System and method for generating attitude determinations using GPS

• US 5,548,293 A
• Filed: 12/10/1993
• Issued: 08/20/1996
• Est. Priority Date: 03/24/1993
• Status: Expired due to Term

• Current Assignee: Board of Trustees of the Leland Stanford Junior University (Stanford Management Co.)
• Original Assignee: Leland Stanford Junior University (Stanford University)
• Inventors: Cohen, Clark E.
• Primary Examiner(s): Issing, Gregory C.
• Application Number:
  US08/165,394
• Time in Patent Office: 984 Days
• Field of Search: 342/357, 342/352, 364/434
• US Class Current: 342/357.38
• CPC Class Codes: G01S 19/04 providing carrier phase data
• CPC Class Codes: G01S 19/071 DGPS corrections
• CPC Class Codes: G01S 19/11 wherein the cooperating elements are pseudolites or satellite radio beacon positioning system signal repeaters
• CPC Class Codes: G01S 19/15 Aircraft landing systems
• CPC Class Codes: G01S 19/41 Differential correction, e.g. DGPS [differential GPS]
• CPC Class Codes: G01S 19/44 Carrier phase ambiguity resolution; Floating ambiguity; LAMBDA [Least-squares AMBiguity Decorrelation Adjustment] method
• CPC Class Codes: G01S 19/55 Carrier phase ambiguity resolution; Floating ambiguity; LAMBDA [Least-squares AMBiguity Decorrelation Adjustment] method
• CPC Class Codes: G01S 5/0009 Transmission of position information to remote stations involving assistance data G01S5/0236

Abstract

A GPS attitude receiver for determining the attitude of a moving vehicle in conjunction with a first, a second, a third, and a fourth antenna mounted to the moving vehicle. Each of the antennas receives a plurality of GPS signals that each include a carrier component. For each of the carrier components of the received GPS signals there is an integer ambiguity associated with the first and fourth antennas, an integer ambiguity associated with second and fourth antennas, and an integer ambiguity associated with the third and fourth antennas. The GPS attitude receiver measures phase values for the carrier components of the GPS signals received from each of the antennas at a plurality of measurement epochs during an initialization period and at a measurement epoch after the initialization period. In response to the phase values measured at the measurement epochs during the initialization period, the GPS attitude receiver computes integer ambiguity resolution values representing resolution of the integer ambiguities. Then, in response to the computed integer ambiguity resolution values and the phase value measured at the measurement epoch after the initialization period, it computes values defining the attitude of the moving vehicle at the measurement epoch after the initialization period.

Claims

1. A GPS attitude system for determining the attitude of a moving vehicle from a plurality of GPS carrier signals, the GPS attitude system comprising:

four antennas mounted to the moving vehicle, each of the antennas receiving the GPS carrier signals;

signal receiving means for receiving the GPS carrier signals from each of the antennas;

phase measuring means for making phase measurements for the GPS carrier signals received from each of the antennas at a plurality of epochs during an initialization period and at a plurality of epochs after the initialization period, wherein the vehicle is moving while the phase measurements are made during and after the initialization period, and wherein there is an integer wavelength ambiguity associated with the phase measurements made for each of the GPS carrier signals received from a first one and a second one of the antennas, there is an integer wavelength ambiguity associated with the phase measurements made for each of the GPS carrier signals received from the first one and a third one of the antennas, and there is an integer wavelength ambiguity associated with the phase measurements made for each of the GPS carrier signals received from the first one and a fourth one of the antennas;

baseline computation means for computing baseline positions for the second, third, and fourth ones of the antennas with respect to the first one of the antennas at an initial one of the epochs during the initialization period and the changes in the baseline positions at subsequent ones of the epochs during the initialization period in response to the phase measurements made at the epochs during the initialization period and based on the constraint relationship at each of the subsequent ones of the epochs during the initialization period

