Methods and apparatuses for reducing errors in the measurement of the coordinates and time offset in satellite positioning system receivers

• US 6,337,657 B1
• Filed: 03/09/2000
• Issued: 01/08/2002
• Est. Priority Date: 03/12/1999
• Status: Expired due to Fees

• Current Assignee: Topcon GPS, LLC
• Original Assignee: Topcon Positioning Systems Incorporated (Topcon Corporation)
• Inventors: Zagnetov, Peter P., Zhodzishsky, Mark I., Ashjaee, Javad
• Primary Examiner(s): Camby, Richard M.
• Application Number:
  US09/522,323
• Time in Patent Office: 670 Days
• Field of Search: 340/357.01, 340/357.02, 340/357.03, 340/357.06, 340/357.17, 701/213, 701/214
• US Class Current: 342/357.31
• CPC Class Codes: G01S 19/396 Determining accuracy or reliability of position or pseudorange measurements
• CPC Class Codes: G01S 19/41 Differential correction, e.g. DGPS [differential GPS]
• CPC Class Codes: G01S 19/43 using carrier phase measurements, e.g. kinematic positioning; using long or short baseline interferometry

Abstract

Disclosed are methods and apparatuses for generating the estimates of receiver'"'"'s coordinates and/or time offset for a moment of time t_n without large errors caused by short-term shading of a part of the observable global positioning satellites and also without large dynamic errors caused by the receiver movement. The receiver may be stationary or mobile (i.e., rovering). A set of snapshot-solution values for the position coordinates and time offset of the receiver at the time moment t_n, and a set of predicted values for the position coordinates and time offset of the receiver at the time moment t_n are generated. The accuracy of each of these sets are determined, and a set of refined estimates for the position and time offset of the receiver is generated based the snapshot solution values, the predicted position values, and the accuracies.

Claims

1. A method of generating a set of one or more refined estimates ({circumflex over (P)}^f_x,n, {circumflex over (P)}^f_y,n, {circumflex over (P)}^f_z,n, {circumflex over (P)}^f_τ

,n) for a selected set of one or more corresponding position-time components of a receiver of global positioning satellite signals for a moment of time t_n, each position-time component of the selected set being one of the receiver'"'"'s position coordinates or the receiver'"'"'s time offset, each satellite signal being transmitted by a corresponding satellite and enabling the receiver to measure a pseudorange between itself and the corresponding satellite, said method comprising the steps of;

(a) obtaining a set of one or more snapshot-solution values ({tilde over (P)}_x,n, {tilde over (P)}_y,n, {tilde over (P)}_z,n, {tilde over (P)}<sub>τ

,n</sub>) for the selected set of one or more position-time components at the time moment t_n, a corresponding snapshot-solution value being obtained for each position-time component in the selected set;

(b) generating a set of one or more predicted values ({circumflex over (P)}′

_x,n, {circumflex over (P)}′

_y,n, {circumflex over (P)}′

_z,n, {circumflex over (P)}′

<sub>τ

,n</sub>) for the selected set of one or more position-time components at the time moment t_n, a corresponding predicted value being generated for each position-time component in the selected set, said predicted values being generated from a measurement of a plurality of satellite carrier phases over a time interval from a previous time moment t<sub>n−

1</sub> to the time moment t_n and from a set of one or more values for the selected set of one or more position-time components at the previous time moment t<sub>n−

1</sub>;

(c) generating a first quality factor Q_n which is representative of the accuracy of the set of one or more snapshot solution values;

(d) generating a second quality factor Q_n′

which is representative of the accuracy of the set of one or more predicted values;

(e) generating said set of one or more refined estimates ({circumflex over (P)}^f_x,n, {circumflex over (P)}^f_y,n, {circumflex over (P)}^f_z,n, {circumflex over (P)}^f<sub>τ

,n</sub>) for the corresponding selected position-time components as a first multiplier (α

_n) of the set of the corresponding snapshot-solution values plus a second multiplier (1−

α

_n) of the set of the corresponding predicted values, with the sum of said first and second multipliers being equal to 1, wherein the first multiplier (α

_n) is greater than the second multiplier (1−

α

_n) when the first and second quality factors indicate that the set of snapshot-solution values are more accurate than the set of predicted values, and wherein the second multiplier (1−

α

_n) is greater that the first multiplier (α

_n) when the first and second quality factors indicate that the set of predicted values is more accurate than the set of snapshot-solution values.

