US5680140A
Expired / Lapsed
US
⏱️ 0.0 years remaining
Post-processing of inverse differential corrections for SATPS mobile stations
Assignee: Trimble Inc
•
Filing: 1996-02-26
•
Granted: 1997-10-21
•
Expires: 2016-02-26
Abstract
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.
Inventors
- 👤 Peter V. W. Loomis
Bibliographic Details
Application Number
—
Jurisdiction
US
Data Source
google_patents
Last Synchronized
2026-10-24 09:51
CPC Classifications
G; G01; G01S; G01S5/00; G01S5/0009; G01S5/0018; G01S5/0036; G01S19/00; G01S19/01; G01S19/03; G01S19/07; G01S19/071; G01S19/38; G01S19/39; G01S19/40; G01S19/41
Claims Analysis
Total Claims: 57
Claim 1
Independent Claim
488 words
A method for determining spatial location and clock bias coordinates with enhanced accuracy for a mobile user Satellite Positioning System (SATPS) station, the method comprising the steps of: providing pseudorange corrections PRC(t f ;j;ref) for uncorrected pseudorange values PR(t f ;j;ref), measured at an SATPS reference station that has location coordinates that are known with high accuracy and that receives SATPS signals at a selected location fix time t=t f from each of M SATPS satellites, numbered j=1, 2, . . . , M (M>4), where the sums PR(t f ;j;ref)+PRC(t f ;j;ref) for j=1, 2, . . . , M provide corrected reference station pseudorange values PR(t f ;j;ref) cor that agree with known pseudorange values for the reference station for the M SATPS satellites for the location fix time t f ; providing an SATPS mobile station that has an SATPS signal antenna and associated SATPS signal receiver/processor, and causing the mobile station to receive and process SATPS signals from each of the M SATPS satellites and to determine uncorrected location fix coordinates, including uncorrected three-dimensional spatial location coordinates (x'(t f ),y'(t f ),z'(t f )) and uncorrected clock bias coordinate b'(t f ), for the mobile station for the location fix time t f ; providing a supplemental data processor with the location fix time t f , with the mobile station uncorrected location fix coordinates (x'(t f ), y'(t f ), z'(t f ), b'(t f )), with spatial coordinate values (x j (t f ), y j (t f ), z j (t f )) of SATPS satellite number j for a time corresponding to the location fix time t f , and with the reference station pseudorange corrections PRC(t f ;j;ref) for j=1, 2, . . . , M; computing at the supplemental data processor an M×4 matrix H(t f ;mob) whose entries are defined by the relations H(t.sub.f ;mob)=(h.sub.ji (t.sub.f)), h.sub.j1 (t.sub.f)=α.sub.j1 (t.sub.f)=(x'(t.sub.f)-x.sub.j (t.sub.f))/r.sub.0j (t.sub.f), h.sub.j2 (t.sub.f)=α.sub.j2 (t.sub.f)=(y'(t.sub.f)-y.sub.j (t.sub.f))/r.sub.0j (t.sub.f), h.sub.j3 (t.sub.f)=α.sub.j3 (t.sub.f)=(z'(t.sub.f)-z.sub.j (t.sub.f))/r.sub.0j (t.sub.f), h.sub.j4 (t.sub.f)=1, (j=1, 2, . . . , M), r.sub.0j (t.sub.f)= (x'(t.sub.f)-x.sub.j (t.sub.f)).sup.2 +(y'(t.sub.f)-y.sub.j (t.sub.f)).sup.2 +(z'(t.sub.f)-z.sub.j (t.sub.f)).sup.2 !.sup.1/2 ; forming a 4×M matrix H(t f ;mob).sup.Λ that satisfies the relation H(t f ;mob).sup.Λ H(t f ;mob)=I, where I is the 4×4 identity matrix; forming a matrix ΔW(t f ;mob)=H(t f ;mob).sup.Λ PRC(t f ;ref), where PRC(t f ;ref) is an M×1 matrix whose entries are the values PRC(t f ;j;ref) for j=1, 2, . . . , M; interpreting four entries Δw 1 (t f ), Δw 2 (t f ), Δw 3 (t f ), and Δw 4 (t f ) of the matrix ΔW(t f ;mob) as corrections to the location fix coordinates for the mobile station; and determining corrected location fix coordinates (x(t f ),y(t f ),z(t f ),b(t f )) for the mobile station for at least one time t=t f using the relations x(t.sub.f)=x'(t.sub.f)+Δw.sub.1 (t.sub.f), y(t.sub.f)=y'(t.sub.f)+Δw.sub.2 (t.sub.f), z(t.sub.f)=z'(t.sub.f)+Δw.sub.3 (t.sub.f), b(t.sub.f)=b'(t.sub.f)+Δw.sub.4 (t.sub.f).
Claim 2
Independent Claim
488 words
A method for determining spatial location and clock bias coordinates with enhanced accuracy for a mobile user Satellite Positioning System (SATPS) station, the method comprising the steps of: providing pseudorange corrections PRC(t f ;j;ref) for uncorrected pseudorange values PR(t f ;j;ref), measured at an SATPS reference station that has location coordinates that are known with high accuracy and that receives SATPS signals at a selected location fix time t=t f from each of M SATPS satellites, numbered j=1, 2, . . . , M (M>4), where the sums PR(t f ;j;ref)+PRC(t f ;j;ref) for j=1, 2, . . . , M provide corrected reference station pseudorange values PR(t f ;j;ref) cor that agree with known pseudorange values for the reference station for the M SATPS satellites for the location fix time t f ; providing an SATPS mobile station that has an SATPS signal antenna and associated SATPS signal receiver/processor, and causing the mobile station to receive and process SATPS signals from each of the M SATPS satellites and to determine uncorrected location fix coordinates, including uncorrected three-dimensional spatial location coordinates (x'(t f ),y'(t f ),z'(t f )) and uncorrected clock bias coordinate b'(t f ), for the mobile station for the location fix time t f ; providing a supplemental data processor with the location fix time t f , with the mobile station uncorrected location fix coordinates (x'(t f ), y'(t f ), z'(t f ), b'(t f )), with spatial coordinate values (x j (t f ), y j (t f ), z j (t f )) of SATPS satellite number j for a time corresponding to the location fix time t f , and with the reference station pseudorange corrections PRC(t f ;j;ref) for j=1, 2, . . . , M; computing at the supplemental data processor an M×4 matrix H(t f ;mob) whose entries are defined by the relations H(t.sub.f ;mob)=(h.sub.ji (t.sub.f)), h.sub.j1 (t.sub.f)=α.sub.j1 (t.sub.f)=(x'(t.sub.f)-x.sub.j (t.sub.f))/r.sub.0j (t.sub.f), h.sub.j2 (t.sub.f)=α.sub.j2 (t.sub.f)=(y'(t.sub.f)-y.sub.j (t.sub.f))/r.sub.0j (t.sub.f), h.sub.j3 (t.sub.f)=α.sub.j3 (t.sub.f)=(z'(t.sub.f)-z.sub.j (t.sub.f))/r.sub.0j (t.sub.f), h.sub.j4 (t.sub.f)=1, (j=1, 2, . . . , M), r.sub.0j (t.sub.f)= (x'(t.sub.f)-x.sub.j (t.sub.f)).sup.2 +(y'(t.sub.f)-y.sub.j (t.sub.f)).sup.2 +(z'(t.sub.f)-z.sub.j (t.sub.f)).sup.2 !.sup.1/2 ; forming a 4×M matrix H(t f ;mob).sup.Λ that satisfies the relation H(t f ;mob).sup.Λ H(t f ;mob)=I, where I is the 4×4 identity matrix; forming a matrix ΔW(t f ;mob)=H(t f ;mob).sup.Λ PRC(t f ;ref), where PRC(t f ;ref) is an M×1 matrix whose entries are the values PRC(t f ;j;ref) for j=1, 2, . . . , M; interpreting four entries Δw 1 (t f ), Δw 2 (t f ), Δw 3 (t f ), and Δw 4 (t f ) of the matrix ΔW(t f ;mob) as corrections to the location fix coordinates for the mobile station; and determining corrected location fix coordinates (x(t f ),y(t f ),z(t f ),b(t f )) for the mobile station for at least one time t=t f using the relations x(t.sub.f)=x'(t.sub.f)+Δw.sub.1 (t.sub.f), y(t.sub.f)=y'(t.sub.f)+Δw.sub.2 (t.sub.f), z(t.sub.f)=z'(t.sub.f)+Δw.sub.3 (t.sub.f), b(t.sub.f)=b'(t.sub.f)+Δw.sub.4 (t.sub.f).
Claim 3
Dependent Claim
221 words
The method of claim 1, further comprising the step of selecting said integer M>5, and wherein said steps of forming said 4×M matrix H(t f ;mob).sup.Λ and forming said matrix ΔW(t f ;mob) comprise the steps of: augmenting said matrix H(t f ;mob) by adding M-4 columns of matrix entries to produce an augmented M×M matrix H*(t f ;mob), where four columns of the matrix H*(t f ;mob) are identical with four columns of said matrix H(t f ;mob) and each of the columns of H*(t f ;mob) forms an M×1 column matrix that is linearly independent of the other M-1 column matrices of the matrix H*(t f ;mob); forming an inverse matrix H*(t f ;mob) -1 , determining an M×1 matrix ΔW*(t f ;mob) by a matrix equation ΔW*(t f ;mob)=H*(t f ;mob) -1 PRC(t f ;ref), where PRC(t f ;ref) is an M×1 matrix whose entries are the values PRC(t f ;j;ref) for j=1, 2, . . . , M; and selecting four of the entries Δw 1 *(t f ), Δw 2 *(t f ), Δw 3 *(t f ), and Δw 4 *(t f ) of the matrix ΔW*(t f ;mob) and forming said 4×1 matrix ΔW(t f ;mob) with entires defined by Δw k (t f )=Δw k *(t f ), for k=1, 2, 3, 4.
Claim 4
Dependent Claim
120 words
The method of claim 2, wherein said step of augmenting said matrix H(t f ;mob) comprises the steps of: forming an M-dimensional vector from the values of said M entries in each column of said M×4 matrix H(t f ;mob); using a Gram-Schmidt orthogonalization procedure to form M-4 additional M-dimensional vectors, with each such vector being orthogonal to each of the M-dimensional vectors formed from said matrix H(t;mob) and with these M-4 additional vectors being orthogonal to each other; and forming an augmented M×M matrix H*(t f ;mob) matrix whose column entries are the entries of the four vectors formed from the matrix H(t f ;mob) and the entries of the additional M-4 vectors formed using the Gram-Schmidt orthogonalization procedure.
Claim 5
Dependent Claim
52 words
The method of claim 1, wherein said step of forming said 4×M matrix H(t f ;mob).sup.Λ comprises the steps of: forming a 4×4 matrix (H(t f ;mob) tr H(t f ;mob)) -1 ; and defining said 4×M matrix H(t f ;mob).sup.Λ by the relation H(t.sub.f ;mob).sup.Λ =(H(t.sub.f ;mob).sup.tr H(t.sub.f ;mob)).sup.-1 H(t.sub.f ;mob).sup.tr.
Claim 6
Dependent Claim
24 words
The method of claim 1, further comprising the step of selecting said integer M=4 and selecting H(t f ;mob).sup.Λ =H(t f ;mob) -1 .
Claim 7
Dependent Claim
26 words
The method of claim 1, further comprising the step of selecting said supplemental data processor station to be said SATPS receiver/processor provided for said reference station.
Claim 8
Dependent Claim
26 words
The method of claim 1, further comprising the step of selecting said supplemental data processor station to be said SATPS receiver/processor provided for said mobile station.
Claim 9
Independent Claim
466 words
A method for determining spatial location and clock bias coordinates with enhanced accuracy for a mobile user Satellite Positioning System (SATPS) station, the method comprising the steps of: providing pseudorange corrections PRC(t f ;j;ref) for uncorrected pseudorange values PR(t f ;j;ref), measured at an SATPS reference station that has location coordinates that are known with high accuracy and that receives SATPS signals at a selected location fix time t=t f from each of M SATPS satellites, numbered j=1, 2, . . . , M (M≧3), where the sums PR(t f ;j;ref)+PRC(t f ;j;ref) for j=1, 2, . . . , M provide corrected reference station pseudorange values PR(t f ;j;ref) cor that agree with known pseudorange values for the reference station for the M SATPS satellites for the location fix time t f ; providing an SATPS mobile station that has an SATPS signal antenna and associated SATPS signal receiver/processor, and causing the mobile station to receive and process SATPS signals from each of the M SATPS satellites and to determine uncorrected location fix coordinates, including uncorrected three-dimensional spatial location coordinates (x'(t f ),y'(t f ),z'(t f )), for the mobile station for the location fix time t f ; providing a supplemental data processor with the location fix time t f , with the mobile station uncorrected location fix coordinates (x'(t f ), y'(t f ), z'(t f )), with spatial coordinate values (x j (t f ), y j (t f ), z j (t f )) of SATPS satellite number j for a time corresponding to the location fix time t f , and with the reference station pseudorange corrections PRC(t f ;j;ref) for j=1, 2, . . . , M; computing at the supplemental data processor an M×3 matrix H(t f ;mob) whose entries are defined by the relations H(t.sub.f ;mob)=(h.sub.ji (t.sub.f)), h.sub.j1 (t.sub.f)=α.sub.j1 (t.sub.f)=(x'(t.sub.f)-x.sub.j (t.sub.f))/r.sub.0j (t.sub.f), h.sub.j2 (t.sub.f)=α.sub.j2 (t.sub.f)=(y'(t.sub.f)-y.sub.j (t.sub.f))/r.sub.0j (t.sub.f), h.sub.j3 (t.sub.f)=α.sub.j3 (t.sub.f)=(z'(t.sub.f)-z.sub.j (t.sub.f))/r.sub.0j (t.sub.f), (j=1, 2, . . . , M), r.sub.0j (t.sub.f)= (x'(t.sub.f)-x.sub.j (t.sub.f)).sup.2 +(y'(t.sub.f)-y.sub.j (t.sub.f)).sup.2 +(z'(t.sub.f)-z.sub.j (t.sub.f)).sup.2 !.sup.1/2 ; forming a 3×M matrix H(t f ;mob).sup.Λ that satisfies the relation H(t f ;mob).sup.Λ H(t f ;mob)=I, where I is the 3×3 identity matrix; forming a matrix ΔW(t f ;mob)=H(t f ;mob).sup.Λ PRC(t f ;ref), where PRC(t f ;ref) is an M×1 matrix whose entries are the values PRC(t f ;j;ref) for j=1, 2, . . . , M; interpreting three entries Δw 1 (t f ), Δw 2 (t f ) and Δw 3 (t f ) of the matrix ΔW(t f ;mob) as corrections to the location fix coordinates for the mobile station; and determining corrected location fix coordinates (x(t f ),y(t f ),z(t f )) for the mobile station for at least one time t=t f using the relations x(t.sub.f)=x'(t.sub.f)+Δw.sub.1 (t.sub.f), y(t.sub.f)=y'(t.sub.f)+Δw.sub.2 (t.sub.f), z(t.sub.f)=z'(t.sub.f)+Δw.sub.3 (t.sub.f).
