Post-processing of inverse DGPS corrections

• US 6,014,101 A
• Filed: 10/20/1997
• Issued: 01/11/2000
• Est. Priority Date: 02/26/1996
• Status: Expired due to Fees

• Current Assignee: Trimble Navigation Limited (Trimble Inc.)
• Original Assignee: Trimble Navigation Limited (Trimble Inc.)
• Inventors: Loomis, Peter V. W.
• Primary Examiner(s): Tarcza, Thomas H.
• Assistant Examiner(s): PHAN, DAO LINDA
• Application Number:
  US08/954,645
• Time in Patent Office: 813 Days
• Field of Search: 342/357, 342/352, 455/12.1, 701/213, 701/215, 701/214
• US Class Current: 342/357.22
• CPC Class Codes: G01S 19/33 Multimode operation in different systems which transmit time stamped messages, e.g. GPS/GLONASS
• CPC Class Codes: G01S 19/41 Differential correction, e.g. DGPS [differential GPS]
• CPC Class Codes: G01S 5/009 Transmission of differential positioning data to mobile

Abstract

A method for enhancing the accuracy of location coordinates and/or clock bias computed for a mobile user station that is part of a Satellite Positioning System (SATPS), such as GPS or GLONASS. A data processing station is provided with pseudorange corrections PRC(t;j;ref) for an SATPS reference station for each of M SATPS satellites (j=1, . . . , M; M≧3) and with uncorrected location fix coordinates x'"'"'(t_f), y'"'"'(t_f)'"'"', z'"'"'(t_f)'"'"' and/or b'"'"'(t_f) for the mobile station for a selected location fix time t_f. A matrix equation H(t_f ;mob)ΔW(t_f ;mob)=PRC(t_f ;ref) relates a matrix ΔW of location fix coordinate corrections for the mobile station to a matrix PRC(t;ref) of the pseudorange correction values, where H(t_f ;mob) is an M×N matrix (M≦N; N=3 or 4) with known entries computed from mobile station data. An inverse or pseudo-inverse matrix H(t_f ;mob).sup.(-1) is formed satisfying the relation H(t_f ;mob).sup.(-1) H(t_f ;mob)=the identity matrix I, and the matrix ΔW(t_f ;mob)=H(t_f ;mob).sup.(-1) PRC(t_f ;ref) is computed. The entries of the matrix ΔW(t_f) are interpreted as additive corrections for the location fix coordinates x'"'"'(t_f), y'"'"'(t_f)'"'"', z'"'"'(t_f)'"'"' and/or b'"'"'(t_f) for the mobile station. Post-processing can be performed to apply the pseudorange corrections to the mobile station data.

Claims

1. A method for determining corrections for spatial location and clock bias coordinates with enhanced accuracy for a mobile Satellite Positioning System (SATPS) station, the method comprising the steps of:

obtaining an M×

1 pseudorange corrections matrix, whose entries are corrections for each of M uncorrected pseudorange values, measured at an SATPS reference station that has known location coordinates and that receives SATPS signals and measures uncorrected pseudorange values approximately at a selected location fix time from each of M selected visible SATPS satellites, where M≧

N and M and N are selected positive integers with N being one of the integers 2, 3 and 4, and where the sum of an uncorrected pseudorange value plus a pseudorange correction value for a selected visible satellite provides a corrected reference station pseudorange value that agrees with a known, correct pseudorange value at the reference station for the selected visible satellite at the location fix time;

receiving and processing SATPS signals from each of the M visible satellites at an SATPS mobile station, and determining an uncorrected location fix coordinate matrix, whose entries include uncorrected spatial location coordinates and an uncorrected clock bias coordinate, for the mobile station at the location fix time;

using the mobile station uncorrected location fix coordinate values and location coordinate values of at least one visible satellite, for a time corresponding to the location fix time, to compute an M×

N transform matrix, with (N-1)·

M entries of the transform matrix being direction cosines for a vector from a visible satellite to the uncorrected mobile station location, for each of the M visible satellites, and with M entries of the transform matrix having the value 1;

forming an N×

M quasi-inverse matrix that is a left inverse for the transform matrix, in the sense that the matrix product of the quasi-inverse matrix, multiplied on the right by the transform matrix, is an N×

N identity matrix;

forming an N×

1 location fix corrections matrix that is a matrix product of the quasi-inverse matrix, multiplied on the right by the pseudorange corrections matrix; and

interpreting N entries of the location fix corrections matrix as corrections to the location fix coordinates for the mobile station.

2. The method of claim 1, further comprising the step of selecting said integer M≧

N+1, and wherein said steps of forming said N×

M quasi-inverse matrix and forming said pseudorange corrections matrix comprise the steps of;

augmenting said transform matrix by adding M-N columns of matrix entries to produce an M×

M augmented transform matrix, where N columns of the augmented transform matrix are identical with N columns of said transform matrix and a column of entries from the augmented transform matrix forms an M×

1 column matrix that is linearly independent of the other M-1 column matrices of the augmented transform matrix;

forming an M×

M augmented quasi-inverse matrix, that is a left inverse matrix for the augmented transform matrix, determining an M×

1 augmented location fix corrections matrix as a matrix product of the augmented quasi-inverse matrix and said pseudorange corrections matrix; and

interpreting N entries of the augmented location fix corrections matrix as corrections to said location fix coordinates for said mobile station.

