position and velocity of the state vector.

31. The method of claim 30, and further comprising propagating the state vector using a force model and an integration routine, and propagating a covariance matrix by computing a partial derivative of the state vector at the next epoch with respect to the state vector at the current epoch.

32. The method of claim 26, wherein estimating comprises propagating the state vector with propagation equations that compute the state vector for the object at time N based on the state vector at time N−

1.

33. The method of claim 26, wherein estimating comprises processing with a Kalman filter an ADR measurement residual for a pair of ranging signal sources with a partials matrix comprising a first partition for the object position and velocity defined by a difference of two terms, each term for a corresponding ranging signal source, and a second partition for the object clock and clock drift.

34. The method of claim 26, wherein computing comprises computing ADR differences between ADR measurements at two epochs separated by said time interval which is several orders of magnitude greater than a time period between consecutive epochs at which ADR measurements are made.

35. The method of claim 26, wherein estimating further comprises propagating the state vector based on inertial measurement data produced by an inertial measurement unit (IMU) associated with said object.

36. The method of claim 35, wherein propagating comprises computing an observation matrix comprising partial derivatives of the ADR differences with respect to a state vector for the object, wherein the state vector further comprises an estimate of the attitude and error states of inertial measurement data produced by the IMU associated with said object.

37. The method of claim 36, wherein computing the observation matrix comprises computing a rotation matrix that transforms a vector representing gyro sensor data in body axes of the IMU to an earth centered inertial (ECI) coordinate system and propagating the rotation matrix over an epoch in order to propagate the attitude component of the state vector.

38. The method of claim 37, wherein computing the observation matrix comprises propagating the position and velocity components of the state vector, and further comprising computing a misalignment vector that characterizes misalignment parameters of the gyro sensor in the IMU, including the misalignment vector in the Kalman filter state vector.

39. The method of claim 38, and further comprising computing partial derivatives of the state vector at the end of each epoch with respect to the state vector at the start of the epoch to produce a forward propagation matrix, wherein at each epoch the attitude partition of the state vector is represented by Euler angles with respect to a current estimate of the attitude.

40. The method of claim 39, and further computing a backward propagation matrix over multiple epochs, and backward propagating the state vector with the backward propagation matrix using recursive.

41. The method of claim 26, wherein the time interval between consecutive ADR measurements is on the order of 100 seconds.

42. The method of claim 26, wherein making ADR measurements comprises making ADR measurements of the object while it has a non-constant velocity between consecutive ADR measurements.

43. The method of claim 26, wherein estimating comprises applying a mathematical formulation that maps the ADR differences to the current state vector of the object.

44. A processor readable medium storing instructions that, when executed by a processor, cause the processor to:

obtain pseudorange (PR) measurements at the object from signals received from ranging signal sources;

obtain accumulated delta range (ADR) measurements at the object from signals received from the ranging signal sources;

compute ADR differences between ADR measurements separated by a time interval that is greater than a time interval between consecutive ADR measurements; and

estimate at least one navigational parameter of the moving object from the PR measurements and the ADR differences by applying a mathematical formulation that maps the ADR differences to a current state vector of the object, wherein the state vector comprises at least position and velocity of the object.

45. The processor readable medium of claim 44, and further comprising instructions that cause the processor to obtain ADR measurements such that the time interval between consecutive ADR measurements is on the order of 100 seconds.

46. The processor readable medium of claim 44, and further comprising instructions that cause the processor to obtain ADR measurements of the object while it has a non-constant velocity between consecutive ADR measurements.

47. A method of determining navigational parameters of a moving object, comprising:

making pseudorange (PR) measurements at the object from signals received from ranging signal sources, wherein making ADR measurements comprises making ADR measurements of the object while it has a non-constant velocity between consecutive ADR measurements;

making accumulated delta range (ADR) measurements at the object from signals received from the ranging signal sources;

computing ADR differences between ADR measurements separated by a time interval that is greater than a time interval between consecutive ADR measurements; and

estimating at least one navigation parameter of the moving object from the PR measurements and the ADR differences.