space="preserve" listing-type="equation">Δ

b.sub.z.sup.T b.sub.y +Δ

b.sub.y.sup.T b.sub.z =-Δ

b.sub.y.sup.T Δ

b.sub.z,

where b_y is the baseline position of the y^th of the second, third, and fourth ones of the antennas, b_z is the baseline position of the z^th of the second, third, and fourth ones of the antennas, Δ

b_y is the change in the baseline position of the y^th of the second, third, and fourth ones of the antennas at a respective one of the subsequent epochs during the initialization period, Δ

b_z is the change in the baseline position of the z^th of the second, third, and fourth ones of the antennas at the respective one of the subsequent epochs during the initialization period, and Δ

b_y^T Δ

b_z is non-zero;

initial guess computation means for computing an initial guess of the attitude of the moving vehicle at each of the epochs during the initialization period in response to the computed baseline positions and the computed changes in the baseline positions;

ambiguity resolution means for resolving the integer wavelength ambiguities in response to the computed initial guesses and the phase measurements made at the epochs during the initialization period; and

attitude computation means for computing the attitude of the moving vehicle at each respective one of the epochs after the initialization period in response to the resolved integer wavelength ambiguities and the phase measurements made at the respective one of the epochs after the initialization period.

2. The GPS system of claim 1 wherein:

the ambiguity resolution means resolves the integer wavelength ambiguities in accordance with a predefined set of simultaneous equations that relate (A) the integer wavelength ambiguities, (B) the phase measurements made at the epochs during the initialization period, (C) estimates of the attitudes of the moving vehicle at the epochs during the initialization period, and (D) corrections to the estimates;

the number of GPS carrier signals and epochs during the initialization period is such that the predefined set of simultaneous equations is overdetermined;

the ambiguity resolution means iteratively resolves the integer wavelength ambiguities by (A) computing the integer ambiguities and the corrections in a plurality of iterations in accordance with the predefined set of equations, (B) in an initial one of the iterations, using the initial guesses as the estimates, and (C) in each subsequent one of the iterations, using as the estimates the estimates used in a previous one of the iterations corrected with the corrections computed in the previous one of the iterations.

3. The GPS system of claim 2 wherein the ambiguity resolution means resolves the integer wavelength ambiguities in accordance with block cholesky factorization of the predefined set of equations.

4. The GPS system of claim 1 wherein the ambiguity resolution means resolves the integer wavelength ambiguities by simultaneously resolving the integer wavelength ambiguities and determining the state of flexure of the moving vehicle during the initialization period.

5. The GPS system of claim 4 wherein:

the ambiguity resolution means simultaneously resolves the integer ambiguities and determines the state of flexure of the moving vehicle in accordance with a predefined set of simultaneous equations that relate (A) the integer wavelength ambiguities, (B) the phase measurements made at the epochs during the initialization period, (C) estimates of the attitudes of the moving vehicle at the epochs during the initialization period, (D) corrections to the estimates, and (E) the state of flexure;

the number of GPS carrier signals and epochs during the initialization period is such that the predefined set of simultaneous equations is overdetermined;

the ambiguity resolution means iteratively and simultaneously resolves the integer wavelength ambiguities and determines the state of flexure of the moving vehicle by (A) computing the integer ambiguities, the corrections, and the state of flexure in a plurality of iterations in accordance with the predefined set of equations, (B) in an initial one of the iterations, using the initial guesses as the estimates, and (C) in each subsequent one of the iterations, using as the estimates the estimates used in a previous one of the iterations corrected by the corrections computed in the previous one of the iterations.

6. The GPS system of claim 5 wherein the ambiguity resolution means resolves the integer wavelength ambiguities in accordance with block cholesky factorization of the predefined set of equations.

