GNSS signal processing methods and apparatus with ambiguity convergence indication

• US 8,368,591 B2
• Filed: 08/05/2009
• Issued: 02/05/2013
• Est. Priority Date: 08/19/2008
• Status: Active Grant

• Current Assignee: Trimble Navigation Limited (Trimble Inc.)
• Original Assignee: Trimble Navigation Limited (Trimble Inc.)
• Inventors: Talbot, Nicholas Charles, Vollath, Ulrich
• Primary Examiner(s): Keith, Jack W
• Assistant Examiner(s): McGue, Frank J
• Application Number:
  US13/059,416
• Publication Number:
  US 20110267226A1
• Time in Patent Office: 1,280 Days
• Field of Search: 342/357.27
• US Class Current: 342/357.27
• CPC Class Codes: G01S 19/44 Carrier phase ambiguity resolution; Floating ambiguity; LAMBDA [Least-squares AMBiguity Decorrelation Adjustment] method

Abstract

Methods and apparatus are provided for estimating parameters, i.e. ambiguities, derived from GNSS signals. Observations of a GNSS signal from each of a plurality of GNSS satellites are obtained (2120). The observations are fed to a filter having a state vector comprising a float ambiguity for each received frequency of the GNSS signals (2140). The filter estimates a float value for each float ambiguity of the state vector and co-variance values associated with the state vector. Integer values are assigned to at least a subgroup of the estimated float values to define a plurality of integer ambiguity candidate sets (2160). A weighted average of the candidate sets is formed (2200). A formal precision value based on covariance values of the filter is determined (2205), the formal precision value being a measure for an achievable precision. An achieved precision value of the weighted average is determined (2210). The achieved precision value is compared with the formal precision value to obtain a convergence value (2215). A convergence of the determination of the state vector is indicated (2218). Ambiguities of the weighted average can be used in subsequent operations to aid in determining a position of the receiver or can be used to prepare data, e.g., in a network processor that can be used to augment position information of a rover.

Claims

1. Method to estimate parameters derived from global navigational satellite system (GNSS) signals useful to determine a position, comprising

obtaining observations of a GNSS signal from each of a plurality of GNSS satellites;

feeding the observations to a filter having a state vector comprising a float ambiguity for each received frequency of the GNSS signals, each float ambiguity constituting a real number estimate of an integer number of wavelengths of the GNSS signal between a receiver of the GNSS signal and the GNSS satellite from which it is received, the filter estimating a float value for each float ambiguity of the state vector and covariance values associated with the state vector;

assigning integer values to at least a subgroup of the estimated float values to define a plurality of integer ambiguity candidate sets;

obtaining a weighted average of the candidate sets;

determining a formal precision value based on covariance values of the filter, the formal precision value being a measure for an achievable precision;

determining an achieved precision value of the weighted average;

comparing the achieved precision value with the formal precision value to obtain a convergence value; and

indicating a convergence of the determination of the state vector.

2. Method of claim 1, wherein the convergence value is obtained as a ratio of the achieved precision value to the formal precision value.

3. Method of claim 1, comprising

determining an instance in time when the convergence value of the position is better than a convergence threshold;

and

indicating a convergence of the determination of the state vector at and after the determined instance in time.

4. Method of claim 1, comprising

estimating an achieved precision of a position of the receiver determined based on the weighted ambiguities;

and

indicating a convergence of the determination of the state vector, if the achieved precision of the position is better than an inclusion threshold.

5. Method of at claim 1, comprising

estimating an achieved precision of a position of the receiver determined based on the weighted ambiguities;

and

indicating a non-convergence of the determination of the state vector, if the achieved precision of the position is worse than an exclusion threshold.

6. Method of claim 1, wherein obtaining a weighted average of the candidate sets comprises;

selecting a first number of candidate sets having a quality measure better than a first threshold, wherein the first threshold is determined based on a reference quality measure of a reference candidate set; and

forming the weighted average of the selected candidate sets by weighing each candidate set in the weighted average based on its quality measure.

7. Method of claim 6, comprising using the weighted average to estimate a position of the receiver of the GNSS signals.

8. Method of claim 6, wherein the reference candidate set is the candidate set having the best quality measure.

9. Method of at claim 6, wherein the quality measure of the candidate sets is constituted by a residual error norm value, the residual error norm value of a candidate set being a measure for a statistical distance of the candidate set to the state vector having the float ambiguities.

10. Method of claim 6, wherein the first threshold is determined as at least one of a fraction of, a multiple of, and a distance to the reference quality measure.

11. Method of claim 6, comprising, if the first number of selected candidate sets is smaller than a second threshold, selecting, for forming the weighted average, a second number of further candidate sets on the basis of the quality measures of the candidate sets in decreasing order starting with the non-selected candidate set having the best quality measure, the second number being constituted by the difference between the first number of selected candidate sets and a second threshold defining a minimum number of candidate sets to be included in the weighted average.