2. The method of claim 1 wherein said set of refined estimates includes three refined estimates ({circumflex over (P)}^f_x,n, {circumflex over (P)}^f_y,n, {circumflex over (P)}^f_z,n) for three corresponding position coordinates and one refined estimate ({circumflex over (P)}^f_τ

,n) for the time offset.

3. The method of claim 1 wherein the first quality factor Q_n generated in step (c) decreases in value as the accuracy of the set of one or more snapshot solution values increases.

4. The method of claim 1 wherein the first quality factor Q_n generated in step (c) increases in value as the accuracy of the set of snapshot solution values increases.

5. The method of claim 3 wherein said step (c) of generating the first quality factor Q_n comprises the steps of:

generating the diagonal elements of a covariance matrix ^γ

_n for the time moment t_n, said covariance matrix ^γ

_n being representative of the errors in the receiver'"'"'s coordinates and time offset caused by measurement errors in the pseudoranges between the receiver and the satellites and having a form equivalent to;

6. The method of claim 4 wherein said step (c) of generating the first quality factor Q_n comprises the steps of:

generating the diagonal elements of a covariance matrix ^γ

_n for the time moment t_n, said covariance matrix ^γ

_n being representative of the errors in the receiver'"'"'s coordinates and time offset caused by measurement errors in the pseudoranges between the receiver and the satellites and having a form equivalent to;

7. The method of claim 3 comprising the step of performing steps (a)-(d) at a preceding time moment t_n−

1, and wherein the magnitude of said second quality factor Q_n′

generated in said step (d) at the time moment t_n increases monotonically compared to its previous value at the preceding time moment t<sub>n−

1</sub>.

8. The method of claim 4 comprising the step of performing steps (a)-(d) at a preceding time moment t_n−

1, and wherein the magnitude of said second quality factor Q_n′

generated in said step (d) at the time moment t_n decreases monotonically compared to its previous value at the preceding time moment t<sub>n−

1</sub>.

9. The method of claim 3 wherein said step (e) further comprises the steps of setting the first multiplier (α

_n) to be equal to a value greater than the second multiplier (1−

α

_n) when the first quality factors Q_n is less than the second quality factor Q_n′

, and setting the second multiplier (1−

α

_n) to be equal to a value greater that the first multiplier (α

_n) when the first quality factor Q_n is greater than the second quality factor Q_n′

.

10. The method of claim 4 wherein said step (e) further comprises the steps of setting the first multiplier (α

_n) to be equal to a value greater than the second multiplier (1−

α

_n) when the first quality factor Q_n is greater than the second quality factor Q_n′

, and setting the second multiplier (1−

α

_n) equal to a value greater that the first multiplier (α

_n) when the first quality factor Q_n is less than the second quality factor Q_n′

.

11. The method of claim 5 wherein the matrix elements of matrix R^γ

_n comprise the a priori known matrix of pseudorange measurement errors for the satellites.

12. The method of claim 6 wherein the matrix elements of matrix R^γ

_n comprise the a priori known matrix of pseudorange measurement errors for the satellites.

13. The method of claim 5 wherein the inverse matrix (R^γ

_n)<sup>−

1</sup> used in step (c) of generating covariance matrix ^γ

_n comprises a diagonal matrix with one diagonal element corresponding to a satellite, and wherein each diagonal element is proportional to the elevation angle of its corresponding satellite.

14. The method of claim 6 wherein the inverse matrix (R^γ

_n)<sup>−

1</sup> used in step (c) of generating covariance matrix ^γ

_n comprises a diagonal matrix with one diagonal element corresponding to a satellite, and wherein each diagonal element is propotional to the elevation angle of its corresponding satellite.

15. The method of claim 5 wherein step (c) further comprises the step of assigning a scalar value for each satellite which is representative of the health of the satellite, and wherein the inverse matrix (R^γ

_n)<sup>−

1</sup> used in step (c) of generating covariance matrix ^γ

_n comprises a diagonal matrix with one diagonal element corresponding to a satellite, and wherein each diagonal element comprises the scalar value representing the health of its corresponding satellite.