Claim 10
Independent Claim
466 words
A method for determining spatial location and clock bias coordinates with enhanced accuracy for a mobile user Satellite Positioning System (SATPS) station, the method comprising the steps of: providing pseudorange corrections PRC(t f ;j;ref) for uncorrected pseudorange values PR(t f ;j;ref), measured at an SATPS reference station that has location coordinates that are known with high accuracy and that receives SATPS signals at a selected location fix time t=t f from each of M SATPS satellites, numbered j=1, 2, . . . , M (M≧3), where the sums PR(t f ;j;ref)+PRC(t f ;j;ref) for j=1, 2, . . . , M provide corrected reference station pseudorange values PR(t f ;j;ref) cor that agree with known pseudorange values for the reference station for the M SATPS satellites for the location fix time t f ; providing an SATPS mobile station that has an SATPS signal antenna and associated SATPS signal receiver/processor, and causing the mobile station to receive and process SATPS signals from each of the M SATPS satellites and to determine uncorrected location fix coordinates, including uncorrected three-dimensional spatial location coordinates (x'(t f ),y'(t f ),z'(t f )), for the mobile station for the location fix time t f ; providing a supplemental data processor with the location fix time t f , with the mobile station uncorrected location fix coordinates (x'(t f ), y'(t f ), z'(t f )), with spatial coordinate values (x j (t f ), y j (t f ), z j (t f )) of SATPS satellite number j for a time corresponding to the location fix time t f , and with the reference station pseudorange corrections PRC(t f ;j;ref) for j=1, 2, . . . , M; computing at the supplemental data processor an M×3 matrix H(t f ;mob) whose entries are defined by the relations H(t.sub.f ;mob)=(h.sub.ji (t.sub.f)), h.sub.j1 (t.sub.f)=α.sub.j1 (t.sub.f)=(x'(t.sub.f)-x.sub.j (t.sub.f))/r.sub.0j (t.sub.f), h.sub.j2 (t.sub.f)=α.sub.j2 (t.sub.f)=(y'(t.sub.f)-y.sub.j (t.sub.f))/r.sub.0j (t.sub.f), h.sub.j3 (t.sub.f)=α.sub.j3 (t.sub.f)=(z'(t.sub.f)-z.sub.j (t.sub.f))/r.sub.0j (t.sub.f), (j=1, 2, . . . , M), r.sub.0j (t.sub.f)= (x'(t.sub.f)-x.sub.j (t.sub.f)).sup.2 +(y'(t.sub.f)-y.sub.j (t.sub.f)).sup.2 +(z'(t.sub.f)-z.sub.j (t.sub.f)).sup.2 !.sup.1/2 ; forming a 3×M matrix H(t f ;mob).sup.Λ that satisfies the relation H(t f ;mob).sup.Λ H(t f ;mob)=I, where I is the 3×3 identity matrix; forming a matrix ΔW(t f ;mob)=H(t f ;mob).sup.Λ PRC(t f ;ref), where PRC(t f ;ref) is an M×1 matrix whose entries are the values PRC(t f ;j;ref) for j=1, 2, . . . , M; interpreting three entries Δw 1 (t f ), Δw 2 (t f ) and Δw 3 (t f ) of the matrix ΔW(t f ;mob) as corrections to the location fix coordinates for the mobile station; and determining corrected location fix coordinates (x(t f ),y(t f ),z(t f )) for the mobile station for at least one time t=t f using the relations x(t.sub.f)=x'(t.sub.f)+Δw.sub.1 (t.sub.f), y(t.sub.f)=y'(t.sub.f)+Δw.sub.2 (t.sub.f), z(t.sub.f)=z'(t.sub.f)+Δw.sub.3 (t.sub.f).
Claim 11
Dependent Claim
217 words
The method of claim 8, further comprising the step of selecting said integer M≧4, and wherein said steps of forming said 3×M matrix H(t f ;mob).sup.Λ and forming said matrix ΔW(t f ;mob) comprise the steps of: augmenting said matrix H(t f ;mob) by adding M-3 columns of matrix entries to produce an augmented M×M matrix H*(t f ;mob), where three columns of the matrix H*(t f ;mob) are identical with three columns of said matrix H(t f ;mob) and each of the columns of H*(t f ;mob) forms an M×1 column matrix that is linearly independent of the other M-1 column matrices of the matrix H*(t f ;mob); forming an inverse matrix H*(t f ;mob) -1 , determining an M×1 matrix ΔW* (t f ;mob) by a matrix equation ΔW* (t f ;mob)=H*(t f ;mob) -1 PRC(t f ;ref), where PRC(t f ;ref) is an M×1 matrix whose entries are the values PRC(t f ;j;ref) for j=1, 2, . . . , M; and selecting three of the entries Δw 1 *(t f ), Δw 2 *(t f ) and Δw 3 *(t f ) of the matrix ΔW*(t f ;mob) and forming said 3×1 matrix ΔW(t f ;mob) with entires defined by Δw k (t f )=Δw k *(t f ), for k=1, 2, 3.
Claim 12
Dependent Claim
120 words
The method of claim 9, wherein said step of augmenting said matrix H(t f ;mob) comprises the steps of: forming an M-dimensional vector from the values of said M entries in each column of said M×3 matrix H(t f ;mob); using a Gram-Schmidt orthogonalization procedure to form M-3 additional M-dimensional vectors, with each such vector being orthogonal to each of the M-dimensional vectors formed from said matrix H(t;mob) and with these M-3 additional vectors being orthogonal to each other; and forming an augmented M×M matrix H*(t f ;mob) matrix whose column entries are the entries of the three vectors formed from the matrix H(t f ;mob) and the entries of the additional M-3 vectors formed using the Gram-Schmidt orthogonalization procedure.
Claim 13
Dependent Claim
53 words
The method of claim 8, wherein said step of forming said 3×M matrix H(t f ;mob).sup.Λ comprises the steps of: forming a 3×3 matrix (H(t f ;mob) tr H(t f ;mob)) -1 ; and defining said 3×M matrix H(t f ;mob).sup.Λ by the relation H(t.sub.f ;mob).sup.Λ =(H(t.sub.f ;mob).sup.tr H(t.sub.f ;mob)).sup.-1 H(t.sub.f ;mob).sup.tr. 12.
Claim 14
Dependent Claim
24 words
The method of claim 8, further comprising the step of selecting said integer M=3 and selecting H(t f ;mob).sup.Λ =H(t f ;mob) -1 .
Claim 15
Dependent Claim
26 words
The method of claim 8, further comprising the step of selecting said supplemental data processor station to be said SATPS receiver/processor provided for said reference station.
Claim 16
Dependent Claim
26 words
The method of claim 8, further comprising the step of selecting said supplemental data processor station to be said SATPS receiver/processor provided for said mobile station.
Claim 17
Independent Claim
462 words
A method for determining spatial location with enhanced accuracy for a mobile user Satellite Positioning System (SATPS) station, the method comprising the steps of: providing pseudorange corrections PRC(t f ;j;ref) for uncorrected pseudorange values PR(t f ;j;ref), measured at an SATPS reference station that has location coordinates that are known with high accuracy and that receives SATPS signals at a selected location fix time t=t f from each of M SATPS satellites, numbered j=1, 2, . . . , M (M≧3), where the sums PR(t f ;j;ref)+PRC(t f ;j;ref) for j=1, 2, . . . , M provide corrected reference station pseudorange values PR(t f ;j;ref) cor that agree with known pseudorange values for the reference station for the M SATPS satellites for the location fix time t f ; providing an SATPS mobile station that has an SATPS signal antenna and associated SATPS signal receiver/processor, and causing the mobile station to receive and process SATPS signals from each of the M SATPS satellites and to determine uncorrected location fix coordinates, including uncorrected three-dimensional spatial location coordinates (x'(t f ),y'(t f ),z'(t f )), for the mobile station for the location fix time t f ; providing a supplemental data processor with the location fix time t f , with the mobile station uncorrected location fix coordinates (x'(t f ), y'(t f ), z'(t f )), with spatial coordinate values (x j (t f ), y j (t f ), z j (t f )) of SATPS satellite number j for a time corresponding to the location fix time t f , and with the reference station pseudorange corrections PRC(t f ;j;ref) for j=1, 2, . . . , M; computing at the supplemental data processor an M×3 matrix H(t f ;mob) whose entries are defined by the relations H(t.sub.f ;mob)=(h.sub.ji (t.sub.f)), h.sub.j1 (t.sub.f)=α.sub.j1 (t.sub.f)=(x'(t.sub.f)-x.sub.j (t.sub.f))/r.sub.0j (t.sub.f), h.sub.j2 (t.sub.f)=α.sub.j2 (t.sub.f)=(y'(t.sub.f)-y.sub.j (t.sub.f))/r.sub.0j (t.sub.f), h.sub.j3 (t.sub.f)=α.sub.j3 (t.sub.f)=(z'(t.sub.f)-z.sub.j (t.sub.f))/r.sub.0j (t.sub.f) (j=1, 2, . . . , M), r.sub.0j (t.sub.f)= (x'(t.sub.f)-x.sub.j (t.sub.f)).sup.2 +(y'(t.sub.f)-y.sub.j (t.sub.f)).sup.2 +(z'(t.sub.f)-z.sub.j (t.sub.f)).sup.2 !.sup.1/2 ; forming a 3×M matrix H(t f ;mob).sup.Λ that satisfies the relation H(t f ;mob).sup.Λ H(t f ;mob)=I, where I is the 3×3 identity matrix; forming a matrix ΔW(t f ;mob)=H(t f ;mob).sup.Λ PRC(t f ;ref), where PRC(t f ;ref) is an M×1 matrix whose entries are the values PRC(t f ;j;ref) for j=1, 2, . . . ,M; interpreting two entries Δw 1 (t f ) and Δw 2 (t f ) of the matrix ΔW(t f ;mob) as corrections to the location fix coordinates x'(t f ) and y'(t f ) for the mobile station; and determining corrected location fix coordinates (x(t f ),y(t f ),z(t f )) for the mobile station for at least one time t=t f using the relations x(t.sub.f)=x'(t.sub.f)+Δw.sub.1 (t.sub.f), y(t.sub.f)=y'(t.sub.f)+Δw.sub.2 (t.sub.f), z(t.sub.f)=z'(t.sub.f).
Claim 18
Independent Claim
462 words
A method for determining spatial location with enhanced accuracy for a mobile user Satellite Positioning System (SATPS) station, the method comprising the steps of: providing pseudorange corrections PRC(t f ;j;ref) for uncorrected pseudorange values PR(t f ;j;ref), measured at an SATPS reference station that has location coordinates that are known with high accuracy and that receives SATPS signals at a selected location fix time t=t f from each of M SATPS satellites, numbered j=1, 2, . . . , M (M≧3), where the sums PR(t f ;j;ref)+PRC(t f ;j;ref) for j=1, 2, . . . , M provide corrected reference station pseudorange values PR(t f ;j;ref) cor that agree with known pseudorange values for the reference station for the M SATPS satellites for the location fix time t f ; providing an SATPS mobile station that has an SATPS signal antenna and associated SATPS signal receiver/processor, and causing the mobile station to receive and process SATPS signals from each of the M SATPS satellites and to determine uncorrected location fix coordinates, including uncorrected three-dimensional spatial location coordinates (x'(t f ),y'(t f ),z'(t f )), for the mobile station for the location fix time t f ; providing a supplemental data processor with the location fix time t f , with the mobile station uncorrected location fix coordinates (x'(t f ), y'(t f ), z'(t f )), with spatial coordinate values (x j (t f ), y j (t f ), z j (t f )) of SATPS satellite number j for a time corresponding to the location fix time t f , and with the reference station pseudorange corrections PRC(t f ;j;ref) for j=1, 2, . . . , M; computing at the supplemental data processor an M×3 matrix H(t f ;mob) whose entries are defined by the relations H(t.sub.f ;mob)=(h.sub.ji (t.sub.f)), h.sub.j1 (t.sub.f)=α.sub.j1 (t.sub.f)=(x'(t.sub.f)-x.sub.j (t.sub.f))/r.sub.0j (t.sub.f), h.sub.j2 (t.sub.f)=α.sub.j2 (t.sub.f)=(y'(t.sub.f)-y.sub.j (t.sub.f))/r.sub.0j (t.sub.f), h.sub.j3 (t.sub.f)=α.sub.j3 (t.sub.f)=(z'(t.sub.f)-z.sub.j (t.sub.f))/r.sub.0j (t.sub.f) (j=1, 2, . . . , M), r.sub.0j (t.sub.f)= (x'(t.sub.f)-x.sub.j (t.sub.f)).sup.2 +(y'(t.sub.f)-y.sub.j (t.sub.f)).sup.2 +(z'(t.sub.f)-z.sub.j (t.sub.f)).sup.2 !.sup.1/2 ; forming a 3×M matrix H(t f ;mob).sup.Λ that satisfies the relation H(t f ;mob).sup.Λ H(t f ;mob)=I, where I is the 3×3 identity matrix; forming a matrix ΔW(t f ;mob)=H(t f ;mob).sup.Λ PRC(t f ;ref), where PRC(t f ;ref) is an M×1 matrix whose entries are the values PRC(t f ;j;ref) for j=1, 2, . . . ,M; interpreting two entries Δw 1 (t f ) and Δw 2 (t f ) of the matrix ΔW(t f ;mob) as corrections to the location fix coordinates x'(t f ) and y'(t f ) for the mobile station; and determining corrected location fix coordinates (x(t f ),y(t f ),z(t f )) for the mobile station for at least one time t=t f using the relations x(t.sub.f)=x'(t.sub.f)+Δw.sub.1 (t.sub.f), y(t.sub.f)=y'(t.sub.f)+Δw.sub.2 (t.sub.f), z(t.sub.f)=z'(t.sub.f).
