Detection and correction of anomalous measurements and ambiguity resolution in a global navigation satellite system receiver

• US 9,891,325 B2
• Filed: 05/08/2014
• Issued: 02/13/2018
• Est. Priority Date: 11/17/2009
• Status: Active Grant

• Current Assignee: Topcon Positioning Systems Incorporated (Topcon Corporation)
• Original Assignee: Topcon Positioning Systems Incorporated (Topcon Corporation)
• Inventors: Milyutin, Daniel, Plenkin, Andrey
• Primary Examiner(s): Gregory, Bernarr E
• Assistant Examiner(s): Mull, Fred H
• Application Number:
  US14/273,120
• Publication Number:
  US 20140240172A1
• Time in Patent Office: 1,377 Days
• CPC Class Codes: G01S 19/20 Integrity monitoring, fault detection or fault isolation of space segment
• CPC Class Codes: G01S 19/43 using carrier phase measurements, e.g. kinematic positioning; using long or short baseline interferometry
• CPC Class Codes: G01S 19/44 Carrier phase ambiguity resolution; Floating ambiguity; LAMBDA [Least-squares AMBiguity Decorrelation Adjustment] method

Abstract

A global navigation system includes a first navigation receiver located in a rover and a second navigation receiver located in a base station. Single differences of measurements of satellite signals received at the two receivers are calculated and compared to single differences derived from an observation model. Anomalous measurements are detected and removed prior to performing computations for determining the output position of the rover and resolving integer ambiguities. Detection criteria are based on the residuals between the calculated and the derived single differences. For resolving integer ambiguities, computations based on Cholesky information Kalman filters and Householder transformations are advantageously applied. Changes in the state of the satellite constellation from one epoch to another are included in the computations.

Claims

1. A method for processing measurements in a global navigation satellite system comprising a first navigation receiver located in a rover and a second navigation receiver located in a base station, the method comprising the steps of:

receiving a first plurality of measurements based on a first plurality of carrier signals received by the first navigation receiver from a plurality of global navigation satellites;

receiving a second plurality of measurements based on a second plurality of carrier signals received by the second navigation receiver from the plurality of global navigation satellites, each carrier signal in the second plurality of carrier signals corresponding to a carrier signal in the first plurality of carrier signals, and each measurement in the second plurality of measurements corresponding to a measurement in the first plurality of measurements;

calculating a first plurality of single differences based on the first plurality of measurements and the second plurality of measurements;

determining a state vector based on a prescribed function using the first plurality of single differences, wherein the prescribed function is a Gauss-Newton method;

calculating a second plurality of single differences based on an observation model represented by a prescribed mathematical model applicable to raw measurements for the global navigation satellite system, wherein the prescribed mathematical model is given by;

ρ

_r,k^f,s=R_r,k^f,s+c(τ

_r,k+δ

τ

_r,k<sup>(ρ

)f,s</sup>−

τ

_k^s)+T_r,k^s+μ

^f/fref,sI_r,k^fref,s+ζ

_r,k<sup>(ρ

)f,s</sup>

and

φ

_r,k^f,s=R_r,k^f,s+c(τ

_r,k+δ

τ

_r,k<sup>(φ

)f,s</sup>−

τ

_k^s)+T_r,k^s+μ

^f/fref,sI_r,k^fref,s+λ

^f,s(M_r^f,s+ψ

_r,k^s)+ζ

_r,k<sup>(φ

)f,s</sup>;

where;

The set of index numbers _r,k^f,s refer to the following;

f is the index number of the frequency band,

s is the index number of a satellite,

r is the index number of a receiver,

k is the index number of a system time instant,

ρ

_r,k^f,s are line-of-sight pseudo-ranges (in meters) between satellite s and receiver r,

φ

_r,k^f,s are line-of-sight carrier phase measurements (in meters) between satellite s and receiver r,

c is the speed of light (2.99792458×

10⁸ m/s),

R_r,k^f,s=R(r_r,k^s+b_r,k^f,s,r_r,k^s+c_r,k^f,s) is the distance from the phase center of the transmitting antenna on satellite s to the phase center of the receiving antenna on receiver r,

r=(x, y, z)^T is the position vector, also referred to herein as the radius vector, in the World Geodetic System 84 (WGS

     84) coordinate frame referenced to the center of the Earth,

r_r,k^s is the radius vector of satellite s at the instant that the satellite signal is received at receiver r,

b_r,k^f,s is the displacement vector of the phase center (for the frequency band f) of the receiving antenna on the receiver r relative to the antenna reference point;

this vector depends on the direction of satellite s,

c_r,k^f,s is the displacement vector of the phase center (for the frequency band f) of the transmitting antenna on the satellite s relative to the center-of-mass of the satellite,

