Detection and Correction of Anomalous Measurements and Ambiguity Resolution in a Global Navigation Satellite System Receiver

• US 20140240172A1
• Filed: 05/08/2014
• Published: 08/28/2014
• 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
• Granted Patent: US 9,891,325 B2
• Time in Patent Office: Days
• US Class Current: 342/357.51
• 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 the first plurality of single differences;

calculating a second plurality of single differences based on an observation model;

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

determining whether the first plurality of measurements and the second plurality of measurements are consistent with the observation model; and

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

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. The method of claim 1, further comprising the steps of:

eliminating the detected anomalous measurements; and

calculating a position of the rover based on the remaining measurements.

11. 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:

means for 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;

means for 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;

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

means for determining a state vector based on the first plurality of single differences;

means for calculating a second plurality of single differences based on an observation model;

means for calculating a plurality of residuals based on the first plurality of single differences and the second plurality of single differences;

means for determining whether the first plurality of measurements and the second plurality of measurements are consistent with the observation model; and

means for, in response to determining that the first plurality of measurements and the second plurality of measurements are not consistent with the observation model, detecting anomalous measurements.

12. The apparatus of claim 11, wherein the means for determining whether the first plurality of measurements and the second plurality of measurements are consistent with the observation model comprises:

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

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

means for 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

means for 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.

13. The apparatus of claim 12, wherein the means for, in response to determining that the first plurality of measurements and the second plurality of measurements are not consistent with the observation model, detecting anomalous measurements comprises:

means for, 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.

14. The apparatus of claim 11, wherein the means for determining whether the first plurality of measurements and the second plurality of measurements are consistent with the observation model comprises:

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

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

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

means for 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

means for 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.

15. The apparatus of claim 14, wherein the means for, in response to determining that the first plurality of measurements and the second plurality of measurements are not consistent with the observation model, detecting anomalous measurements comprises:

means for, 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.

16. The apparatus of claim 11, wherein the means for determining whether the first plurality of measurements and the second plurality of measurements are consistent with the observation model comprises:

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

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

means for 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

means for 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.

17. The apparatus of claim 16, wherein the means for, in response to determining that the first plurality of measurements and the second plurality of measurements are not consistent with the observation model, detecting anomalous measurements comprises:

means for, 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.

18. The apparatus of claim 17, 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.

19. The apparatus of claim 17, 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.

20. The apparatus of claim 11, further comprising:

means for eliminating the detected anomalous measurements; and

means for calculating a position of the rover based on the remaining measurements.

21. A 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, the computer program instructions defining 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 the first plurality of single differences;

calculating a second plurality of single differences based on an observation model;

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

determining whether the first plurality of measurements and the second plurality of measurements are consistent with the observation model; and

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

22. The computer readable medium of claim 21, wherein the computer program instructions defining the step of determining whether the first plurality of measurements and the second plurality of measurements are consistent with the observation model comprise computer program instructions defining 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.

23. The computer readable medium of claim 22, wherein the computer program instructions defining the step of, in response to determining that the first plurality of measurements and the second plurality of measurements are not consistent with the observation model, detecting anomalous measurements comprise computer program instructions defining the step of:

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.

24. The computer readable medium of claim 21, wherein the computer program instructions defining the step of determining whether the first plurality of measurements and the second plurality of measurements are consistent with the observation model comprise computer program instructions defining 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.

25. The computer readable medium of claim 24, wherein the computer program instructions defining the step of, in response to determining that the first plurality of measurements and the second plurality of measurements are not consistent with the observation model, detecting anomalous measurements comprise computer program instructions defining the step of:

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.

26. The computer readable medium of claim 21, wherein the computer program instructions defining the step of determining whether the first plurality of measurements and the second plurality of measurements are consistent with the observation model comprise computer program instructions defining 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.

27. The computer readable medium of claim 26, wherein the computer program instructions defining the step of, in response to determining that the first plurality of measurements and the second plurality of measurements are not consistent with the observation model, detecting anomalous measurements comprise computer program instructions defining the step of:

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.

28. The computer readable medium of claim 21, 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.

29. The computer readable medium of claim 21, 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.

30. The computer readable medium of claim 21, wherein the 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 further comprise computer program instructions defining the steps of:

eliminating the detected anomalous measurements; and

calculating a position of the rover based on the remaining measurements.