Distance dependant error mitigation in real-time kinematic (RTK) positioning

• US 8,035,552 B2
• Filed: 05/12/2008
• Issued: 10/11/2011
• Est. Priority Date: 05/31/2007
• Status: Active Grant

• Current Assignee: Deere & Company
• Original Assignee: Navcom Technology, Inc. (Deere & Company)
• Inventors: Hatch, Ronald R., Eslinger, Daniel J., Dai, Liwen L., Sharpe, Richard T.
• Primary Examiner(s): Issing; Gregory C
• Application Number:
  US12/119,451
• Publication Number:
  US 20090135056A1
• Time in Patent Office: 1,247 Days
• Field of Search: 342/357.23, 342/357.26, 342/357.27
• US Class Current: 342/357.23
• CPC Class Codes: G01S 19/32 Multimode operation in a single same satellite system, e.g. GPS L1/L2
• CPC Class Codes: G01S 19/44 Carrier phase ambiguity resolution; Floating ambiguity; LAMBDA [Least-squares AMBiguity Decorrelation Adjustment] method

Abstract

A method for mitigating atmospheric errors in code and carrier phase measurements based on signals received from a plurality of satellites in a global navigation satellite system is disclosed. A residual tropospheric delay and a plurality of residual ionospheric delays are modeled as states in a Kalman filter. The state update functions of the Kalman filter include at least one baseline distance dependant factor, wherein the baseline distance is the distance between a reference receiver and a mobile receiver. A plurality of ambiguity values are modeled as states in the Kalman filter. The state update function of the Kalman filter for the ambiguity states includes a dynamic noise factor. An estimated position of mobile receiver is updated in accordance with the residual tropospheric delay, the plurality of residual ionospheric delays and/or the plurality of ambiguity values.

Claims

1. A method for mitigating atmospheric errors in code and carrier phase measurements based on signals received from a plurality of satellites in a global navigation satellite system, the method comprising:

estimating a residual tropospheric delay, the residual tropospheric delay modeled as a state in a Kalman filter, and wherein a state update function of the Kalman filter for the residual tropospheric delay includes at least one baseline distance dependent factor, wherein the at least one baseline distance dependent factor corresponds to a baseline distance between a reference receiver and a mobile receiver; and

updating an estimated position of the mobile receiver in accordance with the estimated residual tropospheric delay and the code and carrier phase measurements, wherein the estimated position of the mobile receiver is modeled as coordinate states in the Kalman filter;

wherein the state update function of the Kalman Filter includes a dynamic model Q_k for the residual tropospheric delay given by;

2. The method of claim 1, including:

obtaining code and carrier phase measurements based on signals received from the plurality of satellites at the reference receiver and mobile receiver;

computing double difference values from the obtained measurements to form double difference code and carrier phase measurements; and

updating the estimated position of the mobile receiver in accordance with the estimated residual tropospheric delay and the double difference code and carrier phase measurements.

3. The method of claim 1, wherein the Kalman filter includes a plurality of states, including a single state that scales the residual tropospheric delay.

4. The method of claim 1, wherein the state update function of the Kalman filter for the residual tropospheric delay is based in part on an average elevation angle of a satellite with respect to the reference receiver and the mobile receiver.

5. The method of claim 1, wherein the state update function of the Kalman filter for the residual tropospheric delay includes at least one factor based on the baseline distance and a height difference between the reference receiver and the mobile receiver.

6. The method of claim 1, further comprising:

estimating at least one residual ionospheric delay, the at least one residual ionospheric delay modeled as at least one state in the Kalman filter, and wherein a state update function of the Kalman filter for the at least one residual ionospheric delay includes at least one baseline distance dependent factor; and

updating the estimated position of the mobile receiver in accordance with the at least one estimated residual ionospheric delays and the code and carrier phase measurements.

7. The method of claim 6, including:

obtaining code and carrier phase measurements based on signals received from the plurality of satellites at the reference receiver and mobile receiver;

computing double difference values from the obtained measurements to form double difference code and carrier phase measurements; and

updating the estimated position of the mobile receiver in accordance with the estimated residual tropospheric delay, the at least one estimated residual ionospheric delays, and the double difference code and carrier phase measurements.