λ

^f,s is the wavelength of the carrier signal transmitted by satellite s on frequency band f,

τ

_k^s and τ

_r,k are the clock offsets of the satellite clock and the receiver clock, respectively, relative to the system time,

δ

τ

_r,k<sup>(ρ

)f,s</sup> and δ

τ

_r,k<sup>(φ

)f,s</sup> are the code-measurement channel delay and phase-measurement channel delay, respectively,

T_r,k^s is the troposphere delay,

I_r,k^fref,s is the ionosphere delay caused by propagation of the satellite signal through the ionosphere,

2. The method of claim 1, wherein the step of determining whether the first plurality of measurements and the second plurality of measurements are consistent with the observation model comprises the steps of:

calculating the absolute value of each residual in the plurality of residuals;

comparing the absolute value of each residual in the plurality of residuals to a threshold value;

determining that the first plurality of measurements and the second plurality of measurements are consistent with the observation model when the absolute value of each residual in the plurality of residuals is less than or equal to the threshold value; and

determining that the first plurality of measurements and the second plurality of measurements are not consistent with the observation model when the absolute value of at least one residual in the plurality of residuals is greater than the threshold value.

3. The method of claim 2, wherein detecting anomalous measurements comprises searching for a maximum absolute value of a residual.

4. The method of claim 1, wherein the step of determining whether the first plurality of measurements and the second plurality of measurements are consistent with the observation model comprises the steps of:

calculating a plurality of weighted residuals based on the plurality of residuals;

calculating the absolute value of each weighted residual in the plurality of weighted residuals;

comparing the absolute value of each weighted residual in the plurality of weighted residuals to a threshold value;

determining that the first plurality of measurements and the second plurality of measurements are consistent with the observation model when the absolute value of each weighted residual in the plurality of weighted residuals is less than or equal to the threshold value; and

determining that the first plurality of measurements and the second plurality of measurements are not consistent with the observation model when the absolute value of at least one weighted residual in the plurality of weighted residuals is greater than the threshold value.

5. The method of claim 4, wherein detecting anomalous measurements comprises searching for the maximum absolute value of a weighted residual.

6. The method of claim 1, wherein the step of determining whether the first plurality of measurements and the second plurality of measurements are consistent with the observation model comprises the steps of:

calculating a weighted sum of residual squares based on the plurality of residuals;

comparing the weighted sum of residual squares to a threshold value;

determining that the first plurality of measurements and the second plurality of measurements are consistent with the observation model when the weighted sum of residual squares is less than or equal to the threshold value; and

determining that the first plurality of measurements and the second plurality of measurements are not consistent with the observation model when the weighted sum of residual squares is greater than the threshold value.

7. The method of claim 6, wherein detecting anomalous measurements comprises:

for each particular measurement in the first plurality of measurements and the corresponding particular measurement in the second plurality of measurements;

removing the particular measurement in the first plurality of measurements and the corresponding particular measurement in the second plurality of measurements; and

calculating an updated weighted sum of residual squares based on the remaining measurements in the first plurality of measurements and the remaining measurements in the second plurality of measurements;

determining the minimum value of the updated weighted sums of residual squares; and

determining the particular measurement in the first plurality of measurements and the corresponding particular measurement in the second plurality of measurements corresponding to the minimum value of the updated weighted sums of residual squares.

8. The method of claim 1, wherein the first plurality of measurements comprises a first plurality of pseudo-ranges and the second plurality of measurements comprises a second plurality of pseudo-ranges.

9. The method of claim 1, wherein the first plurality of measurements comprises a first plurality of unambiguous phases and the second plurality of measurements comprises a second plurality of unambiguous phases.

10. An apparatus for processing measurements in a global navigation satellite system comprising a first navigation receiver located in a rover and a second navigation receiver located in a base station, the apparatus comprising:

a data bus interface that receives a first plurality of measurements based on a first plurality of carrier signals received by the first navigation receiver from a plurality of global navigation satellites and receives

a second plurality of measurements based on a second plurality of carrier signals received by the second navigation receiver from the plurality of global navigation satellites, each carrier signal in the second plurality of carrier signals corresponding to a carrier signal in the first plurality of carrier signals, and each measurement in the second plurality of measurements corresponding to a measurement in the first plurality of measurements;

a processor;

a memory, for executing computer program instructions stored in a memory, which when executed by the processor, cause the processor to perform operations comprising;

calculating a first plurality of single differences based on the first plurality of measurements and the second plurality of measurements;

determining a state vector based on a prescribed function using the first plurality of single differences, wherein the prescribed function is a Gauss-Newton method;

calculating a second plurality of single differences based on an observation model represented by a prescribed mathematical model applicable to raw measurements for the global navigation satellite system, wherein the prescribed mathematical model is given by at least;