12. Method of at claim 6, comprising, if the first number of selected candidate sets is larger than a third threshold, excluding a third number of selected candidate sets from forming the weighted average in decreasing order starting with the selected candidate set having the worst quality measure, wherein the third number is constituted by the difference between the first number of selected candidate sets and a third threshold defining a maximum number of candidate sets to be included in the weighted average.

13. Method of claim 1, wherein obtaining the weighted average comprises:

determining the best quality measure of the candidate sets;

determining an expectation value of the candidate set having the best quality measure;

determining an error measure as a ratio of the best quality measure to the expectation value;

adapting the quality measures of the candidate sets as a function of the error measure;

performing a selection of the first number of candidate sets based on the adapted quality measures; and

forming the weighted average on the basis of the quality measures.

14. Method of claim 1, wherein obtaining the weighted average comprises:

determining the best quality measure of the candidate sets;

determining an expectation value of the candidate set having the best quality measure;

determining an error measure as a ratio of the best quality measure to the expectation value;

adapting the quality measures of the candidate sets as a function of the error measure; and

forming the weighted average based on the adapted quality measures.

15. Method of claim 13, comprising adapting the quality measures of the candidate sets as a function of the error measure by adjusting the variance-covariance matrix of the float solution.

16. Method of claim 13, comprising adjusting a variance-covariance matrix of the filter using the error measure, if the error measure is in a predetermined range.

17. Method of claim 13, comprising adjusting a variance-covariance matrix of the filter using the error measure, if the error measure is larger than one.

18. Method of claim 1, wherein defining the integer candidate sets comprises:

selecting a subset of float ambiguities of the state vector to form the subgroup of the float ambiguities of the state vector used to define the plurality of integer ambiguity candidate sets; and

assigning integer values to the estimated float values of the float ambiguities of the subset to define a plurality of integer ambiguity candidate sets.

19. Method of claim 18, wherein the selecting comprises selecting, as float ambiguities of the subset, the float ambiguities of frequencies tracked continuously for the longest period of time.

20. Method of at at claim 1, comprising

obtaining observations of the at least one frequency of the GNSS signals from the plurality of GNSS satellites to obtain observations at a plurality of instances in time;

updating the float ambiguities of the state vector over time on the basis of the observations;

determining that an interruption in tracking of at least one signal of a satellite occurred; and

maintaining the float ambiguity of the state vector for the at least one signal for which an interruption in tracking occurred at the value before the interruption in tracking occurred.

21. Method of claim 20, wherein it is determined that an interruption in tracking of at least one signal of a satellite occurred if an observation for the at least one signal is not available for at least one of the instances in time.

22. Method of claim 20, wherein it is determined that an interruption in tracking of at least one signal of a satellite occurred, if a cycle slip occurred.

23. Method of claim 20 comprising, if, after an interruption in tracking of a signal, tracking of the signal resumes, maintaining the float ambiguity of the state vector for the signal for which an interruption in tracking occurred at the value before the interruption in tracking occurred as a first float ambiguity and introducing into the state vector a second float ambiguity for the signal after resuming tracking.

49. Computer-readable physical storage medium embodying instructions configured, when executed on a computer processing unit, to carry out the method of claim 1.

24. Apparatus to estimate parameters derived from global navigational satellite system (GNSS) signals useful to determine a position, comprising

a receiver adapted to obtain observations of a GNSS signal from each of a plurality of GNSS satellites;

a filter having a state vector comprising a float ambiguity for each received frequency of the GNSS signals, each float ambiguity constituting a real number estimate of an integer number of wavelengths of the GNSS signal between a receiver of the GNSS signal and the GNSS satellite from which it is received, the filter estimating a float value for each float ambiguity of the state vector and covariance values associated with the state vector;

a processing element adapted to

assign integer values to at least a subgroup of the estimated float values to define a plurality of integer ambiguity candidate sets;

obtain a weighted average of the candidate sets;

determine a formal precision value based on covariance values of the filter, the formal precision value being a measure for an achievable precision;

determine an achieved precision value of the weighted average;

compare the achieved precision value with the formal precision value to obtain a convergence value; and

indicate a convergence of the determination of the state vector.

25. Apparatus of claim 24, wherein the processing element is adapted to obtain the convergence value as a ratio of the achieved precision value to the formal precision value.

26. Apparatus of claim 24, wherein the processing element is adapted to

determine an instance in time when the convergence value of the position is better than a convergence threshold;

and

indicate a convergence of the determination of the state vector at and after the determined instance in time.

27. Apparatus of claim 24, wherein the processing element is adapted to

estimate an achieved precision of a position of the receiver determined based on the weighted ambiguities;

and

indicate a convergence of the determination of the state vector, if the achieved precision of the position is better than an inclusion threshold.