Claim 19
Dependent Claim
216 words
The method of claim 15, further comprising the step of selecting said integer M >4, and wherein said steps of forming said 3×M matrix H(t f ;mob).sup.Λ and forming said matrix ΔW(t f ;mob) comprise the steps of: augmenting said matrix H(t f ;mob) by adding M-3 columns of matrix entries to produce an augmented M×M matrix H*(t f ;mob), where three columns of the matrix H*(t f ;mob) are identical with three columns of said matrix H(t f ;mob) and each of the columns of H*(t f ;mob) forms an M×1 column matrix that is linearly independent of the other M-1 column matrices of the matrix H*(t f ;mob); forming an inverse matrix H*(t f ;mob) -1 , determining an M×1 matrix ΔW*(t f ;mob) by a matrix equation ΔW*(t f ;mob)=H*(t f ;mob) -1 PRC(t f ;ref), where PRC(t f ;ref) is an M×1 matrix whose entries are the values PRC(t f ;j;ref) for j=1, 2, . . . , M; and selecting two of the entries Δw 1 *(t f ) and Δw 2 *(t f ) of the matrix ΔW*(t f ;mob) and forming said 3×1 matrix ΔW(t f ;mob) with entries defined by Δw k (t f )=Δw k *(t f ), for k=1, 2 and Δw 3 (t f )=0.
Claim 20
Dependent Claim
120 words
The method of claim 16, wherein said step of augmenting said matrix H(t f ;mob) comprises the steps of: forming an M-dimensional vector from the values of said M entries in each column of said M×3 matrix H(t f ;mob); using a Gram-Schmidt orthogonalization procedure to form M-3 additional M-dimensional vectors, with each such vector being orthogonal to each of the M-dimensional vectors formed from said matrix H(t;mob) and with these M-3 additional vectors being orthogonal to each other; and forming an augmented M×M matrix H*(t f ;mob) matrix whose column entries are the entries of the three vectors formed from the matrix H(t f ;mob) and the entries of the additional M-3 vectors formed using the Gram-Schmidt orthogonalization procedure.
Claim 21
Dependent Claim
52 words
The method of claim 15, wherein said step of forming said 3×M matrix H(t f ;mob).sup.Λ comprises the steps of: forming a 3×3 matrix (H(t f ;mob) tr H(t f ;mob)) -1 ; and defining said 4×M matrix H(t f ;mob).sup.Λ by the relation H(t.sub.f ;mob).sup.Λ =(H(t.sub.f ;mob).sup.tr H(t.sub.f ;mob)).sup.-1 H(t.sub.f ;mob).sup.tr.
Claim 22
Dependent Claim
24 words
The method of claim 15, further comprising the step of selecting said integer M=3 and selecting H(t f ;mob).sup.Λ =H(t f ;mob) -1 .
Claim 23
Dependent Claim
26 words
The method of claim 15, further comprising the step of selecting said supplemental data processor station to be said SATPS receiver/processor provided for said reference station.
Claim 24
Dependent Claim
26 words
The method of claim 15, further comprising the step of selecting said supplemental data processor station to be said SATPS receiver/processor provided for said mobile station.
Claim 25
Independent Claim
597 words
A method for determining spatial location and clock bias coordinates with enhanced accuracy for a mobile user Satellite Positioning System (SATPS) station, the method comprising the steps of: providing pseudorange corrections PRC(t f ;j;ref) for uncorrected pseudorange values PR(t f ;j;ref, measured at an SATPS reference station that has location coordinates that are known with high accuracy and that receives SATPS signals at a selected location fix time t=t f from each of M SATPS satellites, numbered j=1, 2, . . . , M (M>4), where the sums PR(t f ;j;ref)+PRC(t f ;j;ref) for j=1, 2, . . . , M provide corrected reference station pseudorange values PR(t f ;j;ref) cor that agree with known pseudorange values for the reference station for the M SATPS satellites for the location fix time t f ; providing an SATPS mobile station that has an SATPS signal antenna and associated SATPS signal receiver/processor, and causing the mobile station to receive and process SATPS signals from each of the M SATPS satellites and to determine uncorrected location fix coordinates, including uncorrected three-dimensional spatial location coordinates (x'(t f ),y'(t f ),z'(t f )) and uncorrected clock bias coordinate b'(t f ), for the mobile station for the location fix time t f ; providing a supplemental data processor with the location fix time t f , with the mobile station uncorrected location fix coordinates (x'(t f ), y'(t f ), z'(t f ), b'(t f )), with spatial coordinate values (x j (t f ), y j (t f ), z j (t f )) of SATPS satellite number j for a time corresponding to the location fix time t f , and with the reference station pseudorange corrections PRC(t f ;j;ref) for j=1, 2, . . . , M; computing at the supplemental data processor an M×4 matrix H(t f ;mob) whose entries are defined by the relations H(t.sub.f ;mob)=(h.sub.ji (t.sub.f)), h.sub.j1 (t.sub.f)=α.sub.j1 (t.sub.f)=(x'(t.sub.f)-x.sub.j (t.sub.f))/r.sub.0j (t.sub.f), h.sub.j2 (t.sub.f)=α.sub.j2 (t.sub.f)=(y'(t.sub.f)-y.sub.j (t.sub.f))/r.sub.0j (t.sub.f), h.sub.j3 (t.sub.f)=α.sub.j3 (t.sub.f)=(z'(t.sub.f)-z.sub.j (t.sub.f))/r.sub.0j (t.sub.f), h.sub.j4 (t.sub.f)=1, (j=1, 2, . . . , M), r.sub.0j (t.sub.f)- (x'(t.sub.f)-x.sub.j (t.sub.f)).sup.2 +(y'(t.sub.f)-y.sub.j (t.sub.f)).sup.2 +(z'(t.sub.f)-z.sub.j (t.sub.f)).sup.2 !.sup.1/2 ; decomposing the matrix H(t f ;mob) into a 4×4 matrix H f =(h ji ) f (j=j1, j2, j3, j4) and an (M-4)×4 matrix H nf =(h ji ) nf (j=j5, . . . , jM); forming an M×1 matrix v= I-H(H tr H) -1 H tr !PR(t f ;mob) at the mobile station, where PR(t f ;mob) is an M×1 vector whose ordered entries are the uncorrected pseudorange values PR(t f ;j;mob); decomposing the matrix v into a 4×1 matrix v f , consisting of the first four entries of the matrix v, and an (M-4)×1 matrix v nf , consisting of the other M-4 entries of the matrix v; providing the M-4 entries of the matrix v nf and the mobile station location fix coordinates (x',y',z',b') for the supplemental data processor; constructing a matrix v f by the relation v f =-(H f tr ) -1 H nf tr v nf ; reconstructing the vector v= v f |v nf ! as a concatenation of the vectors v f and v nf ; reconstructing an M×1 matrix of uncorrected pseudorange values PR(t f ;mob) from the vector v; adding the pseudorange corrections matrix PRC(t f ;j;ref) to the uncorrected pseudorange matrix PR(t f ;j;mob) to form a corrected pseudorange matrix PR(t f ;j;mob) cor ; and determining corrected location fix coordinates (x(t f ),y(t f ),z(t f ),b(t f )) for the mobile station, using the corrected pseudorange matrix PR(t f ;j;mob) cor .
Claim 26
Independent Claim
597 words
A method for determining spatial location and clock bias coordinates with enhanced accuracy for a mobile user Satellite Positioning System (SATPS) station, the method comprising the steps of: providing pseudorange corrections PRC(t f ;j;ref) for uncorrected pseudorange values PR(t f ;j;ref, measured at an SATPS reference station that has location coordinates that are known with high accuracy and that receives SATPS signals at a selected location fix time t=t f from each of M SATPS satellites, numbered j=1, 2, . . . , M (M>4), where the sums PR(t f ;j;ref)+PRC(t f ;j;ref) for j=1, 2, . . . , M provide corrected reference station pseudorange values PR(t f ;j;ref) cor that agree with known pseudorange values for the reference station for the M SATPS satellites for the location fix time t f ; providing an SATPS mobile station that has an SATPS signal antenna and associated SATPS signal receiver/processor, and causing the mobile station to receive and process SATPS signals from each of the M SATPS satellites and to determine uncorrected location fix coordinates, including uncorrected three-dimensional spatial location coordinates (x'(t f ),y'(t f ),z'(t f )) and uncorrected clock bias coordinate b'(t f ), for the mobile station for the location fix time t f ; providing a supplemental data processor with the location fix time t f , with the mobile station uncorrected location fix coordinates (x'(t f ), y'(t f ), z'(t f ), b'(t f )), with spatial coordinate values (x j (t f ), y j (t f ), z j (t f )) of SATPS satellite number j for a time corresponding to the location fix time t f , and with the reference station pseudorange corrections PRC(t f ;j;ref) for j=1, 2, . . . , M; computing at the supplemental data processor an M×4 matrix H(t f ;mob) whose entries are defined by the relations H(t.sub.f ;mob)=(h.sub.ji (t.sub.f)), h.sub.j1 (t.sub.f)=α.sub.j1 (t.sub.f)=(x'(t.sub.f)-x.sub.j (t.sub.f))/r.sub.0j (t.sub.f), h.sub.j2 (t.sub.f)=α.sub.j2 (t.sub.f)=(y'(t.sub.f)-y.sub.j (t.sub.f))/r.sub.0j (t.sub.f), h.sub.j3 (t.sub.f)=α.sub.j3 (t.sub.f)=(z'(t.sub.f)-z.sub.j (t.sub.f))/r.sub.0j (t.sub.f), h.sub.j4 (t.sub.f)=1, (j=1, 2, . . . , M), r.sub.0j (t.sub.f)- (x'(t.sub.f)-x.sub.j (t.sub.f)).sup.2 +(y'(t.sub.f)-y.sub.j (t.sub.f)).sup.2 +(z'(t.sub.f)-z.sub.j (t.sub.f)).sup.2 !.sup.1/2 ; decomposing the matrix H(t f ;mob) into a 4×4 matrix H f =(h ji ) f (j=j1, j2, j3, j4) and an (M-4)×4 matrix H nf =(h ji ) nf (j=j5, . . . , jM); forming an M×1 matrix v= I-H(H tr H) -1 H tr !PR(t f ;mob) at the mobile station, where PR(t f ;mob) is an M×1 vector whose ordered entries are the uncorrected pseudorange values PR(t f ;j;mob); decomposing the matrix v into a 4×1 matrix v f , consisting of the first four entries of the matrix v, and an (M-4)×1 matrix v nf , consisting of the other M-4 entries of the matrix v; providing the M-4 entries of the matrix v nf and the mobile station location fix coordinates (x',y',z',b') for the supplemental data processor; constructing a matrix v f by the relation v f =-(H f tr ) -1 H nf tr v nf ; reconstructing the vector v= v f |v nf ! as a concatenation of the vectors v f and v nf ; reconstructing an M×1 matrix of uncorrected pseudorange values PR(t f ;mob) from the vector v; adding the pseudorange corrections matrix PRC(t f ;j;ref) to the uncorrected pseudorange matrix PR(t f ;j;mob) to form a corrected pseudorange matrix PR(t f ;j;mob) cor ; and determining corrected location fix coordinates (x(t f ),y(t f ),z(t f ),b(t f )) for the mobile station, using the corrected pseudorange matrix PR(t f ;j;mob) cor .