ρ

_r,k^f,s=R_r,k^f,s+c(τ

_r,k+δ

τ

_r,k<sup>(ρ

)f,s</sup>−

τ

_k^s)+T_r,k^s+μ

^f/fref,sI_r,k^fref,s+ζ

_r,k<sup>(ρ

)f,s</sup>

and

φ

_r,k^f,s=R_r,k^f,s+c(τ

_r,k+δ

τ

_r,k<sup>(φ

)f,s</sup>−

τ

_k^s)+T_r,k^s+μ

^f/fref,sI_r,k^fref,s+λ

^f,s(M_r^f,s+ψ

_r,k^s)+ζ

_r,k<sup>(φ

)f,s</sup>;

where;

The set of index numbers _r,k^f,s refer to the following;

f is the index number of the frequency band,

s is the index number of a satellite,

r is the index number of a receiver,

k is the index number of a system time instant,

ρ

_r,k^f,s are line-of-sight pseudo-ranges (in meters) between satellite s and receiver r,

φ

_r,k^f,s are line-of-sight carrier phase measurements (in meters) between satellite s and receiver r,

c is the speed of light (2.99792458×

10⁸ m/s),

R_r,k^f,s=R(r_r,k^s+b_r,k^f,s,r_r,k^s+c_r,k^f,s) is the distance from the phase center of the transmitting antenna on satellite s to the phase center of the receiving antenna on receiver r,

r=(x, y, z)^T is the position vector, also referred to herein as the radius vector, in the World Geodetic System 84 (WGS

     84) coordinate frame referenced to the center of the Earth,

r_r,k^s is the radius vector of satellite s at the instant that the satellite signal is received at receiver r,

b_r,k^f,s is the displacement vector of the phase center (for the frequency band f) of the receiving antenna on the receiver r relative to the antenna reference point;

this vector depends on the direction of satellite s,

c_r,k^f,s is the displacement vector of the phase center (for the frequency band f) of the transmitting antenna on the satellite s relative to the center-of-mass of the satellite,

λ

_f,s is the wavelength of the carrier signal transmitted by satellite s on frequency band f,

τ

_k^s and τ

_r,k are the clock offsets of the satellite clock and the receiver clock, respectively, relative to the system time,

δ

τ

_r,k<sup>(ρ

)f,s</sup> and δ

τ

_r,k<sup>(φ

)f,s</sup> are the code-measurement channel delay and phase-measurement channel delay, respectively,

T_r,k^s is the troposphere delay,

I_r,k^fref,s is the ionosphere delay caused by propagation of the satellite signal through the ionosphere,

11. The apparatus of claim 10, wherein the determining whether the first plurality of measurements and the second plurality of measurements are consistent with the observation model operation further comprises:

calculating the absolute value of each residual in the plurality of residuals;

comparing the absolute value of each residual in the plurality of residuals to a threshold value;

determining that the first plurality of measurements and the second plurality of measurements are consistent with the observation model when the absolute value of each residual in the plurality of residuals is less than or equal to the threshold value; and

determining that the first plurality of measurements and the second plurality of measurements are not consistent with the observation model when the absolute value of at least one residual in the plurality of residuals is greater than the threshold value.

12. The apparatus of claim 11, wherein the detecting anomalous measurements operation further comprises:

in response to determining that the first plurality of measurements and the second plurality of measurements are not consistent with the observation model, searching for a maximum absolute value of a residual.

13. The apparatus of claim 10, wherein the determining whether the first plurality of measurements and the second plurality of measurements are consistent with the observation model operation further comprises:

calculating a plurality of weighted residuals based on the plurality of residuals;

calculating the absolute value of each weighted residual in the plurality of weighted residuals;

comparing the absolute value of each weighted residual in the plurality of weighted residuals to a threshold value;

determining that the first plurality of measurements and the second plurality of measurements are consistent with the observation model when the absolute value of each weighted residual in the plurality of weighted residuals is less than or equal to the threshold value; and

determining that the first plurality of measurements and the second plurality of measurements are not consistent with the observation model when the absolute value of at least one weighted residual in the plurality of weighted residuals is greater than the threshold value.