7. A method of determining the attitude of a moving vehicle from a plurality of GPS carrier signals, the method comprising the steps of:

receiving the GPS carrier signals with each of four antennas mounted to the moving vehicle;

receiving the GPS carrier signals from each of the antennas;

making phase measurements for the GPS carrier signals received from each of the antennas at a plurality of epochs during an initialization period and at a plurality of epochs after the initialization period, wherein the vehicle is moving while the phase measurements are made during and after the initialization period, and wherein there is an integer wavelength ambiguity associated with the phase measurements made for each of the GPS carrier signals received from a first one and a second one of the antennas, there is an integer wavelength ambiguity associated with the phase measurements made for each of the GPS carrier signals received from the first one and a third one of the antennas, and there is an integer wavelength ambiguity associated with the phase measurements made for each of the GPS carrier signals received from the first one and a fourth one of the antennas;

computing baseline positions for the second, third, and fourth ones of the antennas with respect to the first one of the antennas at an initial one of the epochs during the initialization period and the changes in the baseline positions at subsequent ones of the epochs during the initialization period in response to the phase measurements made at the epochs during the initialization period and based on the constraint relationship at each of the subsequent ones of the epochs during the initialization period

space="preserve" listing-type="equation">Δ

b.sub.z.sup.T b.sub.y +Δ

b.sub.y.sup.T b.sub.z =-Δ

b.sub.y.sup.T Δ

b.sub.z,

where b_y is the baseline position of the y^th of the second, third, and fourth ones of the antennas, b_z is the baseline position of the z^th of the second, third, and fourth ones of the antennas, Δ

b_y is the change in the baseline position of the y^th of the second, third, and fourth ones of the antennas at a respective one of the subsequent epochs during the initialization period, Δ

b_z is the change in the baseline position of the z^th of the second, third, and fourth ones of the antennas at the respective one of the subsequent epochs during the initialization period, and Δ

b_y^T Δ

b_z is non-zero;

computing an initial guess of the attitude of the moving vehicle at each of the epochs during the initialization period in response to the computed baseline positions and the computed changes in the baseline positions;

resolving the integer wavelength ambiguities in response to the computed initial guesses and the phase measurements made at the epochs during the initialization period; and

computing the attitude of the moving vehicle at each respective one of the epochs after the initialization period in response to the resolved integer wavelength ambiguities and the phase measurements made at the respective one of the epochs after the initialization period.

8. The method of claim 7 wherein:

the integer wavelength ambiguities are resolved in the ambiguity resolving step in accordance with a predefined set of simultaneous equations that relate (A) the integer wavelength ambiguities, (B) the phase measurements made at the epochs during the initialization period, (C) estimates of the attitudes of the moving vehicle at the epochs during the initialization period, and (D) corrections to the estimates;

the number of GPS carrier signals and epochs during the initialization period is such that the predefined set of simultaneous equations is overdetermined;

the integer wavelength ambiguities are iteratively resolved in accordance with the predefined set of equations in the ambiguity resolving step by (A) computing the integer ambiguities and the corrections in a plurality of iterations, (B) in an initial one of the iterations, using the initial guesses as the estimates, and (C) in each subsequent one of the iterations, using as the estimates the estimates used in a previous one of the iterations corrected with the corrections computed in the previous one of the iterations.

9. The method of claim 8 wherein the integer wavelength ambiguities are iteratively resolved in the ambiguity resolving step in accordance with block cholesky factorization of the predefined set of equations.

10. The method of claim 7 wherein the integer wavelength ambiguities are resolved in the ambiguity resolving step by simultaneously resolving the integer wavelength ambiguities and determining the state of flexure of the moving vehicle during the initialization period.