Claim 27
Independent Claim
577 words
A method for determining spatial location and clock bias coordinates with enhanced accuracy for a mobile user Satellite Positioning System (SATPS) station, the method comprising the steps of: providing pseudorange corrections PRC(t f ;j;ref) for uncorrected pseudorange values PR(t f ;j;ref), measured at an SATPS reference station that has location coordinates that are known with high accuracy and that receives SATPS signals at a selected location fix time t=t f from each of M SATPS satellites, numbered j=1, 2, . . . , M (M>3), where the sums PR(t f ;j;ref)+PRC(t f ;j;ref) for j=1, 2, . . . , M provide corrected reference station pseudorange values PR(t f ;j;ref) cor that agree with known pseudorange values for the reference station for the M SATPS satellites for the location fix time t f ; providing an SATPS mobile station that has an SATPS signal antenna and associated SATPS signal receiver/processor, and causing the mobile station to receive and process SATPS signals from each of the M SATPS satellites and to determine uncorrected location fix coordinates, including uncorrected three-dimensional spatial location coordinates (x'(t f ),y'(t f ),z'(t f )), for the mobile station for the location fix time t f ; providing a supplemental data processor with the location fix time t f , with the mobile station uncorrected location fix coordinates (x'(t f ), y'(t f ), z'(t f )), with spatial coordinate values (x j (t f ), y j (t f ), z j (t f )) of SATPS satellite number j for a time corresponding to the location fix time t f , and with the reference station pseudorange corrections PRC(t f ;j;ref) for j=1, 2, . . . , M; computing at the supplemental data processor an M×3 matrix H(t f ;mob) whose entries are defined by the relations H(t.sub.f ;mob)=(h.sub.ji (t.sub.f)), h.sub.j1 (t.sub.f)=α.sub.j1 (t.sub.f)=(x'(t.sub.f)-x.sub.j (t.sub.f))/r.sub.0j (t.sub.f), h.sub.j2 (t.sub.f)=α.sub.j2 (t.sub.f)=(y'(t.sub.f)-y.sub.j (t.sub.f))/r.sub.0j (t.sub.f), h.sub.j3 (t.sub.f)=α.sub.j3 (t.sub.f)=(z'(t.sub.f)-z.sub.j (t.sub.f))/r.sub.0j (t.sub.f), (j=1, 2, . . . , M), r.sub.0j (t.sub.f)= (x'(t.sub.f)-x.sub.j (t.sub.f)).sup.2 +(y'(t.sub.f)-y'(t.sub.f)).sup.2 !.sup.1/2. decomposing the matrix H(t f ;mob) into a 3×3 matrix H f= (h ji ) f (j=j1, j2, j3) and an (M-3)×3 matrix H nf =(h ji ) nf (j=j4, . . . , jM); forming an M×1 matrix v= I-H(H tr H) -1 H tr !PR(t f ;mob) at the mobile station, where PR(t f ;mob) is an M×1 vector whose ordered entries are the uncorrected pseudorange values PR(t f ;j;mob); decomposing the matrix v into a 3×1 matrix v f , consisting of the first three entries of the matrix v, and an (M-3)×1 matrix v nf , consisting of the other M-3 entries of the matrix v; providing the M-3 entries of the matrix v nf and the mobile station location fix coordinates (x',y',b') for the supplemental data processor; constructing a matrix v f by the relation v f =-(H f tr ) -1 H nf tr v nf ; reconstructing the vector v= v f |v nf ! as a concatenation of the vectors v f and v nf ; reconstructing an M×1 matrix of uncorrected pseudorange values PR(t f ;mob) from the vector v; adding the pseudorange corrections matrix PRC(t f ;j;ref) to the uncorrected pseudorange matrix PR(t f ;j;mob) to form a corrected pseudorange matrix PR(t f ;j;mob) cor ; and determining corrected location fix coordinates (x(t f ),y(t f ),z(t f )) for the mobile station, using the corrected pseudorange matrix PR(t f ;j;mob) cor .
Claim 28
Independent Claim
577 words
A method for determining spatial location and clock bias coordinates with enhanced accuracy for a mobile user Satellite Positioning System (SATPS) station, the method comprising the steps of: providing pseudorange corrections PRC(t f ;j;ref) for uncorrected pseudorange values PR(t f ;j;ref), measured at an SATPS reference station that has location coordinates that are known with high accuracy and that receives SATPS signals at a selected location fix time t=t f from each of M SATPS satellites, numbered j=1, 2, . . . , M (M>3), where the sums PR(t f ;j;ref)+PRC(t f ;j;ref) for j=1, 2, . . . , M provide corrected reference station pseudorange values PR(t f ;j;ref) cor that agree with known pseudorange values for the reference station for the M SATPS satellites for the location fix time t f ; providing an SATPS mobile station that has an SATPS signal antenna and associated SATPS signal receiver/processor, and causing the mobile station to receive and process SATPS signals from each of the M SATPS satellites and to determine uncorrected location fix coordinates, including uncorrected three-dimensional spatial location coordinates (x'(t f ),y'(t f ),z'(t f )), for the mobile station for the location fix time t f ; providing a supplemental data processor with the location fix time t f , with the mobile station uncorrected location fix coordinates (x'(t f ), y'(t f ), z'(t f )), with spatial coordinate values (x j (t f ), y j (t f ), z j (t f )) of SATPS satellite number j for a time corresponding to the location fix time t f , and with the reference station pseudorange corrections PRC(t f ;j;ref) for j=1, 2, . . . , M; computing at the supplemental data processor an M×3 matrix H(t f ;mob) whose entries are defined by the relations H(t.sub.f ;mob)=(h.sub.ji (t.sub.f)), h.sub.j1 (t.sub.f)=α.sub.j1 (t.sub.f)=(x'(t.sub.f)-x.sub.j (t.sub.f))/r.sub.0j (t.sub.f), h.sub.j2 (t.sub.f)=α.sub.j2 (t.sub.f)=(y'(t.sub.f)-y.sub.j (t.sub.f))/r.sub.0j (t.sub.f), h.sub.j3 (t.sub.f)=α.sub.j3 (t.sub.f)=(z'(t.sub.f)-z.sub.j (t.sub.f))/r.sub.0j (t.sub.f), (j=1, 2, . . . , M), r.sub.0j (t.sub.f)= (x'(t.sub.f)-x.sub.j (t.sub.f)).sup.2 +(y'(t.sub.f)-y'(t.sub.f)).sup.2 !.sup.1/2. decomposing the matrix H(t f ;mob) into a 3×3 matrix H f= (h ji ) f (j=j1, j2, j3) and an (M-3)×3 matrix H nf =(h ji ) nf (j=j4, . . . , jM); forming an M×1 matrix v= I-H(H tr H) -1 H tr !PR(t f ;mob) at the mobile station, where PR(t f ;mob) is an M×1 vector whose ordered entries are the uncorrected pseudorange values PR(t f ;j;mob); decomposing the matrix v into a 3×1 matrix v f , consisting of the first three entries of the matrix v, and an (M-3)×1 matrix v nf , consisting of the other M-3 entries of the matrix v; providing the M-3 entries of the matrix v nf and the mobile station location fix coordinates (x',y',b') for the supplemental data processor; constructing a matrix v f by the relation v f =-(H f tr ) -1 H nf tr v nf ; reconstructing the vector v= v f |v nf ! as a concatenation of the vectors v f and v nf ; reconstructing an M×1 matrix of uncorrected pseudorange values PR(t f ;mob) from the vector v; adding the pseudorange corrections matrix PRC(t f ;j;ref) to the uncorrected pseudorange matrix PR(t f ;j;mob) to form a corrected pseudorange matrix PR(t f ;j;mob) cor ; and determining corrected location fix coordinates (x(t f ),y(t f ),z(t f )) for the mobile station, using the corrected pseudorange matrix PR(t f ;j;mob) cor .
Claim 29
Independent Claim
586 words
A method for determining spatial location coordinates with enhanced accuracy for a mobile user Satellite Positioning System (SATPS) station, the method comprising the steps of: providing pseudorange corrections PRC(t f ;j;ref) for uncorrected pseudorange values PR(t f ;j;ref), measured at an SATPS reference station that has location coordinates that are known with high accuracy and that receives SATPS signals at a selected location fix time t=t f from each of M SATPS satellites, numbered j=1, 2, . . . , M (M≧3), where the sums PR(t f ;j;ref)+PRC(t f ;j;ref) for j=1, 2, . . . , M provide corrected reference station pseudorange values PR(t f ;j;ref) cor that agree with known pseudorange values for the reference station for the M SATPS satellites for the location fix time t f ; providing an SATPS mobile station that has an SATPS signal antenna and associated SATPS signal receiver/processor, and causing the mobile station to receive and process SATPS signals from each of the M SATPS satellites and to determine uncorrected location fix coordinates, including uncorrected three-dimensional spatial location coordinates (x'(t f ),y'(t f ),z'(t f )), for the mobile station for the location fix time t f ; providing a supplemental data processor with the location fix time t f , with the mobile station uncorrected location fix coordinates (x'(t f ), y'(t f ), z'(t f )), with spatial coordinate values (x j (t f ), y j (t f ), z j (t f )) of SATPS satellite number j for a time corresponding to the location fix time t f , and with the reference station pseudorange corrections PRC(t f ;j;ref) for j=1, 2, . . . , M; computing at the supplemental data processor an M×3 matrix H(t f ;mob) whose entries are defined by the relations H(t.sub.f ;mob)=(h.sub.ji (t.sub.f)), h.sub.j1 (t.sub.f)=α.sub.j1 (t.sub.f)=(x'(t.sub.f)-x.sub.j (t.sub.f))/r.sub.0j (t.sub.f), h.sub.j2 (t.sub.f)=α.sub.j2 (t.sub.f)=(y'(t.sub.f)-y.sub.j (t.sub.f))/r.sub.0j (t.sub.f), h.sub.j3 (t.sub.f)=α.sub.j3 (t.sub.f)=(z'(t.sub.f)-z.sub.j (t.sub.f))/r.sub.0j (t.sub.f), (j=1, 2, . . . , M), r.sub.0j (t.sub.f)= (x'(t.sub.f)-x.sub.j (t.sub.f)).sup.2 +(y'(t.sub.f)-y.sub.j (t.sub.f)).sup.2 +(z'(t.sub.f)-z.sub.j (t.sub.f))2!.sup.-1/2 ; decomposing the matrix H(t f ;mob) into a 3×3 matrix H f =(h ji )f (j=j1, j2, j3) and an (M-3)×3 matrix H nf =(h ji ) nf (j=j4, . . . , jM); forming an M×1 matrix v= I-H(H tr H) -1 H tr !PR(t f ;mob) at the mobile station, where PR(t f ;mob) is an M×1 vector whose ordered entries are the uncorrected pseudorange values PR(t f ;j;mob); decomposing the matrix v into a 3×1 matrix v f , consisting of the first three entries of the matrix v, and an (M-3)×1 matrix v nf , consisting of the other M-3 entries of the matrix v; providing the M-3 entries of the matrix v nf and the mobile station location fix coordinates (x',y',z') for the supplemental data processor; constructing a matrix v f by the relation v f =-(H f tr ) -1 H nf tr v nf ; reconstructing the vector v= v f |v nf ! as a concatenation of the vectors v f and v nf ; reconstructing an M×1 matrix of uncorrected pseudorange values PR(t f ;mob) from the vector v; adding the pseudorange corrections matrix PRC(t f ;j;ref) to the uncorrected pseudorange matrix PR(t f ;j;mob) to form a corrected pseudorange matrix PR(t f ;j;mob) cor ; and determining corrected location fix coordinates (x(t f ),y(t f )) for the mobile station, using the corrected pseudorange matrix PR(t f ;j;mob) cor , and defining the corrected location fix coordinate z(t f )=z'(t f ).
Claim 30
Independent Claim
586 words
A method for determining spatial location coordinates with enhanced accuracy for a mobile user Satellite Positioning System (SATPS) station, the method comprising the steps of: providing pseudorange corrections PRC(t f ;j;ref) for uncorrected pseudorange values PR(t f ;j;ref), measured at an SATPS reference station that has location coordinates that are known with high accuracy and that receives SATPS signals at a selected location fix time t=t f from each of M SATPS satellites, numbered j=1, 2, . . . , M (M≧3), where the sums PR(t f ;j;ref)+PRC(t f ;j;ref) for j=1, 2, . . . , M provide corrected reference station pseudorange values PR(t f ;j;ref) cor that agree with known pseudorange values for the reference station for the M SATPS satellites for the location fix time t f ; providing an SATPS mobile station that has an SATPS signal antenna and associated SATPS signal receiver/processor, and causing the mobile station to receive and process SATPS signals from each of the M SATPS satellites and to determine uncorrected location fix coordinates, including uncorrected three-dimensional spatial location coordinates (x'(t f ),y'(t f ),z'(t f )), for the mobile station for the location fix time t f ; providing a supplemental data processor with the location fix time t f , with the mobile station uncorrected location fix coordinates (x'(t f ), y'(t f ), z'(t f )), with spatial coordinate values (x j (t f ), y j (t f ), z j (t f )) of SATPS satellite number j for a time corresponding to the location fix time t f , and with the reference station pseudorange corrections PRC(t f ;j;ref) for j=1, 2, . . . , M; computing at the supplemental data processor an M×3 matrix H(t f ;mob) whose entries are defined by the relations H(t.sub.f ;mob)=(h.sub.ji (t.sub.f)), h.sub.j1 (t.sub.f)=α.sub.j1 (t.sub.f)=(x'(t.sub.f)-x.sub.j (t.sub.f))/r.sub.0j (t.sub.f), h.sub.j2 (t.sub.f)=α.sub.j2 (t.sub.f)=(y'(t.sub.f)-y.sub.j (t.sub.f))/r.sub.0j (t.sub.f), h.sub.j3 (t.sub.f)=α.sub.j3 (t.sub.f)=(z'(t.sub.f)-z.sub.j (t.sub.f))/r.sub.0j (t.sub.f), (j=1, 2, . . . , M), r.sub.0j (t.sub.f)= (x'(t.sub.f)-x.sub.j (t.sub.f)).sup.2 +(y'(t.sub.f)-y.sub.j (t.sub.f)).sup.2 +(z'(t.sub.f)-z.sub.j (t.sub.f))2!.sup.-1/2 ; decomposing the matrix H(t f ;mob) into a 3×3 matrix H f =(h ji )f (j=j1, j2, j3) and an (M-3)×3 matrix H nf =(h ji ) nf (j=j4, . . . , jM); forming an M×1 matrix v= I-H(H tr H) -1 H tr !PR(t f ;mob) at the mobile station, where PR(t f ;mob) is an M×1 vector whose ordered entries are the uncorrected pseudorange values PR(t f ;j;mob); decomposing the matrix v into a 3×1 matrix v f , consisting of the first three entries of the matrix v, and an (M-3)×1 matrix v nf , consisting of the other M-3 entries of the matrix v; providing the M-3 entries of the matrix v nf and the mobile station location fix coordinates (x',y',z') for the supplemental data processor; constructing a matrix v f by the relation v f =-(H f tr ) -1 H nf tr v nf ; reconstructing the vector v= v f |v nf ! as a concatenation of the vectors v f and v nf ; reconstructing an M×1 matrix of uncorrected pseudorange values PR(t f ;mob) from the vector v; adding the pseudorange corrections matrix PRC(t f ;j;ref) to the uncorrected pseudorange matrix PR(t f ;j;mob) to form a corrected pseudorange matrix PR(t f ;j;mob) cor ; and determining corrected location fix coordinates (x(t f ),y(t f )) for the mobile station, using the corrected pseudorange matrix PR(t f ;j;mob) cor , and defining the corrected location fix coordinate z(t f )=z'(t f ).