14. The apparatus of claim 13, wherein detecting anomalous measurements operation further comprises:

in response to determining that the first plurality of measurements and the second plurality of measurements are not consistent with the observation model, searching for the maximum absolute value of a weighted residual.

15. The apparatus of claim 10, wherein the determining whether the first plurality of measurements and the second plurality of measurements are consistent with the observation model operation further comprises:

calculating a weighted sum of residual squares based on the plurality of residuals;

comparing the weighted sum of residual squares to a threshold value;

determining that the first plurality of measurements and the second plurality of measurements are consistent with the observation model when the weighted sum of residual squares is less than or equal to the threshold value; and

determining that the first plurality of measurements and the second plurality of measurements are not consistent with the observation model when the weighted sum of residual squares is greater than the threshold value.

16. The apparatus of claim 15, wherein the detecting anomalous measurements operation further comprises:

in response to determining that the first plurality of measurements and the second plurality of measurements are not consistent with the observation model,

for each particular measurement in the first plurality of measurements and the corresponding particular measurement in the second plurality of measurements;

removing the particular measurement in the first plurality of measurements and the corresponding particular measurement in the second plurality of measurements; and

calculating an updated weighted sum of residual squares based on the remaining measurements in the first plurality of measurements and the remaining measurements in the second plurality of measurements;

determining the minimum value of the updated weighted sums of residual squares; and

determining the particular measurement in the first plurality of measurements and the corresponding particular measurement in the second plurality of measurements corresponding to the minimum value of the updated weighted sums of residual squares.

17. The apparatus of claim 16, wherein the first plurality of measurements comprises a first plurality of pseudo-ranges and the second plurality of measurements comprises a second plurality of pseudo-ranges.

18. The apparatus of claim 16, wherein the first plurality of measurements comprises a first plurality of unambiguous phases and the second plurality of measurements comprises a second plurality of unambiguous phases.

19. A non-transitory computer readable medium storing computer program instructions for processing measurements in a global navigation satellite system comprising a first navigation receiver located in a rover and a second navigation receiver located in a base station, which, when executed on a processor, cause the processor to perform operations comprising:

receiving a first plurality of measurements based on a first plurality of carrier signals received by the first navigation receiver from a plurality of global navigation satellites;

receiving a second plurality of measurements based on a second plurality of carrier signals received by the second navigation receiver from the plurality of global navigation satellites, each carrier signal in the second plurality of carrier signals corresponding to a carrier signal in the first plurality of carrier signals, and each measurement in the second plurality of measurements corresponding to a measurement in the first plurality of measurements;

calculating a first plurality of single differences based on the first plurality of measurements and the second plurality of measurements;

determining a state vector based on a prescribed function using the first plurality of single differences, wherein the prescribed function is a Gauss-Newton method;

calculating a second plurality of single differences based on an observation model represented by a prescribed mathematical model applicable to raw measurements for the global navigation satellite system, wherein the prescribed mathematical model is given by at least;

ρ

_r,k^f,s=R_r,k^f,s+c(τ

_r,k+δ

τ

_r,k<sup>(ρ

)f,s</sup>−

τ

_k^s)+T_r,k^s+μ

^f/fref,sI_r,k^fref,s+ζ

_r,k<sup>(ρ

)f,s</sup>

and

φ

_r,k^f,s=R_r,k^f,s+c(τ

_r,k+δ

τ

_r,k<sup>(φ

)f,s</sup>−

τ

_k^s)+T_r,k^s+μ

^f/fref,sI_r,k^fref,s+λ

^f,s(M_r^f,s+ψ

_r,k^s)+ζ

_r,k<sup>(φ

)f,s</sup>;

where;

The set of index numbers _r,k^f,s refer to the following;

f is the index number of the frequency band,

s is the index number of a satellite,

r is the index number of a receiver,

k is the index number of a system time instant,

ρ

_r,k^f,s are line-of-sight pseudo-ranges (in meters) between satellite s and receiver r,

φ

_r,k^f,s are line-of-sight carrier phase measurements (in meters) between satellite s and receiver r,

c is the speed of light (2.99792458×

10⁸ m/s),

R_r,k^f,s=R(r_r,k^s+b_r,k^f,s,r_r,k^s+c_r,k^f,s) is the distance from the phase center of the transmitting antenna on satellite s to the phase center of the receiving antenna on receiver r,

r=(x, y, z)^T is the position vector, also referred to herein as the radius vector, in the World Geodetic System 84 (WGS