3. The method of claim 2, wherein said step forming said augmented transform matrix comprises the steps of:

forming an M×

1 vector from the values of said M entries in each column of said M×

N transform matrix;

using a Gram-Schmidt orthogonalization procedure to form M-N additional M-dimensional vectors, with each such additional vector being linearly independent of each of the M-dimensional vectors formed from said matrix and with these M-N additional vectors being linearly independent of each other; and

forming an augmented M×

M transform matrix whose column entries are the entries of the N vectors formed from the matrix and the entries of the additional M-N vectors formed using a Gram-Schmidt orthogonalization procedure.

4. The method of claim 1, wherein said step of forming said N×

M quasi-inverse matrix comprises the steps of;

forming an N×

N intermediate matrix that is a matrix product of the N×

M transpose of the transform matrix, multiplied on the right by the transform matrix; and

defining said N×

M quasi-inverse matrix as a matrix product of the intermediate matrix, multiplied on the right by the N×

M transpose of the transform matrix.

5. The method of claim 1, further comprising the step of selecting said integer M=N and selecting the quasi-inverse matrix to be the inverse matrix for the transform matrix.

6. The method of claim 1, further comprising the step of computing said transform matrix at a supplemental data processor.

7. The method of claim 1, further comprising the step of computing said matrix transform at at least one of said mobile station and said reference station.

10. The method of claim 3, wherein said step forming said augmented transform matrix comprises the steps of:

forming an M×

1 vector from the values of said M entries in each column of said M×

N transform matrix;

using a Gram-Schmidt orthogonalization procedure to form M-N additional M-dimensional vectors, with each such additional vector being linearly independent of each of the M-dimensional vectors formed from said matrix and with these M-N additional vectors being linearly independent of each other; and

forming an augmented M×

M transform matrix whose column entries are the entries of the N vectors formed from the matrix and the entries of the additional M-N vectors formed using a Gram-Schmidt orthogonalization procedure.

8. A method for determining corrections for spatial location and clock bias coordinates with enhanced accuracy for a mobile Satellite Positioning System (SATPS) station, the method comprising the steps of:

obtaining an M×

1 pseudorange corrections matrix, whose entries are corrections for each of M uncorrected pseudorange values, measured at an SATPS reference station that has known location coordinates and that receives SATPS signals and measures uncorrected pseudorange values approximately at a selected location fix time from each of M selected visible SATPS satellites, where M≧

N and M and N are selected positive integers with N being one of the integers 2 and 3, and where the sum of an uncorrected pseudorange value plus a pseudorange correction value for a selected visible satellite provides a corrected reference station pseudorange value that agrees with a known, correct pseudorange value at the reference station for the selected visible satellite at the location fix time;

receiving and processing SATPS signals from each of the M visible satellites at an SATPS mobile station, and determining an uncorrected location fix coordinate matrix, whose entries include uncorrected spatial location coordinates and an uncorrected clock bias coordinate, for the mobile station at the location fix time;

using the mobile station uncorrected location fix coordinate values and location coordinate values of at least one visible satellite, for a time corresponding to the location fix time, to compute an M×

N transform matrix, where the entries of the transform matrix are direction cosines for a vector from a visible satellite to the uncorrected mobile station location, for each of the M visible satellites;

forming an N×

M quasi-inverse matrix that is a left inverse for the transform matrix, in the sense that the matrix product of the quasi-inverse matrix, multiplied on the right by the transform matrix, is an N×

N identity matrix;

forming an N×

1 location fix corrections matrix that is a matrix product of the quasi-inverse matrix, multiplied on the right by the pseudorange corrections matrix; and

interpreting N entries of the location fix corrections matrix as corrections to the location fix coordinates for the mobile station.

9. The method of claim 8, further comprising the step of selecting said integer M≧

N+1, and wherein said steps of forming said N×

M quasi-inverse matrix and forming said pseudorange corrections matrix comprise the steps of;

augmenting said transform matrix by adding M-N columns of matrix entries to produce an M×

M augmented transform matrix, where N columns of the augmented transform matrix are identical with N columns of said transform matrix and a column of entries from the augmented transform matrix forms an M×

1 column matrix that is linearly independent of the other M-1 column matrices of the augmented transform matrix;

forming an M×

M augmented quasi-inverse matrix, that is a left inverse matrix for the augmented transform matrix, determining an M×

1 augmented location fix corrections matrix as a matrix product of the augmented quasi-inverse matrix and said pseudorange corrections matrix; and

interpreting N entries of the augmented location fix corrections matrix as corrections to said location fix coordinates for said mobile station.

11. The method of claim 8, wherein said step of forming said N×

M quasi-inverse matrix comprises the steps of;

forming an N×

N intermediate matrix that is a matrix product of the N×

M transpose of the transform matrix, multiplied on the right by the transform matrix; and

defining said N×

M quasi-inverse matrix as a matrix product of the intermediate matrix, multiplied on the right by the N×

M transpose of the transform matrix.

12. The method of claim 8, further comprising the step of selecting said integer M=N and selecting the quasi-inverse matrix to be the inverse matrix for the transform matrix.

13. The method of claim 8, further comprising the step of computing said transform matrix at a supplemental data processor.

14. The method of claim 8, further comprising the step of computing said matrix transform at at least one of said mobile station and said reference station.