Claim 31
Dependent Claim
355 words
Apparatus for determining spatial location and clock bias coordinates with enhanced accuracy for a mobile user Satellite Positioning System (SATPS) station, the apparatus comprising: a data processor that receives (1) uncorrected location fix coordinates (x'(t f ),y'(t f ),z'(t f ),b'(t f )) for a selected location fix time t=t f for an SATPS mobile station that has an SATPS signal antenna and associated SATPS signal receiver/processor for receiving and processing SATPS signals from each of a plurality of M SATPS satellites, numbered j=1, 2, . . . , M (M≧4) to determine uncorrected three-dimensional spatial location coordinates (x'(t f ),y'(t f ),z'(t f )) and uncorrected clock bias coordinate b'(t f ) for the mobile station, based upon SATPS signals received from the M SATPS satellites and (2) pseudorange correction values PRC(t f ;j;ref), determined for an SATPS reference station having a known location from SATPS signals received from each of the M SATPS satellites, wherein the data processor is programmed to: (i) compute an M×4 matrix H(t f ;mob) whose entries are defined by the relations H(t.sub.f ;mob)=(h.sub.ji (t.sub.f)), h.sub.j1 (t.sub.f)=α.sub.j1 (t.sub.f)=(x'(t.sub.f)-x.sub.j (t.sub.f))/r.sub.0j (t.sub.f), h.sub.j2 (t.sub.f)=α.sub.j2 (t.sub.f)=(y'(t.sub.f)-y.sub.j (t.sub.f))/r.sub.0j (t.sub.f), h.sub.j3 (t.sub.f)=α.sub.j3 (t.sub.f)=(z'(t.sub.f)-z.sub.j (t.sub.f))/r.sub.0j (t.sub.f), h.sub.j4 (t.sub.f)=1, (j=1, 2, . . . , M), r.sub.0j (t.sub.f)= (x'(t.sub.f)-x.sub.j (t.sub.f)).sup.2 +(y'(t.sub.f)-y'(t.sub.f)).sup.2 +(z'(t.sub.f)-z.sub.j (t.sub.f)).sup.2 !.sup.1/2 ; (ii) form a 4×M matrix H(t f ;mob).sup.Λ that satisfies the relation H(t f ;mob).sup.Λ H(t f ;mob)=I, where I is the 4×4 identity matrix; (iii) form a matrix ΔW(t f ;mob)=H(t f ;mob).sup.Λ PRC(t f ;ref), where PRC(t f ;ref) is an M×1 matrix whose entries are the values PRC(t f ;j;ref) for j=1, 2, . . . ,M; (iv) interpret four entries Δw 1 (t f ), Δw 2 (t f ), Δw 3 (t f ), and Δw 4 (t f ) of the matrix ΔW(t f ;mob) as corrections to the location fix coordinates for the mobile station; and (v) determine corrected location fix coordinates (x(t f ),y(t f ),z(t f ),b(t f )) for the mobile station for at least one time t=t f using the relations x(t.sub.f)=x'(t.sub.f)+Δw.sub.1 (t.sub.f), y(t.sub.f)=y'(t.sub.f)+Δw.sub.2 (t.sub.f), z(t.sub.f)=z'(t.sub.f)+Δw.sub.3 (t.sub.f), b(t.sub.f)=b'(t.sub.f)+Δw.sub.4 (t.sub.f). 26.
Claim 32
Dependent Claim
355 words
Apparatus for determining spatial location and clock bias coordinates with enhanced accuracy for a mobile user Satellite Positioning System (SATPS) station, the apparatus comprising: a data processor that receives (1) uncorrected location fix coordinates (x'(t f ),y'(t f ),z'(t f ),b'(t f )) for a selected location fix time t=t f for an SATPS mobile station that has an SATPS signal antenna and associated SATPS signal receiver/processor for receiving and processing SATPS signals from each of a plurality of M SATPS satellites, numbered j=1, 2, . . . , M (M≧4) to determine uncorrected three-dimensional spatial location coordinates (x'(t f ),y'(t f ),z'(t f )) and uncorrected clock bias coordinate b'(t f ) for the mobile station, based upon SATPS signals received from the M SATPS satellites and (2) pseudorange correction values PRC(t f ;j;ref), determined for an SATPS reference station having a known location from SATPS signals received from each of the M SATPS satellites, wherein the data processor is programmed to: (i) compute an M×4 matrix H(t f ;mob) whose entries are defined by the relations H(t.sub.f ;mob)=(h.sub.ji (t.sub.f)), h.sub.j1 (t.sub.f)=α.sub.j1 (t.sub.f)=(x'(t.sub.f)-x.sub.j (t.sub.f))/r.sub.0j (t.sub.f), h.sub.j2 (t.sub.f)=α.sub.j2 (t.sub.f)=(y'(t.sub.f)-y.sub.j (t.sub.f))/r.sub.0j (t.sub.f), h.sub.j3 (t.sub.f)=α.sub.j3 (t.sub.f)=(z'(t.sub.f)-z.sub.j (t.sub.f))/r.sub.0j (t.sub.f), h.sub.j4 (t.sub.f)=1, (j=1, 2, . . . , M), r.sub.0j (t.sub.f)= (x'(t.sub.f)-x.sub.j (t.sub.f)).sup.2 +(y'(t.sub.f)-y'(t.sub.f)).sup.2 +(z'(t.sub.f)-z.sub.j (t.sub.f)).sup.2 !.sup.1/2 ; (ii) form a 4×M matrix H(t f ;mob).sup.Λ that satisfies the relation H(t f ;mob).sup.Λ H(t f ;mob)=I, where I is the 4×4 identity matrix; (iii) form a matrix ΔW(t f ;mob)=H(t f ;mob).sup.Λ PRC(t f ;ref), where PRC(t f ;ref) is an M×1 matrix whose entries are the values PRC(t f ;j;ref) for j=1, 2, . . . ,M; (iv) interpret four entries Δw 1 (t f ), Δw 2 (t f ), Δw 3 (t f ), and Δw 4 (t f ) of the matrix ΔW(t f ;mob) as corrections to the location fix coordinates for the mobile station; and (v) determine corrected location fix coordinates (x(t f ),y(t f ),z(t f ),b(t f )) for the mobile station for at least one time t=t f using the relations x(t.sub.f)=x'(t.sub.f)+Δw.sub.1 (t.sub.f), y(t.sub.f)=y'(t.sub.f)+Δw.sub.2 (t.sub.f), z(t.sub.f)=z'(t.sub.f)+Δw.sub.3 (t.sub.f), b(t.sub.f)=b'(t.sub.f)+Δw.sub.4 (t.sub.f). 26.
Claim 33
Dependent Claim
207 words
The apparatus of claim 25, wherein said integer M≧5 and wherein said data processor is programmed to perform steps (ii) and (iii) by: augmenting said matrix H(t f ;mob) by adding M-4 columns of matrix entries to produce an augmented M×M matrix H*(t f ;mob), where four columns of the matrix H*(t f ;mob) are identical with four columns of said matrix H(t f ;mob) and each of the columns of H*(t f ;mob) forms an M×1 column matrix that is linearly independent of the other M-1 column matrices of the matrix H*(t f ;mob); forming an inverse matrix H*(t f ;mob) -1 , determining an M×1 matrix ΔW*(t f ;mob) by a matrix equation ΔW*(t f ;mob)=H*(t f ;mob) -1 PRC(t f ;ref), where PRC(t f ;ref) is an M×1 matrix whose entries are the values PRC(t f ;j;ref) for j=1, 2, . . . , M; and selecting four of the entries Δw 1 *(t f ), Δw 2 *(t f ), Δw 3 *(t f ), and Δw 4 *(t f ) of the matrix ΔW*(t f ;mob) and forming said 4×1 matrix ΔW(t f ;mob) with entires defined by Δw k (t f )=Δw k *(t f ), for k=1, 2, 3, 4.
Claim 34
Dependent Claim
49 words
The apparatus of claim 25, wherein said said data processor is programmed to perform step (ii) by: forming a 4×4 matrix (H(t f ;mob) tr H(t f ;mob)) -1 ; and defining said 4×M matrix H(t f ;mob).sup.Λ by the relation H(t.sub.f ;mob).sup.Λ =(H(t.sub.f ;mob).sup.tr H(t.sub.f ;mob)).sup.-1 H(t.sub.f ;mob).sup.tr.
Claim 35
Dependent Claim
26 words
The apparatus of claim 25, wherein said integer M=4 and said data processor performs step (ii) by setting H(t f ;mob).sup.Λ =H(t f ;mob) -1 .
Claim 36
Dependent Claim
336 words
Apparatus for determining spatial location and clock bias coordinates with enhanced accuracy for a mobile user Satellite Positioning System (SATPS) station, the apparatus comprising: a data processor that receives (1) uncorrected location fix coordinates (x'(t f ),y'(t f ),z'(t f )) for a selected location fix time t=t f for an SATPS mobile station that has an SATPS signal antenna and associated SATPS signal receiver/processor for receiving and processing SATPS signals from each of a plurality of M SATPS satellites, numbered j=1, 2, . . . , M (M≧3) to determine uncorrected three-dimensional spatial location coordinates (x'(t f ),y'(t f ),z'(t f )) for the mobile station, based upon SATPS signals received from the M SATPS satellites and (2) pseudorange correction values PRC(t f ;j;ref), determined for an SATPS reference station having a known location from SATPS signals received from each of the M SATPS satellites, wherein the data processor is programmed to: (i) compute an M×3 matrix H(t f ;mob) whose entries are defined by the relations H(t.sub.f ;mob)=(h.sub.ji (t.sub.f)), h.sub.j1 (t.sub.f)=α.sub.j1 (t.sub.f)=(x'(t.sub.f)-x.sub.j (t.sub.f))/r.sub.0j (t.sub.f), h.sub.j2 (t.sub.f)=α.sub.j2 (t.sub.f)=(y'(t.sub.f)-y.sub.j (t.sub.f))/r.sub.0j (t.sub.f), h.sub.j3 (t.sub.f)=α.sub.j3 (t.sub.f)=(z'(t.sub.f)-z.sub.j (t.sub.f))/r.sub.0j (t.sub.f), (j=1, 2, . . . , M), r.sub.0j (t.sub.f)= (x'(t.sub.f)-x.sub.j (t.sub.f)).sup.2 +(y'(t.sub.f)-y.sub.j (t.sub.f)).sup.2 +(z'(t.sub.f)-z.sub.j (t.sub.f)).sup.2 !.sup.1/2 ; (ii) form a 3×M matrix H(t f ;mob).sup.Λ that satisfies the relation H(t f ;mob).sup.Λ H(t f ;mob)=I, where I is the 3×3 identity matrix; (iii) form a matrix ΔW(t f ;mob)=H(t f ;mob).sup.Λ PRC(t f ;ref), where PRC(t f ;ref) is an M×1 matrix whose entries are the values PRC(t f ;j;ref) for j=1, 2, . . . , M; (iv) interpret three entries Δw 1 (t f ), Δw 2 (t f ) and Δw 3 (t f ) of the matrix ΔW(t f ;mob) as corrections to the location fix coordinates for the mobile station; and (v) determine corrected location fix coordinates (x(t f ),y(t f ),z(t f )) for the mobile station for at least one time t=t f using the relations x(t.sub.f)=x'(t.sub.f)+Δw.sub.1 (t.sub.f), y(t.sub.f)=y'(t.sub.f)+Δw.sub.2 (t.sub.f), z(t.sub.f)=z'(t.sub.f)+Δw.sub.3 (t.sub.f). 30.