16. The method of claim 6 wherein step (c) further comprises the step of assigning a scalar value for each satellite which is representative of the health of the satellite, and wherein the inverse matrix (R^γ

_n)<sup>−

1</sup> used in step (c) of generating covariance matrix ^γ

_n comprises a diagonal matrix with one diagonal element corresponding to a satellite, and wherein each diagonal element comprises the scalar value representing the health of its corresponding satellite.

17. The method of claim 5 wherein the matrix elements of matrix (R^γ

_n)<sup>−

1</sup> comprise the unit matrix.

18. The method of claim 6 wherein the matrix elements of matrix (R^γ

_n)<sup>−

1</sup> comprise the unit matrix.

19. The method of claim 7 wherein a temporary parameter MQ_n′

is set equal to the initial value of the first quality factor Q_n at an initial time moment (n=0);

20. The method of claim 19 wherein the MIN{*} operation comprises the steps of determining if Q′

_n is greater than Q_n, and if so, setting the parameter MQ_n+1 to the value of Q_n, and otherwise setting the parameter MQ_n+1 to the value of Q′

_n.

21. The method of claim 7 wherein a temporary parameter MQ_n′

is set equal to the initial value of the first quality factor Q_n at an initial time moment (n=0);

22. The method of claim 7 wherein a temporary parameter MQ_n′

is set equal to the initial value of the first quality factor Q_n at an initial time moment (n=0);

23. The method of claim 22 wherein the MIN{*} operation comprises the steps of determining if Q′

_n is greater than Q_n, and if so, setting the parameter MQ_n+1 to the value of Q_n, and otherwise setting the parameter MQ_n+1 to the value of Q′

_n.

24. The method of claim 7 wherein a temporary parameter MQ_n′

is set equal to the initial value of the first quality factor Q_n at an initial time moment (n=0);

25. The method of claim 7 wherein the second quality factor Q_n′

is set equal to the initial value of the first quality factor Q_n at an initial time moment (n=0);

26. The method of claim 25 wherein step (d) generates the second quality factor Q_n′

such that it is proportional to at least one of the forms of;

27. The method of claim 8 wherein a temporary parameter MQ_n′

is set equal to the initial value of the first quality factor Q_n at an initial time moment (n=0);

28. The method of claim 27 wherein the MAX{*} operation comprises the steps of determining if Q′

_n is less than Q_n, and if so, setting the parameter MQ_n+1 to the value of Q_n, and otherwise setting the parameter MQ_n+1 to the value of Q′

_n.

29. The method of claim 8 wherein a temporary parameter MQ_n′

is set equal to the initial value of the first quality factor Q_n at an initial time moment (n=0);

30. The method of claim 8 wherein a temporary parameter MQ_n′

is set equal to the initial value of the first quality factor Q_n at an initial time moment (n=0);

31. The method of claim 30 wherein the MAX{*} operation comprises the steps of determining if Q′

_n is greater than Q_n, and if so, setting the parameter MQ_n+1 to the value of Q′

_n, and otherwise setting the parameter MQ_n+1 to the value of Q_n.

32. The method of claim 8 wherein a temporary parameter MQ_n′

is set equal to the initial value of the first quality factor Q_n at an initial time moment (n=0);

33. The method of claim 8 wherein the second quality factor Q_n′

is set equal to the initial value of the first quality factor Q_n at an initial time moment (n=0);

 

Q_n′

=Q_n(n=0);

wherein a set of four parameters Φ

₁, Φ

₂, Φ

₃, and Φ

₄ are set equal to the square roots of the corresponding diagonal elements of said covariance matrix ^γ

_n at the initial time moment (n=0);

34. The method of claim 33 wherein step (d) generates the second quality factor Q_n′

such that it is proportional to at least one of the forms of;

35. The method of claim 9 wherein said step (d) further comprises the step of generating the first multiplier α

_n in a form equivalent to;

36. The method of claim 10 wherein step (d) further comprises the step of generating the first multiplier α

_n in a form equivalent to;