8. The method of claim 6, wherein the updating includes updating a distinct residual ionospheric delay state in the Kalman filter for each of a plurality of satellites.

9. The method of claim 6, wherein the state update function of the Kalman filter for the at least one residual ionospheric delay includes at least one factor based on local time and ionosphere activity.

10. The method of claim 1, further comprising:

estimating N−

1 residual ionospheric delays, the N−

1 residual ionospheric delays modeled as N−

1 states in the Kalman filter, and wherein a state update function of the Kalman filter for the N−

1 residual ionospheric delays includes at least one baseline distance dependent factor for each of the N−

1 states, wherein N comprises a number of satellites from which signals are received and for which code and carrier phase measurements are made; and

updating the estimated position of the mobile receiver in accordance with the N−

1 estimated residual ionospheric delays and the code and carrier phase measurements.

11. The method of claim 10, including:

obtaining code and carrier phase measurements based on signals received from the plurality of satellites at the reference receiver and mobile receiver;

computing double difference values from the obtained measurements to form double difference code and carrier phase measurements; and

updating the estimated position of the mobile receiver in accordance with the estimated residual tropospheric delay, the estimated N−

1 residual ionospheric delays, and the double difference code and carrier phase measurements.

12. The method of claim 10, wherein the updating includes updating a distinct residual ionospheric delay state in the Kalman filter for each of a plurality of satellites.

13. The method of claim 10, wherein the state update function of the Kalman filter for the N−

1 residual ionospheric delays includes at least one factor based on local time and ionosphere activity.

38. The method of claim 6, wherein the state update function of the Kalman filter for the at least one residual ionospheric delay includes the least one baseline distance dependent factor and a satellite elevation dependent factor.

14. A method for mitigating atmospheric errors in code and carrier phase measurements based on signals received from a plurality of satellites in a global navigation satellite system, the method comprising:

estimating at least one residual ionospheric delay, the at least one residual ionospheric delay modeled as at least one state in the Kalman filter, and wherein a state update function of the Kalman filter for the at least one residual ionospheric delay includes at least one baseline distance dependent factor, wherein the at least one baseline distance dependent factor corresponds to a distance between a reference receiver and a mobile receiver; and

updating an estimated position of the mobile receiver in accordance with the at least one estimated residual ionospheric delays and the code and carrier phase measurements, wherein the estimated position of the mobile receiver is modeled as a state in the Kalman filter;

wherein the state update function of the Kalman Filter for the at least one residual ionospheric delay includes a dynamic model Q_k for the residual ionospheric delay given by;

15. The method of claim 14, including:

obtaining code and carrier phase measurements based on signals received from the plurality of satellites at the reference receiver and mobile receiver;

computing double difference values from the obtained measurements to form double difference code and carrier phase measurements; and

updating the estimated position of the mobile receiver in accordance with the at least one estimated residual ionospheric delays and the double difference code and carrier phase measurements.

16. The method of claim 14, wherein the updating includes updating a distinct residual ionospheric delay state in the Kalman filter for each of a plurality of satellites.

17. A method for mitigating atmospheric errors in code and carrier phase measurements based on signals received from a plurality of satellites in a global navigation satellite system, the method comprising:

estimating N−

1 residual ionospheric delays, the N−

1 residual ionospheric delays modeled as N−

1 states in the Kalman filter, and wherein a state update function of the Kalman filter for the N−

1 residual ionospheric delays includes at least one baseline distance dependent factor for each of the N−

1 states, wherein N comprises a number of satellites from which signals are received and for which code and carrier phase measurements are made, and wherein the at least one baseline distance dependent factor corresponds to a distance between a reference receiver and a mobile receiver; and

updating an estimated position of the mobile receiver in accordance with the N−

1 estimated residual ionospheric delays and the code and carrier phase measurements, wherein the estimated position of the mobile receiver is modeled as a state in the Kalman filter;

wherein the state update function of the Kalman Filter for the N−

1 residual ionospheric delays includes a dynamic model for the residual delays given by;

18. The method of claim 17, including:

obtaining code and carrier phase measurements based on signals received from the plurality of satellites at the reference receiver and mobile receiver;

computing double difference values from the obtained measurements to form double difference code and carrier phase measurements; and

updating the estimated position of the mobile receiver in accordance with the estimated N−

1 residual ionospheric delays and the double difference code and carrier phase measurements.