Claim 37
Dependent Claim
336 words
Apparatus for determining spatial location and clock bias coordinates with enhanced accuracy for a mobile user Satellite Positioning System (SATPS) station, the apparatus comprising: a data processor that receives (1) uncorrected location fix coordinates (x'(t f ),y'(t f ),z'(t f )) for a selected location fix time t=t f for an SATPS mobile station that has an SATPS signal antenna and associated SATPS signal receiver/processor for receiving and processing SATPS signals from each of a plurality of M SATPS satellites, numbered j=1, 2, . . . , M (M≧3) to determine uncorrected three-dimensional spatial location coordinates (x'(t f ),y'(t f ),z'(t f )) for the mobile station, based upon SATPS signals received from the M SATPS satellites and (2) pseudorange correction values PRC(t f ;j;ref), determined for an SATPS reference station having a known location from SATPS signals received from each of the M SATPS satellites, wherein the data processor is programmed to: (i) compute an M×3 matrix H(t f ;mob) whose entries are defined by the relations H(t.sub.f ;mob)=(h.sub.ji (t.sub.f)), h.sub.j1 (t.sub.f)=α.sub.j1 (t.sub.f)=(x'(t.sub.f)-x.sub.j (t.sub.f))/r.sub.0j (t.sub.f), h.sub.j2 (t.sub.f)=α.sub.j2 (t.sub.f)=(y'(t.sub.f)-y.sub.j (t.sub.f))/r.sub.0j (t.sub.f), h.sub.j3 (t.sub.f)=α.sub.j3 (t.sub.f)=(z'(t.sub.f)-z.sub.j (t.sub.f))/r.sub.0j (t.sub.f), (j=1, 2, . . . , M), r.sub.0j (t.sub.f)= (x'(t.sub.f)-x.sub.j (t.sub.f)).sup.2 +(y'(t.sub.f)-y.sub.j (t.sub.f)).sup.2 +(z'(t.sub.f)-z.sub.j (t.sub.f)).sup.2 !.sup.1/2 ; (ii) form a 3×M matrix H(t f ;mob).sup.Λ that satisfies the relation H(t f ;mob).sup.Λ H(t f ;mob)=I, where I is the 3×3 identity matrix; (iii) form a matrix ΔW(t f ;mob)=H(t f ;mob).sup.Λ PRC(t f ;ref), where PRC(t f ;ref) is an M×1 matrix whose entries are the values PRC(t f ;j;ref) for j=1, 2, . . . , M; (iv) interpret three entries Δw 1 (t f ), Δw 2 (t f ) and Δw 3 (t f ) of the matrix ΔW(t f ;mob) as corrections to the location fix coordinates for the mobile station; and (v) determine corrected location fix coordinates (x(t f ),y(t f ),z(t f )) for the mobile station for at least one time t=t f using the relations x(t.sub.f)=x'(t.sub.f)+Δw.sub.1 (t.sub.f), y(t.sub.f)=y'(t.sub.f)+Δw.sub.2 (t.sub.f), z(t.sub.f)=z'(t.sub.f)+Δw.sub.3 (t.sub.f). 30.
Claim 38
Dependent Claim
201 words
The apparatus of claim 29, wherein said integer M≧4 and wherein said data processor is programmed to perform steps (ii) and (iii) by: augmenting said matrix H(t f ;mob) by adding M-3 columns of matrix entries to produce an augmented M×M matrix H*(t f ;mob), where three columns of the matrix H*(t f ;mob) are identical with three columns of said matrix H(t f ;mob) and each of the columns of H*(t f ;mob) forms an M×1 column matrix that is linearly independent of the other M-1 column matrices of the matrix H*(t f ;mob); forming an inverse matrix H*(t f ;mob) -1 , determining an M×1 matrix ΔW*(t f ;mob) by a matrix equation ΔW*(t f ;mob)=H*(t f ;mob) -1 PRC(t f ;ref), where PRC(t f ;ref) is an M×1 matrix whose entries are the values PRC(t f ;j;ref) for j=1, 2, . . . , M; and selecting three of the entries Δw 1 *(t f ), Δw 2 *(t f ) and Δw 3 *(t f ) of the matrix ΔW*(t f ;mob) and forming said 3×1 matrix ΔW(t f ;mob) with entries defined by Δw k (t f )=Δw k *(t f ), for k=1, 2, 3.
Claim 39
Dependent Claim
49 words
The apparatus of claim 29, wherein said said data processor is programmed to perform step (ii) by: forming a 3×3 matrix (H(t f ;mob) tr H(t f ;mob)) -1 ; and defining said 3×M matrix H(t f ;mob).sup.Λ by the relation H(t.sub.f ;mob).sup.Λ =(H(t.sub.f ;mob).sup.tr H(t.sub.f ;mob)).sup.-1 H(t.sub.f ;mob).sup.tr.
Claim 40
Dependent Claim
26 words
The apparatus of claim 29, wherein said integer M=3 and said data processor performs step (ii) by setting H(t f ;mob).sup.Λ =H(t f ;mob) -1 .
Claim 41
Dependent Claim
334 words
Apparatus for determining spatial location coordinates with enhanced accuracy for a mobile user Satellite Positioning System (SATPS) station, the apparatus comprising: a data processor that receives (1) uncorrected location fix coordinates (x'(t f ),y'(t f ),z'(t f )) for a selected location fix time t=t f for an SATPS mobile station that has an SATPS signal antenna and associated SATPS signal receiver/processor for receiving and processing SATPS signals from each of a plurality of M SATPS satellites, numbered j=1, 2, . . . , M (M≧3) to determine uncorrected three-dimensional spatial location coordinates (x'(t f ),y'(t f ),z'(t f )) for the mobile station, based upon SATPS signals received from the M SATPS satellites and (2) pseudorange correction values PRC(t f ;j;ref), determined for an SATPS reference station having a known location from SATPS signals received from each of the M SATPS satellites, wherein the data processor is programmed to: (i) compute an M×3 matrix H(t f ;mob) whose entries are defined by the relations H(t.sub.f ;mob)=(h.sub.ji (t.sub.f)), h.sub.j1 (t.sub.f)=α.sub.j1 (t.sub.f)=(x'(t.sub.f)-x.sub.j (t.sub.f))/r.sub.0j (t.sub.f), h.sub.j2 (t.sub.f)=α.sub.j2 (t.sub.f)=(y'(t.sub.f)-y.sub.j (t.sub.f))/r.sub.0j (t.sub.f), h.sub.j3 (t.sub.f)=α.sub.j3 (t.sub.f)=(z'(t.sub.f)-z.sub.j (t.sub.f))/r.sub.0j (t.sub.f) (j=1, 2, . . . , M), r.sub.0j (t.sub.f)= (x'(t.sub.f)-x.sub.j (t.sub.f)).sup.2 +(y'(t.sub.f)-y.sub.j (t.sub.f)).sup.2 +(z'(t.sub.f)-z.sub.j (t.sub.f)).sup.2 !.sup.1/2 ; (ii) form a 3×M matrix H(t f ;mob).sup.Λ that satisfies the relation H(t f ;mob).sup.Λ H(t f ;mob)=I, where I is the 4×4 identity matrix; (iii) form a matrix ΔW(t f ;mob)=H(t f ;mob).sup.Λ PRC(t f ;ref), where PRC(t f ;ref) is an M×1 matrix whose entries are the values PRC(t f ;j;ref) for j=1, 2, . . . , M; (iv) interpret two entries Δw 1 (t f ) and Δw 2 (t f ) of the matrix ΔW(t f ;mob) as corrections to the location fix coordinates x'(t f ) and y'(t f ) for the mobile station; and (v) determine corrected location fix coordinates (x(t f ),y(t f ),z(t f )) for the mobile station for at least one time t=t f using the relations x(t.sub.f)=x'(t.sub.f)+Δw.sub.1 (t.sub.f), y(t.sub.f)=y'(t.sub.f)+Δw.sub.2 (t.sub.f), z(t.sub.f)=z'(t.sub.f). 34.
Claim 42
Dependent Claim
334 words
Apparatus for determining spatial location coordinates with enhanced accuracy for a mobile user Satellite Positioning System (SATPS) station, the apparatus comprising: a data processor that receives (1) uncorrected location fix coordinates (x'(t f ),y'(t f ),z'(t f )) for a selected location fix time t=t f for an SATPS mobile station that has an SATPS signal antenna and associated SATPS signal receiver/processor for receiving and processing SATPS signals from each of a plurality of M SATPS satellites, numbered j=1, 2, . . . , M (M≧3) to determine uncorrected three-dimensional spatial location coordinates (x'(t f ),y'(t f ),z'(t f )) for the mobile station, based upon SATPS signals received from the M SATPS satellites and (2) pseudorange correction values PRC(t f ;j;ref), determined for an SATPS reference station having a known location from SATPS signals received from each of the M SATPS satellites, wherein the data processor is programmed to: (i) compute an M×3 matrix H(t f ;mob) whose entries are defined by the relations H(t.sub.f ;mob)=(h.sub.ji (t.sub.f)), h.sub.j1 (t.sub.f)=α.sub.j1 (t.sub.f)=(x'(t.sub.f)-x.sub.j (t.sub.f))/r.sub.0j (t.sub.f), h.sub.j2 (t.sub.f)=α.sub.j2 (t.sub.f)=(y'(t.sub.f)-y.sub.j (t.sub.f))/r.sub.0j (t.sub.f), h.sub.j3 (t.sub.f)=α.sub.j3 (t.sub.f)=(z'(t.sub.f)-z.sub.j (t.sub.f))/r.sub.0j (t.sub.f) (j=1, 2, . . . , M), r.sub.0j (t.sub.f)= (x'(t.sub.f)-x.sub.j (t.sub.f)).sup.2 +(y'(t.sub.f)-y.sub.j (t.sub.f)).sup.2 +(z'(t.sub.f)-z.sub.j (t.sub.f)).sup.2 !.sup.1/2 ; (ii) form a 3×M matrix H(t f ;mob).sup.Λ that satisfies the relation H(t f ;mob).sup.Λ H(t f ;mob)=I, where I is the 4×4 identity matrix; (iii) form a matrix ΔW(t f ;mob)=H(t f ;mob).sup.Λ PRC(t f ;ref), where PRC(t f ;ref) is an M×1 matrix whose entries are the values PRC(t f ;j;ref) for j=1, 2, . . . , M; (iv) interpret two entries Δw 1 (t f ) and Δw 2 (t f ) of the matrix ΔW(t f ;mob) as corrections to the location fix coordinates x'(t f ) and y'(t f ) for the mobile station; and (v) determine corrected location fix coordinates (x(t f ),y(t f ),z(t f )) for the mobile station for at least one time t=t f using the relations x(t.sub.f)=x'(t.sub.f)+Δw.sub.1 (t.sub.f), y(t.sub.f)=y'(t.sub.f)+Δw.sub.2 (t.sub.f), z(t.sub.f)=z'(t.sub.f). 34.
Claim 43
Dependent Claim
201 words
The apparatus of claim 33, wherein said integer M≧4 and wherein said data processor is programmed to perform steps (ii) and (iii) by: augmenting said matrix H(t f ;mob) by adding M-3 columns of matrix entries to produce an augmented M×M matrix H*(t f ;mob), where three columns of the matrix H*(t f ;mob) are identical with three columns of said matrix H(t f ;mob) and each of the columns of H*(t f ;mob) forms an M×1 column matrix that is linearly independent of the other M-1 column matrices of the matrix H*(t f ;mob); forming an inverse matrix H*(t f ;mob) -1 , determining an M×1 matrix ΔW*(t f ;mob) by a matrix equation ΔW*(t f ;mob)=H*(t f ;mob) -1 PRC(t f ;ref), where PRC(t f ;ref) is an M×1 matrix whose entries are the values PRC(t f ;j;ref) for j=1, 2, . . . , M; and selecting three of the entries Δw 1 *(t f ), Δw 2 *(t f ) and Δw 3 *(t f ) of the matrix ΔW*(t f ;mob) and forming said 3×1 matrix ΔW(t f ;mob) with entries defined by Δw k (t f )=Δw k *(t f ), for k=1, 2, 3.
Claim 44
Dependent Claim
49 words
The apparatus of claim 33, wherein said said data processor is programmed to perform step (ii) by: forming a 3×3 matrix (H(t f ;mob) tr H(t f ;mob)) -1 ; and defining said 4×M matrix H(t f ;mob).sup.Λ by the relation H(t.sub.f ;mob).sup.Λ =(H(t.sub.f ;mob).sup.tr H(t.sub.f ;mob)).sup.-1 H(t.sub.f ;mob).sup.tr.
Claim 45
Dependent Claim
26 words
The apparatus of claim 33, wherein said integer M=3 and said data processor performs step (ii) by setting H(t f ;mob).sup.Λ =H(t f ;mob) -1 .
Claim 46
Dependent Claim
471 words
Apparatus for determining spatial location and clock bias coordinates with enhanced accuracy for a mobile user Satellite Positioning System (SATPS) station, the apparatus comprising: a data processor that receives (1) uncorrected location fix coordinates (x'(t f ),y'(t f ),z'(t f ),b'(t f )) for a selected location fix time t=t f for an SATPS mobile station that has an SATPS signal antenna and associated SATPS signal receiver/processor for receiving and processing SATPS signals from each of a plurality of M SATPS satellites, numbered j=1, 2, . . . , M (M≧4) to determine uncorrected three-dimensional spatial location coordinates (x'(t f ),y'(t f ),z'(t f )) and uncorrected clock bias coordinate b'(t f ) for the mobile station, based upon SATPS signals received from the M SATPS satellites and (2) pseudorange correction values PRC(t f ;j;ref), determined for an SATPS reference station having a known location from SATPS signals received from each of the M SATPS satellites, wherein the data processor is programmed to: (i) compute an M×4 matrix H(t f ;mob) whose entries are defined by the relations H(t.sub.f ;mob)=(h.sub.ji (t.sub.f)), h.sub.j1 (t.sub.f)=α.sub.j1 (t.sub.f)=(x'(t.sub.f)-x.sub.j (t.sub.f))/r.sub.0j (t.sub.f), h.sub.j2 (t.sub.f)=α.sub.j2 (t.sub.f)=(y'(t.sub.f)-y.sub.j (t.sub.f))/r.sub.0j (t.sub.f), h.sub.j3 (t.sub.f)=α.sub.j3 (t.sub.f)=(z'(t.sub.f)-z.sub.j (t.sub.f))/r.sub.0j (t.sub.f), h.sub.j4 (t.sub.f)=1, (j=1, 2, . . . , M), r.sub.0j (t.sub.f)= (x'(t.sub.f)-x.sub.j (t.sub.f)).sup.2 +(y'(t.sub.f)-y.sub.j (t.sub.f)).sup.2 +(z'(t.sub.f)-z.sub.j (t.sub.f)).sup.2 !.sup.1/2 ; (ii) decompose the matrix H(t f ;mob) into a 4×4 matrix H f =(h ji ) f (j=j1, j2, j3, j4) and an (M-b 4)×4 matrix H nf =(h ji ) nf (j=j5, . . . , jM); (iii) form an M×1 matrix v= I-H(H tr H) -1 H tr !PR(t f ;mob) at the mobile station, where PR(t f ;mob) is an M×1 vector whose ordered entries are the uncorrected pseudorange values PR(t f ;j;mob); (iv) decompose the matrix v into a 4×1 matrix v f , consisting of the first four entries of the matrix v, and an (M-4)×1 matrix v nf , consisting of the other M-4 entries of the matrix v; (v) provide the M-4 entries of the matrix v nf and the mobile station location fix coordinates (x',y',z',b') for the supplemental data processor; (vi) form a matrix v f by the relation v f =-(H f tr ) -1 H nf tr v nf ; (vii) reconstruct the vector v= v f |v nf ! as a concatenation of the vectors v f and v nf ; (viii) reconstruct an M×1 matrix of uncorrected pseudorange values PR(t f ;mob) from the vector v; (ix) add the pseudorange corrections matrix PRC(t f ;j;ref) to the uncorrected pseudorange matrix PR(t f ;j;mob) to form a corrected pseudorange matrix PR(t f ;j;mob) cor ; and (x) determine corrected location fix coordinates (x(t f ),y(t f ),z(t f ),b(t f )) for the mobile station, using the corrected pseudorange matrix PR(t f ;j;mob) cor .