11. The method of claim 10 wherein:

the integer wavelength ambiguities are resolved and the state of flexure of the moving vehicle is determined in the ambiguity resolving step in accordance with a predefined set of simultaneous equations that relate (A) the integer wavelength ambiguities, (B) the phase measurements made at the epochs during the initialization period, (C) estimates of the attitudes of the moving vehicle at the epochs during the initialization period, (D) corrections to the estimates, and (E) the state of flexure;

the number of GPS carrier signals and epochs during the initialization period is such that the predefined set of simultaneous equations is overdetermined;

the integer wavelength ambiguities are resolved and the state of flexure of the moving vehicle is determined iteratively and simultaneously in the ambiguity resolving step by (A) computing the integer ambiguities, the corrections, and the state of flexure in a plurality of iterations in accordance with the predefined set of equations, (B) in an initial one of the iterations, using the initial guesses as the estimates, and (C) in each subsequent one of the iterations, using as the estimates the estimates used in a previous one of the iterations corrected by the corrections computed in the previous one of the iterations.

12. The method of claim 11 wherein the integer wavelength ambiguities are resolved and the state of flexure of the moving vehicle is determined iteratively and simultaneously in the ambiguity resolving step in accordance with block cholesky factorization of the predefined set of equations.

13. A GPS attitude system for determining the attitude of a moving vehicle from a plurality of GPS carrier signals, the GPS attitude system comprising:

four antennas mounted to the moving vehicle, each of the antennas receiving the GPS carrier signals;

signal receiving means for receiving the GPS carrier signals from each of the antennas;

phase measuring means for making phase measurements for the GPS carrier signals received from each of the antennas at a plurality of epochs during an initialization period and at a plurality of epochs after the initialization period, wherein there is an integer wavelength ambiguity associated with the phase measurements made for each of the GPS carrier signals received from a first one and a second one of the antennas, there is an integer wavelength ambiguity associated with the phase measurements made for each of the GPS carrier signals received from the first one and a third one of the antennas, and there is an integer wavelength ambiguity associated with the phase measurements made for each of the GPS carrier signals received from the first one and a fourth one of the antennas;

ambiguity resolution means for simultaneously resolving the integer wavelength ambiguities and determining the state of flexure of the moving vehicle during the initialization period in response to the phase measurements made at the epochs during the initialization period;

attitude computation means for computing the attitude of the moving vehicle at each respective one of the epochs after the initialization period in response to the resolved integer wavelength ambiguities and the phase measurements made at the respective one of the epochs after the initialization period.

14. The GPS system of claim 13 further comprising:

initial guess computation means for computing an initial guess of the attitude of the moving vehicle at each of the epochs during the initialization period;

the ambiguity resolution means simultaneously resolving the integer wavelength ambiguities and determining the state of flexure of the moving vehicle in accordance with a predefined set of simultaneous equations that relate (A) the integer wavelength ambiguities, (B) the phase measurements made at the epochs during the initialization period, (C) estimates of the attitudes of the moving vehicle at the epochs during the initialization period, (D) corrections to the estimates, and (E) the state of flexure;

the number of GPS carrier signals and epochs during the initialization period being such that the predefined set of simultaneous equations is overdetermined;

the ambiguity resolution means iteratively and simultaneously resolving the integer wavelength ambiguities and determining the state of flexure of the moving vehicle by (A) computing the integer wavelength ambiguities, the corrections, and the state of flexure in a plurality of iterations in accordance with the predefined set of simultaneous equations, (B) in an initial one of the iterations, using the initial guesses as the estimates, and (C) in each subsequent one of the iterations, using as the estimates the estimates used in a previous one of the iterations corrected by the corrections computed in the previous one of the iterations.

15. The GPS system of claim 14 wherein the ambiguity resolution means resolves the integer wavelength ambiguities in accordance with block cholesky factorization of the predefined set of equations.

16. The GPS system of claim 13 wherein the attitude computation means simultaneously computes the attitude and determines the state of flexure of the moving vehicle at each one of the epochs after the initialization period.