19. The method of claim 17, wherein the updating includes updating a distinct residual ionospheric delay state in the Kalman filter for each of a plurality of satellites.

20. A positioning or navigation system, comprising:

a mobile receiver configured to receive satellite signals from a plurality of satellites in a global navigation system;

a computer system coupled to the receiver, the computer system including one or more processors and a memory coupled to the one or more processors, the memory storing one or more programs for configured for execution by the one or more processors, the one or more programs for mitigating atmospheric errors in code and carrier phase measurements based on the signals received from the satellites, the one or more programs including;

instructions for estimating a residual tropospheric delay, the residual tropospheric delay modeled as a state in a Kalman filter, and wherein a state update function of the Kalman filter includes at least one baseline distance dependent factor, wherein the at least one baseline distance dependent factor corresponds to a distance between a reference receiver and the mobile receiver; and

instructions for updating an estimated position of the mobile receiver in accordance with the estimated residual tropospheric delay and the code and carrier phase measurements, wherein the estimated position of the mobile receiver is modeled as a state in the Kalman filter;

wherein the state update function of the Kalman Filter includes a dynamic model Q_k for the residual tropospheric delay given by;

21. The system of claim 20, wherein the one or more programs include:

instructions for obtaining code and carrier phase measurements based on signals received from the-plurality of satellites at the reference receiver and mobile receiver;

instructions for computing double difference values from the obtained measurements to form double difference code and carrier phase measurements; and

instructions for updating the estimated position of the mobile receiver in accordance with the estimated residual tropospheric delay and the double difference code and carrier phase measurements.

22. The system of claim 20, wherein the Kalman filter operates in a plurality of states, including a single state comprising the residual tropospheric delay.

23. The system of claim 20, wherein the state update function of the Kalman filter is based in part on an average elevation angle of a satellite with respect to the reference receiver and the mobile receiver.

24. The system of claim 20, wherein the state update function of the Kalman filter includes at least one factor based on the baseline distance and a height difference between the reference receiver and the mobile receiver.

25. A positioning or navigation system, comprising:

a mobile receiver configured to receive satellite signals from a plurality of satellites in a global navigation system;

a computer system coupled to the receiver, the computer system including one or more processors and a memory coupled to the one or more processors, the memory storing one or more programs configured for execution by the one or more processors, the one or more programs for mitigating atmospheric errors in code and carrier phase measurements based on the signals received from the satellites, the one or more programs including;

instructions for estimating N−

1 residual ionospheric delays, the N−

1 residual ionospheric delays modeled as a state in a Kalman filter, and wherein a state update function of the Kalman filter includes at least one baseline distance dependent factor, wherein the at least one baseline distance dependent factor corresponds to a distance between a reference receiver and the mobile receiver; and

instructions for updating an estimated position of the mobile receiver in accordance with the estimated N−

1 residual ionospheric delays and the code and carrier phase measurements, wherein the estimated position of the mobile receiver is modeled as a state in the Kalman filter;

wherein the state update function of the Kalman Filter for the N−

1 residual ionospheric delays includes a dynamic model for the residual ionospheric delays given by;

26. The system of claim 25, wherein the one or more programs include:

instructions for obtaining code and carrier phase measurements based on signals received from the-plurality of satellites at the reference receiver and mobile receiver;

instructions for computing double difference values from the obtained measurements to form double difference code and carrier phase measurements; and

instructions for updating the estimated position of the mobile receiver in accordance with the estimated N−

1 residual ionospheric delays and the double difference code and carrier phase measurements.

27. The system of claim 25, wherein the updating includes updating a distinct residual ionospheric delay state in the Kalman filter for each of a plurality of satellites.