Claim 47
Dependent Claim
471 words
Apparatus for determining spatial location and clock bias coordinates with enhanced accuracy for a mobile user Satellite Positioning System (SATPS) station, the apparatus comprising: a data processor that receives (1) uncorrected location fix coordinates (x'(t f ),y'(t f ),z'(t f ),b'(t f )) for a selected location fix time t=t f for an SATPS mobile station that has an SATPS signal antenna and associated SATPS signal receiver/processor for receiving and processing SATPS signals from each of a plurality of M SATPS satellites, numbered j=1, 2, . . . , M (M≧4) to determine uncorrected three-dimensional spatial location coordinates (x'(t f ),y'(t f ),z'(t f )) and uncorrected clock bias coordinate b'(t f ) for the mobile station, based upon SATPS signals received from the M SATPS satellites and (2) pseudorange correction values PRC(t f ;j;ref), determined for an SATPS reference station having a known location from SATPS signals received from each of the M SATPS satellites, wherein the data processor is programmed to: (i) compute an M×4 matrix H(t f ;mob) whose entries are defined by the relations H(t.sub.f ;mob)=(h.sub.ji (t.sub.f)), h.sub.j1 (t.sub.f)=α.sub.j1 (t.sub.f)=(x'(t.sub.f)-x.sub.j (t.sub.f))/r.sub.0j (t.sub.f), h.sub.j2 (t.sub.f)=α.sub.j2 (t.sub.f)=(y'(t.sub.f)-y.sub.j (t.sub.f))/r.sub.0j (t.sub.f), h.sub.j3 (t.sub.f)=α.sub.j3 (t.sub.f)=(z'(t.sub.f)-z.sub.j (t.sub.f))/r.sub.0j (t.sub.f), h.sub.j4 (t.sub.f)=1, (j=1, 2, . . . , M), r.sub.0j (t.sub.f)= (x'(t.sub.f)-x.sub.j (t.sub.f)).sup.2 +(y'(t.sub.f)-y.sub.j (t.sub.f)).sup.2 +(z'(t.sub.f)-z.sub.j (t.sub.f)).sup.2 !.sup.1/2 ; (ii) decompose the matrix H(t f ;mob) into a 4×4 matrix H f =(h ji ) f (j=j1, j2, j3, j4) and an (M-b 4)×4 matrix H nf =(h ji ) nf (j=j5, . . . , jM); (iii) form an M×1 matrix v= I-H(H tr H) -1 H tr !PR(t f ;mob) at the mobile station, where PR(t f ;mob) is an M×1 vector whose ordered entries are the uncorrected pseudorange values PR(t f ;j;mob); (iv) decompose the matrix v into a 4×1 matrix v f , consisting of the first four entries of the matrix v, and an (M-4)×1 matrix v nf , consisting of the other M-4 entries of the matrix v; (v) provide the M-4 entries of the matrix v nf and the mobile station location fix coordinates (x',y',z',b') for the supplemental data processor; (vi) form a matrix v f by the relation v f =-(H f tr ) -1 H nf tr v nf ; (vii) reconstruct the vector v= v f |v nf ! as a concatenation of the vectors v f and v nf ; (viii) reconstruct an M×1 matrix of uncorrected pseudorange values PR(t f ;mob) from the vector v; (ix) add the pseudorange corrections matrix PRC(t f ;j;ref) to the uncorrected pseudorange matrix PR(t f ;j;mob) to form a corrected pseudorange matrix PR(t f ;j;mob) cor ; and (x) determine corrected location fix coordinates (x(t f ),y(t f ),z(t f ),b(t f )) for the mobile station, using the corrected pseudorange matrix PR(t f ;j;mob) cor .
Claim 48
Dependent Claim
456 words
Apparatus for determining spatial location and clock bias coordinates with enhanced accuracy for a mobile user Satellite Positioning System (SATPS) station, the apparatus comprising: a data processor that receives (1) uncorrected location fix coordinates (x'(t f ),y'(t f ),z'(t f )) for a selected location fix time t=t f for an SATPS mobile station that has an SATPS signal antenna and associated SATPS signal receiver/processor for receiving and processing SATPS signals from each of a plurality of M SATPS satellites, numbered j=1, 2, . . . , M (M≧3) to determine uncorrected three-dimensional spatial location coordinates (x'(t f ),y'(t f ),z'(t f )) for the mobile station, based upon SATPS signals received from the M SATPS satellites and (2) pseudorange correction values PRC(t f ;j;ref), determined for an SATPS reference station having a known location from SATPS signals received from each of the M SATPS satellites, wherein the data processor is programmed to: (i) compute an M×3 matrix H(t f ;mob) whose entries are defined by the relations H(t.sub.f ;mob)-(h.sub.ji (t.sub.f)), h.sub.j1 (t.sub.f)=α.sub.j1 (t.sub.f)=(x'(t.sub.f)-x.sub.j (t.sub.f))/r.sub.0j (t.sub.f), h.sub.j2 (t.sub.f)=α.sub.j2 (t.sub.f)=(y'(t.sub.f)-y.sub.j (t.sub.f))/r.sub.0j (t.sub.f), h.sub.j3 (t.sub.f)=α.sub.j3 (t.sub.f)=(z'(t.sub.f)-z.sub.j (t.sub.f))/r.sub.0j (t.sub.f), (j=1, 2, . . . , M), r.sub.0j (t.sub.f)= (x'(t.sub.f)-x.sub.j (t.sub.f)).sup.2 +(y'(t.sub.f)-y.sub.j (t.sub.f)).sup.2 +(z'(t.sub.f)-z.sub.j (t.sub.f)).sup.2 !.sup.1/2 ; (ii) decompose the matrix H(t f ;mob) into a 3×3 matrix H f =(h ji ) f (j=j1, j2, j3) and an (M-3)×3 matrix H nf =(h ji ) nf (j=j4, . . . , jM); (iii) form an M×1 matrix v= I -H(H tr H) -1 H tr !PR(t f ;mob) at the mobile station, where PR(t f ;mob) is an M×1 vector whose ordered entries are the uncorrected pseudorange values PR(t f ;j;mob); (iv) decompose the matrix v into a 3×1 matrix v f , consisting of the first four entries of the matrix v, and an (M-3)×1 matrix v nf , consisting of the other M-3 entries of the matrix v; (v) provide the M-4 entries of the matrix v nf and the mobile station location fix coordinates (x',y',b') for the supplemental data processor; (vi) form a matrix v f by the relation v f =-(H f tr ) -1 H nf tr v nf ; (vii) reconstruct the vector v= v f |v nf ! as a concatenation of the vectors v f and v nf ; (viii) reconstruct an M×1 matrix of uncorrected pseudorange values PR(t f ;mob) from the vector v; (ix) add the pseudorange corrections matrix PRC(t f ;j;ref) to the uncorrected pseudorange matrix PR(t f ;j;mob) to form a corrected pseudorange matrix PR(t f ;j;mob) cor ; and (x) determine corrected location fix coordinates (x(t f ),y(t f ),z(t f )) for the mobile station, using the corrected pseudorange matrix PR(t f ;j;mob) cor .
Claim 49
Dependent Claim
456 words
Apparatus for determining spatial location and clock bias coordinates with enhanced accuracy for a mobile user Satellite Positioning System (SATPS) station, the apparatus comprising: a data processor that receives (1) uncorrected location fix coordinates (x'(t f ),y'(t f ),z'(t f )) for a selected location fix time t=t f for an SATPS mobile station that has an SATPS signal antenna and associated SATPS signal receiver/processor for receiving and processing SATPS signals from each of a plurality of M SATPS satellites, numbered j=1, 2, . . . , M (M≧3) to determine uncorrected three-dimensional spatial location coordinates (x'(t f ),y'(t f ),z'(t f )) for the mobile station, based upon SATPS signals received from the M SATPS satellites and (2) pseudorange correction values PRC(t f ;j;ref), determined for an SATPS reference station having a known location from SATPS signals received from each of the M SATPS satellites, wherein the data processor is programmed to: (i) compute an M×3 matrix H(t f ;mob) whose entries are defined by the relations H(t.sub.f ;mob)-(h.sub.ji (t.sub.f)), h.sub.j1 (t.sub.f)=α.sub.j1 (t.sub.f)=(x'(t.sub.f)-x.sub.j (t.sub.f))/r.sub.0j (t.sub.f), h.sub.j2 (t.sub.f)=α.sub.j2 (t.sub.f)=(y'(t.sub.f)-y.sub.j (t.sub.f))/r.sub.0j (t.sub.f), h.sub.j3 (t.sub.f)=α.sub.j3 (t.sub.f)=(z'(t.sub.f)-z.sub.j (t.sub.f))/r.sub.0j (t.sub.f), (j=1, 2, . . . , M), r.sub.0j (t.sub.f)= (x'(t.sub.f)-x.sub.j (t.sub.f)).sup.2 +(y'(t.sub.f)-y.sub.j (t.sub.f)).sup.2 +(z'(t.sub.f)-z.sub.j (t.sub.f)).sup.2 !.sup.1/2 ; (ii) decompose the matrix H(t f ;mob) into a 3×3 matrix H f =(h ji ) f (j=j1, j2, j3) and an (M-3)×3 matrix H nf =(h ji ) nf (j=j4, . . . , jM); (iii) form an M×1 matrix v= I -H(H tr H) -1 H tr !PR(t f ;mob) at the mobile station, where PR(t f ;mob) is an M×1 vector whose ordered entries are the uncorrected pseudorange values PR(t f ;j;mob); (iv) decompose the matrix v into a 3×1 matrix v f , consisting of the first four entries of the matrix v, and an (M-3)×1 matrix v nf , consisting of the other M-3 entries of the matrix v; (v) provide the M-4 entries of the matrix v nf and the mobile station location fix coordinates (x',y',b') for the supplemental data processor; (vi) form a matrix v f by the relation v f =-(H f tr ) -1 H nf tr v nf ; (vii) reconstruct the vector v= v f |v nf ! as a concatenation of the vectors v f and v nf ; (viii) reconstruct an M×1 matrix of uncorrected pseudorange values PR(t f ;mob) from the vector v; (ix) add the pseudorange corrections matrix PRC(t f ;j;ref) to the uncorrected pseudorange matrix PR(t f ;j;mob) to form a corrected pseudorange matrix PR(t f ;j;mob) cor ; and (x) determine corrected location fix coordinates (x(t f ),y(t f ),z(t f )) for the mobile station, using the corrected pseudorange matrix PR(t f ;j;mob) cor .
Claim 50
Dependent Claim
471 words
Apparatus for determining spatial location coordinates with enhanced accuracy for a mobile user Satellite Positioning System (SATPS) station, the apparatus comprising: a data processor that receives (1) uncorrected location fix coordinates (x'(t f ),y'(t f ),z'(t f )) for a selected location fix time t=t f for an SATPS mobile station that has an SATPS signal antenna and associated SATPS signal receiver/processor for receiving and processing SATPS signals from each of a plurality of M SATPS satellites, numbered j=1, 2, . . . , M (M≧3) to determine uncorrected three-dimensional spatial location coordinates (x'(t f ),y'(t f ),z'(t f )) for the mobile station, based upon SATPS signals received from the M SATPS satellites and (2) pseudorange correction values PRC(t f ;j;ref), determined for an SATPS reference station having a known location from SATPS signals received from each of the M SATPS satellites, wherein the data processor is programmed to: (i) compute an M×3 matrix H(t f ;mob) whose entries are defined by the relations H(t.sub.f ;mob)=(h.sub.ji (t.sub.f)), h.sub.j1 (t.sub.f)=α.sub.j1 (t.sub.f)=(x'(t.sub.f)-x.sub.j (t.sub.f))/r.sub.0j (t.sub.f), h.sub.j2 (t.sub.f)=α.sub.j2 (t.sub.f)=(y'(t.sub.f)-y.sub.j (t.sub.f))/r.sub.0j (t.sub.f), h.sub.j3 (t.sub.f)=α.sub.j3 (t.sub.f)=(z'(t.sub.f)-z.sub.j (t.sub.f))/r.sub.0j (t.sub.f), (j=1, 2, . . . , M), r.sub.0j (t.sub.f)= (x'(t.sub.f)-x.sub.j (t.sub.f)).sup.2 +(y'(t.sub.f)-y.sub.j (t.sub.f)).sup.2 +(z'(t.sub.f)-z.sub.j (t.sub.f)).sup.2 !.sup.1/2 ; (ii) decompose the matrix H(t f ;mob) into a 3×3 matrix H f= (h ji ) f (j=j1, j2, j3) and an (M-3)×3 matrix H nf =(h ji ) nf (j=j4, . . . , jM); (iii) form an M×1 matrix v= I-H(H tr H) -1 H tr !PR(t f ;mob) at the mobile station, where PR(t f ;mob) is an M×1 vector whose ordered entries are the uncorrected pseudorange values PR(t f ;j;mob); (iv) decompose the matrix v into a 3×1 matrix v f , consisting of the first four entries of the matrix v, and an (M-3)×1 matrix v nf , consisting of the other M-3 entries of the matrix v; (v) provide the M-4 entries of the matrix v nf and the mobile station location fix coordinates (x',y',z') for the supplemental data processor; (vi) form a matrix v f by the relation v f =-(H f tr ) -1 H nf tr v nf ; (vii) reconstruct the vector v= v f |v nf ! as a concatenation of the vectors v f and v nf ; (viii) reconstruct an M×1 matrix of uncorrected pseudorange values PR(t f ;mob) from the vector v; (ix) add the pseudorange corrections matrix PRC(t f ;j;ref) to the uncorrected pseudorange matrix PR(t f ;j;mob) to form a corrected pseudorange matrix PR(t f ;j;mob) cor ; and (x) determine corrected location fix coordinates (x(t f ),y(t f ),z(t f )) for the mobile station, using the corrected pseudorange matrix PR(t f ;j;mob) cor for the coordinates x(t f ) and y(t f ), and define the corrected coordinate z(t f )=z'(t f ).