17. A method of determining the attitude of a moving vehicle from a plurality of GPS carrier signals, the method comprising:

receiving the GPS carrier signals with each of four antennas mounted to the moving vehicle;

receiving the GPS carrier signals from each of the antennas;

making phase measurements for the GPS carrier signals received from each of the antennas at a plurality of epochs during an initialization period and at a plurality of epochs after the initialization period, wherein there is an integer wavelength ambiguity associated with the phase measurements made for each of the GPS carrier signals received from a first one and a second one of the antennas, there is an integer wavelength ambiguity associated with the phase measurements made for each of the GPS carrier signals received from the first one and a third one of the antennas, and there is an integer wavelength ambiguity associated with the phase measurements made for each of the GPS carrier signals received from the first one and a fourth one of the antennas;

simultaneously resolving the integer wavelength ambiguities and determining the state of flexure of the moving vehicle during the initialization period in response to the phase measurements made at the epochs during the initialization period;

computing the attitude of the moving vehicle at each respective one of the epochs after the initialization period in response to the resolved integer wavelength ambiguities and the phase measurements made at the respective one of the epochs after the initialization period.

18. The GPS system of claim 17 further comprising the step of:

computing an initial guess of the attitude of the moving vehicle at each of the epochs during the initialization period;

the integer wavelength ambiguities are resolved and the state of flexure of the moving vehicle are determined simultaneously in the ambiguity resolving step in accordance with a predefined set of simultaneous equations that relate (A) the integer wavelength ambiguities, (B) the phase measurements made at the epochs during the initialization period, (C) estimates of the attitudes of the moving vehicle at the epochs during the initialization period, (D) corrections to the estimates, and (E) the state of flexure;

the number of GPS carrier signals and epochs during the initialization period being such that the predefined set of simultaneous equations is overdetermined;

the integer wavelength ambiguities being resolved and the state of flexure of the moving vehicle being determined iteratively and simultaneously by (A) computing the integer wavelength ambiguities, the corrections, and the state of flexure in a plurality of iterations in accordance with the predefined set of simultaneous equations, (B) in an initial one of the iterations, using the initial guesses as the estimates, and (C) in each subsequent one of the iterations, using as the estimates the estimates used in a previous one of the iterations corrected by the corrections computed in the previous one of the iterations.

19. The method of claim 18 wherein the integer wavelength ambiguities are resolved and the state of flexure of the moving vehicle is determined iteratively and simultaneously in the ambiguity resolving step in accordance with block cholesky factorization of the predefined set of equations.

20. The method of claim 17 wherein the attitude of the moving vehicle is computed and the state of flexure of the moving vehicle is determined simultaneously at each one of the epochs after the initialization period in the attitude computing step.

21. A GPS attitude system for determining the attitude of a moving vehicle from a plurality of GPS carrier signals, the GPS attitude system comprising:

a plurality of antennas mounted to the moving vehicle, each of the antennas receiving the GPS carrier signals;

signal receiving means for receiving the GPS signals from each of the antennas;

phase measuring means for making phase measurements for the GPS carrier signals received from each of the antennas at a plurality of epochs;

attitude computation means for simultaneously computing the attitude and determining the state of flexure of the moving vehicle at each respective one of the epochs in response to the phase measurements made at the respective one of the epochs.

22. The GPS attitude system of claim 21 wherein:

the plurality of antennas comprises four antennas;

there is an integer wavelength ambiguity associated with the phase measurements made for each of the GPS carrier signals received from a first one and a second one of the antennas, there is an integer wavelength ambiguity associated with the phase measurements made for each of the GPS carrier signals received from the first one and a third one of the antennas, and there is an integer wavelength ambiguity associated with the phase measurements made for each of the GPS carrier signals received from the first one and a fourth one of the antennas;

the GPS attitude system further comprises ambiguity resolution means for resolving the integer wavelength ambiguities;

the attitude computation means simultaneously computes the attitude and determines the state of flexure of the moving vehicle at each respective one of the epochs also in response to the resolved integer wavelength ambiguities.