28. The system of claim 25, wherein the state update function of the Kalman filter for the N−

1 residual ionospheric delays includes at least one factor based on local time and ionosphere activity.

39. The method of claim 28, wherein the state update function of the Kalman Filter for the at least one residual ionospheric delay includes a dynamic model Q_k for the residual ionospheric delay given by:

29. A positioning or navigation device, comprising:

a mobile receiver configured to receive satellite signals from a plurality of satellites in a global navigation system;

memory;

one or more processors;

one or more programs stored in the memory for execution by the one or more processors, the one or more programs for mitigating atmospheric errors in code and carrier phase measurements based on the signals received from the satellites, the one or more programs including;

instructions for estimating a residual tropospheric delay, the residual tropospheric delay modeled as a state in a Kalman filter, and wherein a state update function of the Kalman filter includes at least one baseline distance dependent factor, wherein the at least one baseline distance dependent factor corresponds to a distance between a reference receiver and the mobile receiver; and

instructions for updating an estimated position of the mobile receiver in accordance with the estimated residual tropospheric delay and the code and carrier phase measurements, wherein the estimated position of the mobile receiver is modeled as a state in the Kalman filter;

wherein the state update function of the Kalman Filter includes a dynamic model Q_k for the residual tropospheric delay given by;

30. The device of claim 29, wherein the one or more programs include:

instruction for obtaining code and carrier phase measurements based on signals received from the plurality of satellites at the reference receiver and mobile receiver;

instruction for computing double difference values from the obtained measurements to form double difference code and carrier phase measurements; and

instruction for updating the estimated position of the mobile receiver in accordance with the estimated residual tropospheric delay and the double difference code and carrier phase measurements.

31. The device of claim 29, wherein the Kalman filter operates in a plurality of states, including a single state comprising the residual tropospheric delay.

32. The device of claim 29, wherein the state update function of the Kalman filter is based in part on an average elevation angle of a satellite with respect to the reference receiver and the mobile receiver.

33. The device of claim 29, wherein the state update function of the Kalman filter includes at least one factor based on the baseline distance and a height difference between the reference receiver and the mobile receiver.

34. A positioning or navigation device, comprising:

a mobile receiver configured to receive satellite signals from a plurality of satellites in a global navigation system;

memory;

one or more processors;

one or more programs stored in the memory for execution by the one or more processors, the one or more programs for mitigating atmospheric errors in code and carrier phase measurements based on the signals received from the satellites, the one or more programs including;

instructions for estimating N−

1 residual ionospheric delays, the N−

1 residual ionospheric delays modeled as a state in a Kalman filter, and wherein a state update function of the Kalman filter includes at least one baseline distance dependent factor, wherein the at least one baseline distance dependent factor corresponds to a distance between a reference receiver and the mobile receiver; and

instructions for updating an estimated position of the mobile receiver in accordance with the estimated N−

1 residual ionospheric delays and the code and carrier phase measurements, wherein the estimated position of the mobile receiver is modeled as a state in the Kalman filter;

wherein the state update function of the Kalman filter for the N−

1 residual ionospheric delays includes the least one baseline distance dependent factor and a satellite elevation dependent factor; and

wherein the state update function of the Kalman Filter for the N−

1 residual ionospheric delays includes a dynamic model for the residual ionospheric delays given by;

35. The device of claim 34, wherein the one or more programs include:

instruction for obtaining code and carrier phase measurements based on signals received from the-plurality of satellites at the reference receiver and mobile receiver;

instruction for computing double difference values from the obtained measurements to form double difference code and carrier phase measurements; and

instruction for updating the estimated position of the mobile receiver in accordance with the estimated N−

1 residual ionospheric delays and the double difference code and carrier phase measurements.

36. The device of claim 34, wherein the updating includes updating a distinct residual ionospheric delay state in the Kalman filter for each of a plurality of satellites.

37. The device of claim 34, wherein the state update function of the Kalman filter for the N−

1 residual ionospheric delays includes at least one factor based on local time and ionosphere activity.