37. The method of claim 1 wherein the following quantities were obtained for the previous time moment t_n−

1;

a previous instance of the first quality factor Q<sub>n−

1</sub> for a set of snapshot-solution values ({tilde over (P)}<sub>x,n−

1</sub>, {tilde over (P)}<sub>y,n−

1</sub>, {tilde over (P)}<sub>z,n−

1</sub>, {tilde over (P)}<sub>τ

,n−

1</sub>) at the previous time moment t<sub>−

1</sub>, and a previous instance of the second quality factor Q<sub>n−

1</sub>′

for a set of predicted values ({circumflex over (P)}′

<sub>x,n−

1</sub>, {circumflex over (P)}′

<sub>y,n−

1</sub>, {circumflex over (P)}′

<sub>z,n−

1</sub> and {circumflex over (P)}′

<sub>τ

,n−

1</sub>) at the previous time moment t<sub>n−

1</sub>; and

wherein the second quality factor Q_n′

for the time moment t_n is generated in step (d) as a scalar factor k multiplied by the value of the first quality factor Q<sub>n−

1</sub> at the previous time moment t<sub>n−

1</sub> when the set of snapshot-solution values at said previous time moment were more accurate than the set of predicted values at said previous time moment, and wherein the second quality factor Q_n′

for the time moment t_n is generated as the scalar factor k multiplied by the value of the second quality factor Q<sub>n−

1</sub>′

at the previous time moment t<sub>n−

1</sub> when the set of predicted values at said previous time moment were more accurate than the set of snapshot-solution values at said previous time moment.

38. The method of claim 37 wherein said scalar factor k is greater than 1.

39. The method of claim 37 wherein said scalar factor k is less than 1.

40. The method of claim 37 wherein the value of k is selected from a set of values kq[*] and wherein k is set equal to one of the members of said set kq[*] at each time moment;

wherein the value of k is initially set equal to a predetermined member of said set kq[*]; and

wherein, for at least two successive time moments, the value of k at each said time moment is set equal to a different member of said set kq[*] when the first and second quality factors Q<sub>n−

1</sub> and Q<sub>n−

1</sub>′

at the previous time moment t<sub>n−

1</sub> indicate that the set of predicted values at said previous time moment were more accurate than the set of snapshot-solution values at said previous time moment; and

wherein the value of k is set equal to said predetermined member of the said set kq[*] when the first and second quality factors Q<sub>n−

1</sub> and Q<sub>n−

1</sub>′

at the previous time moment t<sub>n−

1</sub> indicate that the set of snapshot-solution values at said previous time moment were more accurate than the set of predicted values at said previous time moment.

41. The method of claim 1 wherein the following quantities were obtained for the previous time moment t_n−

1;

a previous instance of the first quality factor Q<sub>n−

1</sub> for a set of snapshot-solution values ({tilde over (P)}<sub>x,n−

1</sub>, {tilde over (P)}<sub>y,n−

1</sub>, {tilde over (P)}<sub>z,n−

1</sub>, {tilde over (P)}<sub>τ

,n−

1</sub>) for the position coordinates and time offset of the receiver at the previous time moment t<sub>n−

1</sub>, and a previous instance of the second quality factor Q<sub>n−

1</sub>′

for a set of predicted position coordinates and time offset ({circumflex over (P)}′

<sub>x,n−

1</sub>, {circumflex over (P)}′

<sub>y,n−

1</sub>, {circumflex over (P)}′

<sub>z,n−

1</sub> and {circumflex over (P)}′

<sub>τ

,n−

1</sub>) for the previous time moment t<sub>n−

1</sub>; and

wherein the second quality factor Q_n′

for the time moment t_n is generated as the previous instance of the first quality factor Q<sub>n−

1</sub> raised to the power of a scalar factor k;

42. The method of claim 41 wherein the value of k is selected from a set of values kq[*] and wherein k is set equal to one of the members of said set kq[*] at each time moment;

wherein the value of k is initially set equal to a predetermined member of said set kq[*]; and

wherein, for at least two successive time moments, the value of k at each said time moment is set equal to a different member of said set kq{*} when the first and second quality factors Q<sub>n−

1</sub> and Q<sub>n−

1</sub>′

at the previous time moment t<sub>n−

1</sub> indicate that the set of predicted values at said previous time moment were more accurate than the set of snapshot-solution values at said previous time moment; and

wherein the value of k is set equal to said predetermined member of the said set kq[*] when the first and second quality factors Q<sub>n−

1</sub> and Q<sub>n−

1</sub>′

at the previous time moment t<sub>n−

1</sub> indicate that the set of snapshot-solution values at said previous time moment were more accurate than the set of predicted values at said previous time moment.