23. The GPS system of claim 22 wherein:

the attitude computation means simultaneously computes the attitude and determines the state of flexure of the moving vehicle at each respective one of the epochs after the initialization period in accordance with a predefined set of simultaneous equations that relate (A) the resolved integer wavelength ambiguities, (B) the phase measurements made at the respective one of the epochs, (C) an estimate of the attitude of the moving vehicle at the respective one of the epochs, (D) a correction to the estimate of the attitude, (E) an estimate of the state of flexure of the moving vehicle at the respective one of the epochs, and (F) a correction to the estimate of the state of flexure;

the attitude computation means iteratively and simultaneously computes the attitude and determines the state of flexure of the moving vehicle at each respective one of the epochs by (A) computing the corrections to the estimates of the attitude and the state of flexure in a plurality of iterations in accordance with the predefined set of simultaneous equations, (B) in each respective one of the iterations, using as the estimates of the attitude and the state of flexure the estimates of the attitude and the state of flexure used in a directly preceding one of the iterations corrected by the corrections to the estimates of the attitude and state of flexure computed in the directly preceding one of the iterations.

24. A method of determining the attitude of a moving vehicle from a plurality of GPS carrier signals, the method comprising:

receiving the GPS carrier signals with each of a plurality of antennas mounted to the moving vehicle;

receiving the GPS signals from each of the antennas;

making phase measurements for the GPS carrier signals received from each of the antennas at a plurality of epochs;

simultaneously computing the attitude and determining the state of flexure of the moving vehicle at each respective one of the epochs in response to the phase measurements made at the respective one of the epochs.

25. The method of claim 24 wherein:

the plurality of antennas comprises four antennas;

there is an integer wavelength ambiguity associated with the phase measurements made for each of the GPS carrier signals received from a first one and a second one of the antennas, there is an integer wavelength ambiguity associated with the phase measurements made for each of the GPS carrier signals received from the first one and a third one of the antennas, and there is an integer wavelength ambiguity associated with the phase measurements made for each of the GPS carrier signals received from the first one and a fourth one of the antennas;

the method further comprises the step of resolving the integer wavelength ambiguities;

the attitude of the moving vehicle is computed and the state of flexure of the moving vehicle is determined simultaneously at each respective one of the epochs in the attitude computing step also in response to the resolved integer wavelength ambiguities.

26. The method of claim 25 wherein:

the attitude of the moving vehicle is computed and the state of flexure of the moving vehicle is determined simultaneously at each respective one of the epochs after the initialization period in the attitude computing step in accordance with a predefined set of simultaneous equations that relate (A) the resolved integer wavelength ambiguities, (B) the phase measurements made at the respective one of the epochs, (C) an estimate of the attitude of the moving vehicle at the respective one of the epochs, (D) a correction to the estimate of the attitude, (E) an estimate of the state of flexure of the moving vehicle at the respective one of the epochs, and (F) a correction to the estimate of the state of flexure;

the attitude of the moving vehicle is computed and the state of flexure of the moving vehicle is determined iteratively and simultaneously at each respective one of the epochs after the initialization period in the attitude computing step by (A) computing the corrections to the estimates of the attitude and the state of flexure in a plurality of iterations in accordance with the predefined set of simultaneous equations, (B) in each respective one of the iterations, using as the estimates of the attitude and the state of flexure the estimates of the attitude and the state of flexure used in a directly preceding one of the iterations corrected by the corrections to the estimates of the attitude and state of flexure computed in the directly preceding one of the iterations.