28. Apparatus of claim 24, wherein the processing element is adapted to

estimate an achieved precision of a position of the receiver determined based on the weighted ambiguities;

and

indicate a non-convergence of the determination of the state vector, if the achieved precision of the position is worse than an exclusion threshold.

29. Apparatus of claim 24, wherein the processing element is adapted to, in order to obtain the weighted average of the candidate sets;

select a first number of candidate sets having a quality measure better than a first threshold, wherein the first threshold is determined based on a reference quality measure of a reference candidate set; and

form the weighted average of the selected candidate sets by weighing each candidate set in the weighted average based on its quality measure.

30. Apparatus of claim 29, wherein the processing element is adapted to use the weighted average to estimate a position of the receiver of the GNSS signals.

31. Apparatus of claims 29, wherein the reference candidate set is the candidate set having the best quality measure.

32. Apparatus of claim 29, wherein the quality measure of the candidate sets is constituted by a residual error norm value, the residual error norm value of a candidate set being a measure for a statistical distance of the candidate set to the state vector having the float ambiguities.

33. Apparatus of claim 29, wherein the processing element is adapted to determine the first threshold as at least one of a fraction of, a multiple of, and a distance to the reference quality measure.

34. Apparatus of claim 29, wherein the processing element is adapted to, if the first number of selected candidate sets is smaller than a second threshold, select, for forming the weighted average, a second number of further candidate sets on the basis of the quality measures of the candidate sets in decreasing order starting with the non-selected candidate set having the best quality measure, the second number being constituted by the difference between the first number of selected candidate sets and a second threshold defining a minimum number of candidate sets to be included in the weighted average.

35. Apparatus of claim 29, wherein the processing element is adapted to, if the first number of selected candidate sets is larger than a third threshold, exclude a third number of selected candidate sets from forming the weighted average in decreasing order starting with the selected candidate set having the worst quality measure, wherein the third number is constituted by the difference between the first number of selected candidate sets and a third threshold defining a maximum number of candidate sets to be included in the weighted average.

36. Apparatus of claim 24, wherein the processing element is adapted to, in order to obtain the weighted average:

determine the best quality measure of the candidate sets;

determine an expectation value of the candidate set having the best quality measure;

determine an error measure as a ratio of the best quality measure to the expectation value;

adapt the quality measures of the candidate sets as a function of the error measure;

perform a selection of the first number of candidate sets based on the adapted quality measures; and

form the weighted average on the basis of the quality measures.

37. Apparatus of claim 24, wherein the processing element is adapted to, in order to obtain the weighted average:

determine the best quality measure of the candidate sets;

determine an expectation value of the candidate set having the best quality measure;

determine an error measure as a ratio of the best quality measure to the expectation value;

adapt the quality measures of the candidate sets as a function of the error measure; and

form the weighted average based on the adapted quality measures.

38. Apparatus of claim 36, wherein the processing element is adapted to adapt the quality measures of the candidate sets as a function of the error measure by adjusting the variance-covariance matrix of the float solution.

39. Apparatus of claim 36, wherein the processing element is adapted to adjust a variance-covariance matrix of the filter using the error measure, if the error measure is in a predetermined range.

40. Apparatus of claim 36, wherein the processing element is adapted to adjust a variance-covariance matrix of the filter using the error measure, if the error measure is larger than one.

41. Apparatus of claim 24, wherein the processing element is adapted to, so as to define the integer candidate sets:

select a subset of float ambiguities of the state vector to form the subgroup of the float ambiguities of the state vector used to define the plurality of integer ambiguity candidate sets; and

assign integer values to the estimated float values of the float ambiguities of the subset to define a plurality of integer ambiguity candidate sets.

42. Apparatus of claim 41, wherein the processing element is adapted to select, as float ambiguities of the subset, the float ambiguities of frequencies tracked continuously for the longest period of time.

43. Apparatus of claim 24, adapted to

obtain observations of the at least one frequency of the GNSS signals from the plurality of GNSS satellites to obtain observations at a plurality of instances in time;

update the float ambiguities of the state vector over time on the basis of the observations;

determine that an interruption in tracking of at least one signal of a satellite occurred; and

maintain the float ambiguity of the state vector for the at least one signal for which an interruption in tracking occurred at the value before the interruption in tracking occurred.

44. Apparatus of claim 43, adapted to determine that an interruption in tracking of at least one signal of a satellite occurred if an observation for the at least one signal is not available for at least one of the instances in time.

45. Apparatus of claim 43, adapted to determine that an interruption in tracking of at least one signal of a satellite occurred, if a cycle slip occurred.

46. Apparatus of claim 43 adapted to, if, after an interruption in tracking of a signal, tracking of the signal resumes, maintain the float ambiguity of the state vector for the signal for which an interruption in tracking occurred at the value before the interruption in tracking occurred as a first float ambiguity and introducing into the state vector a second float ambiguity for the signal after resuming tracking.

47. Rover comprising an apparatus according to claim 24.

48. Network station comprising an apparatus according to claim 24.