     84) coordinate frame referenced to the center of the Earth,

r_r,k^s is the radius vector of satellite s at the instant that the satellite signal is received at receiver r,

b_r,k^f,s is the displacement vector of the phase center (for the frequency band f) of the receiving antenna on the receiver r relative to the antenna reference point;

this vector depends on the direction of satellite s,

c_r,k^f,s is the displacement vector of the phase center (for the frequency band f) of the transmitting antenna on the satellite s relative to the center-of-mass of the satellite,

λ

^f,s the wavelength of the carrier signal transmitted by satellite s on frequency band f,

τ

_k^s and τ

_r,k are the clock offsets of the satellite clock and the receiver clock, respectively, relative to the system time,

δ

τ

_r,k<sup>(ρ

)f,s</sup> and δ

τ

_r,k<sup>(φ

)f,s</sup> are the code-measurement channel delay and phase-measurement channel delay, respectively,

T_r,k^s is the troposphere delay,

I_r,k^fref,s is the ionosphere delay caused by propagation of the satellite signal through the ionosphere,

20. The non-transitory computer readable medium of claim 19, wherein the determining whether the first plurality of measurements and the second plurality of measurements are consistent with the observation model operation further comprises:

calculating the absolute value of each residual in the plurality of residuals;

comparing the absolute value of each residual in the plurality of residuals to a threshold value;

determining that the first plurality of measurements and the second plurality of measurements are consistent with the observation model when the absolute value of each residual in the plurality of residuals is less than or equal to the threshold value; and

determining that the first plurality of measurements and the second plurality of measurements are not consistent with the observation model when the absolute value of at least one residual in the plurality of residuals is greater than the threshold value.

21. The non-transitory computer readable medium of claim 20, wherein the detecting anomalous measurements operation further comprises:

in response to determining that the first plurality of measurements and the second plurality of measurements are not consistent with the observation model, searching for a maximum absolute value of a residual.

22. The non-transitory computer readable medium of claim 19, wherein the determining whether the first plurality of measurements and the second plurality of measurements are consistent with the observation model operation further comprises:

calculating a plurality of weighted residuals based on the plurality of residuals;

calculating the absolute value of each weighted residual in the plurality of weighted residuals;

comparing the absolute value of each weighted residual in the plurality of weighted residuals to a threshold value;

determining that the first plurality of measurements and the second plurality of measurements are consistent with the observation model when the absolute value of each weighted residual in the plurality of weighted residuals is less than or equal to the threshold value; and

determining that the first plurality of measurements and the second plurality of measurements are not consistent with the observation model when the absolute value of at least one weighted residual in the plurality of weighted residuals is greater than the threshold value.

23. The non-transitory computer readable medium of claim 22, wherein the detecting anomalous measurements operation further comprises:

in response to determining that the first plurality of measurements and the second plurality of measurements are not consistent with the observation model, searching for the maximum absolute value of a weighted residual.

24. The non-transitory computer readable medium of claim 19, wherein the determining whether the first plurality of measurements and the second plurality of measurements are consistent with the observation model operation further comprises:

calculating a weighted sum of residual squares based on the plurality of residuals;

comparing the weighted sum of residual squares to a threshold value;

determining that the first plurality of measurements and the second plurality of measurements are consistent with the observation model when the weighted sum of residual squares is less than or equal to the threshold value; and

determining that the first plurality of measurements and the second plurality of measurements are not consistent with the observation model when the weighted sum of residual squares is greater than the threshold value.

25. The non-transitory computer readable medium of claim 24, wherein the detecting anomalous measurements operation further comprises:

in response to determining that the first plurality of measurements and the second plurality of measurements are not consistent with the observation model;

for each particular measurement in the first plurality of measurements and the corresponding particular measurement in the second plurality of measurements;

removing the particular measurement in the first plurality of measurements and the corresponding particular measurement in the second plurality of measurements; and

calculating an updated weighted sum of residual squares based on the remaining measurements in the first plurality of measurements and the remaining measurements in the second plurality of measurements;

determining the minimum value of the updated weighted sums of residual squares; and

determining the particular measurement in the first plurality of measurements and the corresponding particular measurement in the second plurality of measurements corresponding to the minimum value of the updated weighted sums of residual squares.

26. The non-transitory computer readable medium of claim 19, wherein the first plurality of measurements comprises a first plurality of pseudo-ranges and the second plurality of measurements comprises a second plurality of pseudo-ranges.

27. The non-transitory computer readable medium of claim 19, wherein the first plurality of measurements comprises a first plurality of unambiguous phases and the second plurality of measurements comprises a second plurality of unambiguous phases.