27. A GPS attitude system for determining the attitude of a moving vehicle from a plurality of GPS carrier signals, the GPS attitude system comprising:

four antennas mounted to the moving vehicle, each of the antennas receiving the GPS carrier signals;

signal receiving means for receiving the GPS signals from each of the antennas;

phase measuring means for making phase measurements for the GPS carrier signals received from each of the antennas at a plurality of epochs during an initialization period and at a plurality of epochs after the initialization period, wherein there is an integer wavelength ambiguity associated with the phase measurements made for each of the GPS carrier signals received from a first one and a second one of the antennas, there is an integer wavelength ambiguity associated with the phase measurements made for each of the GPS carrier signals received from the first one and a third one of the antennas, and there is an integer wavelength ambiguity associated with the phase measurements made for each of the GPS carrier signals received from the first one and a fourth one of the antennas;

ambiguity resolution means for (A) resolving the integer wavelength ambiguities, and (B) generating a status report indicating that the resolved integer ambiguities are valid;

integrity checking means for (A) determining when an erroneous integer wavelength change has occurred in the phase measurement made for a particular one of the GPS carrier signals received by a particular one of the antennas at a particular one of the epochs after the initialization period, the erroneous integer wavelength change creating one or more new integer wavelength ambiguities associated with the phase measurements made for the particular one of the GPS carrier signals received by the particular one of the antennas at succeeding ones of the epochs after the initialization period, and (B) updating the status report to indicate that each one of the resolved integer wavelength ambiguities associated with the phase measurement made for the particular one of the GPS carrier signals received by the particular one of the antennas at the particular one of the epochs is no longer valid;

attitude computation means for computing the attitude of the moving vehicle at each respective one of the epochs after the initialization period in response to the resolved integer wavelength ambiguities designated as being valid in the status report and the phase measurements made at the respective one of the epochs after the initialization period associated with the resolved integer ambiguities designated as being valid in the status report;

the integrity checking means also (C) resolving the new integer wavelength ambiguities in response to the attitude of the moving vehicle computed at an initial one of the succeeding ones of the epochs after the initialization period and the phase measurements made at the initial one of the succeeding ones of the epochs after the initialization period associated with the new integer wavelength ambiguities, and (D) updating the status report to indicate that the resolved new integer wavelength ambiguities are valid.

28. A method of determining the attitude of a moving vehicle from a plurality of GPS carrier signals, the method comprising:

receiving the GPS carrier signals with each of four antennas mounted to the moving vehicle;

receiving the GPS signals from each of the antennas;

making phase measurements for the GPS carrier signals received from each of the antennas at a plurality of epochs during an initialization period and at a plurality of epochs after the initialization period, wherein there is an integer wavelength ambiguity associated with the phase measurements made for each of the GPS carrier signals received from a first one and a second one of the antennas, there is an integer wavelength ambiguity associated with the phase measurements made for each of the GPS carrier signals received from the first one and a third one of the antennas, and there is an integer wavelength ambiguity associated with the phase measurements made for each of the GPS carrier signals received from the first one and a fourth one of the antennas;

resolving the integer wavelength ambiguities;

generating a status report indicating that the resolved integer ambiguities are valid;

determining when an erroneous integer wavelength change has occurred in the phase measurement made for a particular one of the GPS carrier signals received by a particular one of the antennas at a particular one of the epochs after the initialization period, the erroneous integer wavelength change creating one or more new integer wavelength ambiguities associated with the phase measurements made for the particular one of the GPS carrier signals received by the particular one of the antennas at succeeding ones of the epochs after the initialization period;

updating the status report to indicate that each one of the resolved integer wavelength ambiguities associated with the phase measurement made for the particular one of the GPS carrier signals received by the particular one of the antennas at the particular one of the epochs is no longer valid;

computing the attitude of the moving vehicle at each respective one of the epochs after the initialization period in response to the resolved integer wavelength ambiguities designated as being valid in the status report and the phase measurements made at the respective one of the epochs after the initialization period associated with the resolved integer ambiguities;

resolving the new integer wavelength ambiguities in response to the attitude of the moving vehicle computed at an initial one of the succeeding ones of the epochs after the initialization period and the phase measurements made at the initial one of the succeeding ones of the epochs after the initialization period associated with the new integer wavelength ambiguities; and

updating the status report to indicate that the resolved new integer wavelength ambiguities are valid.