Claim 51
Dependent Claim
471 words
Apparatus for determining spatial location coordinates with enhanced accuracy for a mobile user Satellite Positioning System (SATPS) station, the apparatus comprising: a data processor that receives (1) uncorrected location fix coordinates (x'(t f ),y'(t f ),z'(t f )) for a selected location fix time t=t f for an SATPS mobile station that has an SATPS signal antenna and associated SATPS signal receiver/processor for receiving and processing SATPS signals from each of a plurality of M SATPS satellites, numbered j=1, 2, . . . , M (M≧3) to determine uncorrected three-dimensional spatial location coordinates (x'(t f ),y'(t f ),z'(t f )) for the mobile station, based upon SATPS signals received from the M SATPS satellites and (2) pseudorange correction values PRC(t f ;j;ref), determined for an SATPS reference station having a known location from SATPS signals received from each of the M SATPS satellites, wherein the data processor is programmed to: (i) compute an M×3 matrix H(t f ;mob) whose entries are defined by the relations H(t.sub.f ;mob)=(h.sub.ji (t.sub.f)), h.sub.j1 (t.sub.f)=α.sub.j1 (t.sub.f)=(x'(t.sub.f)-x.sub.j (t.sub.f))/r.sub.0j (t.sub.f), h.sub.j2 (t.sub.f)=α.sub.j2 (t.sub.f)=(y'(t.sub.f)-y.sub.j (t.sub.f))/r.sub.0j (t.sub.f), h.sub.j3 (t.sub.f)=α.sub.j3 (t.sub.f)=(z'(t.sub.f)-z.sub.j (t.sub.f))/r.sub.0j (t.sub.f), (j=1, 2, . . . , M), r.sub.0j (t.sub.f)= (x'(t.sub.f)-x.sub.j (t.sub.f)).sup.2 +(y'(t.sub.f)-y.sub.j (t.sub.f)).sup.2 +(z'(t.sub.f)-z.sub.j (t.sub.f)).sup.2 !.sup.1/2 ; (ii) decompose the matrix H(t f ;mob) into a 3×3 matrix H f= (h ji ) f (j=j1, j2, j3) and an (M-3)×3 matrix H nf =(h ji ) nf (j=j4, . . . , jM); (iii) form an M×1 matrix v= I-H(H tr H) -1 H tr !PR(t f ;mob) at the mobile station, where PR(t f ;mob) is an M×1 vector whose ordered entries are the uncorrected pseudorange values PR(t f ;j;mob); (iv) decompose the matrix v into a 3×1 matrix v f , consisting of the first four entries of the matrix v, and an (M-3)×1 matrix v nf , consisting of the other M-3 entries of the matrix v; (v) provide the M-4 entries of the matrix v nf and the mobile station location fix coordinates (x',y',z') for the supplemental data processor; (vi) form a matrix v f by the relation v f =-(H f tr ) -1 H nf tr v nf ; (vii) reconstruct the vector v= v f |v nf ! as a concatenation of the vectors v f and v nf ; (viii) reconstruct an M×1 matrix of uncorrected pseudorange values PR(t f ;mob) from the vector v; (ix) add the pseudorange corrections matrix PRC(t f ;j;ref) to the uncorrected pseudorange matrix PR(t f ;j;mob) to form a corrected pseudorange matrix PR(t f ;j;mob) cor ; and (x) determine corrected location fix coordinates (x(t f ),y(t f ),z(t f )) for the mobile station, using the corrected pseudorange matrix PR(t f ;j;mob) cor for the coordinates x(t f ) and y(t f ), and define the corrected coordinate z(t f )=z'(t f ).
Claim 52
Independent Claim
654 words
A method for determining spatial location and clock bias coordinates with enhanced accuracy for a mobile user Satellite Positioning System (SATPS) station, the method comprising the steps of: providing pseudorange corrections PRC(t f ;j;ref) for uncorrected pseudorange values PR(t f ;j;ref), measured at an SATPS reference station that has location coordinates that are known with high accuracy and that receives SATPS signals at a selected location fix time t=t f from each of M SATPS satellites, numbered j=1, 2, . . . , M (M≧4), where the sums PR(t f ;j;ref)+PRC(t f ;j;ref) for j=1, 2, . . . , M provide corrected reference station pseudorange values PR(t f ;j;ref) cor that agree with known pseudorange values for the reference station for the M SATPS satellites for the location fix time t f ; providing an SATPS mobile station that has an SATPS signal antenna and associated SATPS signal receiver/processor, and causing the mobile station to receive and process SATPS signals from each of the M SATPS satellites and to determine uncorrected location fix coordinates, including uncorrected three-dimensional spatial location coordinates (x'(t f ),y'(t f ),z'(t f )) and uncorrected clock bias coordinate b'(t f ), for the mobile station for the location fix time t f ; providing a supplemental data processor with the location fix time t f , with the mobile station uncorrected location fix coordinates (x'(t f ), y'(t f ), z'(t f ), b'(t f )), with spatial coordinate values (x j (t f ), y j (t f ), z j (t f )) of SATPS satellite number j for a time corresponding to the location fix time t f , and with the reference station pseudorange corrections PRC(t f ;j;ref) for j=1, 2, . . . M; computing at the supplemental data processor an M×4 matrix H(t f ;mob) that approximately expresses each of M pseudorange correction values PRC(t f ;j;mob) that would be computed at the mobile station as a linear combination of location fix coordinate differences (x'(t f )-x j (t f ))/r 0j (t f ), (y'(t f )-y j (t f ))/r 0j (t f ), (z'(t f )-z j (t f ))/r 0j (t f ), and b'(t f )-0, where the quantity r 0j (t f ) is the distance at the location fix time t f from a location given by the uncorrected spatial location coordinates (x'(t f ),y'(t f ),z'(t f )) for the mobile station to the location of SATPS satellite number j (j=1, 2, . . . , M); identifying the M pseudorange correction values PRC(t f ;j;mob) that would be computed at the mobile station with the respective M pseudorange correction values PRC(t f ;j;ref) computed for the reference station; forming an M×1 matrix PRC(t f ;ref) whose entries are the values PRC(t f ;j;ref) for j=1, 2, . . . , M; forming a 4×M matrix H(t f ;mob).sup.Λ that satisfies the relation H(t f ;mob).sup.Λ H(t f ;mob)=I, where I is the 4×4 identity matrix; forming a 4×1 matrix ΔW(t f ;mob) whose entries are given by the product H(t f ;mob).sup.Λ PRC(t f ;ref) of the matrices H(t f ;mob).sup.Λ and PRC(t f ;ref); interpreting four entries Δw 1 (t f ), Δw 2 (t f ), Δw 3 (t f ), and Δw 4 (t f ) of the matrix ΔW(t f ;mob) as corrections to the location fix coordinates for the mobile station; and adding the location fix coordinate corrections Δw 1 (t f ), Δw 2 (t f ), Δw 3 (t f ), and Δw 4 (t f ) to the respective location fix coordinates x'(t f ), y'(t f ), z'(t f ) and b'(t f ) to produce corrected location fix coordinates x(t f ), y(t f ), z(t f ) and b(t f )) for the mobile station for the location fix time t=t f .
Claim 53
Independent Claim
654 words
A method for determining spatial location and clock bias coordinates with enhanced accuracy for a mobile user Satellite Positioning System (SATPS) station, the method comprising the steps of: providing pseudorange corrections PRC(t f ;j;ref) for uncorrected pseudorange values PR(t f ;j;ref), measured at an SATPS reference station that has location coordinates that are known with high accuracy and that receives SATPS signals at a selected location fix time t=t f from each of M SATPS satellites, numbered j=1, 2, . . . , M (M≧4), where the sums PR(t f ;j;ref)+PRC(t f ;j;ref) for j=1, 2, . . . , M provide corrected reference station pseudorange values PR(t f ;j;ref) cor that agree with known pseudorange values for the reference station for the M SATPS satellites for the location fix time t f ; providing an SATPS mobile station that has an SATPS signal antenna and associated SATPS signal receiver/processor, and causing the mobile station to receive and process SATPS signals from each of the M SATPS satellites and to determine uncorrected location fix coordinates, including uncorrected three-dimensional spatial location coordinates (x'(t f ),y'(t f ),z'(t f )) and uncorrected clock bias coordinate b'(t f ), for the mobile station for the location fix time t f ; providing a supplemental data processor with the location fix time t f , with the mobile station uncorrected location fix coordinates (x'(t f ), y'(t f ), z'(t f ), b'(t f )), with spatial coordinate values (x j (t f ), y j (t f ), z j (t f )) of SATPS satellite number j for a time corresponding to the location fix time t f , and with the reference station pseudorange corrections PRC(t f ;j;ref) for j=1, 2, . . . M; computing at the supplemental data processor an M×4 matrix H(t f ;mob) that approximately expresses each of M pseudorange correction values PRC(t f ;j;mob) that would be computed at the mobile station as a linear combination of location fix coordinate differences (x'(t f )-x j (t f ))/r 0j (t f ), (y'(t f )-y j (t f ))/r 0j (t f ), (z'(t f )-z j (t f ))/r 0j (t f ), and b'(t f )-0, where the quantity r 0j (t f ) is the distance at the location fix time t f from a location given by the uncorrected spatial location coordinates (x'(t f ),y'(t f ),z'(t f )) for the mobile station to the location of SATPS satellite number j (j=1, 2, . . . , M); identifying the M pseudorange correction values PRC(t f ;j;mob) that would be computed at the mobile station with the respective M pseudorange correction values PRC(t f ;j;ref) computed for the reference station; forming an M×1 matrix PRC(t f ;ref) whose entries are the values PRC(t f ;j;ref) for j=1, 2, . . . , M; forming a 4×M matrix H(t f ;mob).sup.Λ that satisfies the relation H(t f ;mob).sup.Λ H(t f ;mob)=I, where I is the 4×4 identity matrix; forming a 4×1 matrix ΔW(t f ;mob) whose entries are given by the product H(t f ;mob).sup.Λ PRC(t f ;ref) of the matrices H(t f ;mob).sup.Λ and PRC(t f ;ref); interpreting four entries Δw 1 (t f ), Δw 2 (t f ), Δw 3 (t f ), and Δw 4 (t f ) of the matrix ΔW(t f ;mob) as corrections to the location fix coordinates for the mobile station; and adding the location fix coordinate corrections Δw 1 (t f ), Δw 2 (t f ), Δw 3 (t f ), and Δw 4 (t f ) to the respective location fix coordinates x'(t f ), y'(t f ), z'(t f ) and b'(t f ) to produce corrected location fix coordinates x(t f ), y(t f ), z(t f ) and b(t f )) for the mobile station for the location fix time t=t f .
Claim 54
Independent Claim
625 words
A method for determining spatial location and clock bias coordinates with enhanced accuracy for a mobile user Satellite Positioning System (SATPS) station, the method comprising the steps of: providing pseudorange corrections PRC(t f ;j;ref) for uncorrected pseudorange values PR(t f ;j;ref), measured at an SATPS reference station that has location coordinates that are known with high accuracy and that receives SATPS signals at a selected location fix time t=t f from each of M SATPS satellites, numbered j=1, 2, . . . , M (M≧3), where the sums PR(t f ;j;ref)+PRC(t f ;j;ref) for j=1, 2, . . . , M provide corrected reference station pseudorange values PR(t f ;j;ref) cor that agree with known pseudorange values for the reference station for the M SATPS satellites for the location fix time t f ; providing an SATPS mobile station that has an SATPS signal antenna and associated SATPS signal receiver/processor, and causing the mobile station to receive and process SATPS signals from each of the M SATPS satellites and to determine uncorrected location fix coordinates, including uncorrected three-dimensional spatial location coordinates (x'(t f ),y'(t f ),z'(t f )), for the mobile station for the location fix time t f ; providing a supplemental data processor with the location fix time t f , with the mobile station uncorrected location fix coordinates (x'(t f ), y'(t f ), z'(t f )), with spatial coordinate values (x j (t f ), y j (t f ), z j (t f )) of SATPS satellite number j for a time corresponding to the location fix time t f , and with the reference station pseudorange corrections PRC(t f ;j;ref) for j=1, 2, . . . , M; computing at the supplemental data processor an M×3 matrix H(t f ;mob) that approximately expresses each of M pseudorange correction values PRC(t f ;j;mob) that would be computed at the mobile station as a linear combination of location fix coordinate differences (x'(t f )-x j (t f ))/r 0j (t f ), (y'(t f )-y j (t f ))/r 0j (t f ) and (z'(t f )-z j (t f ))/r 0j (t f ), where the quantity r 0j (t f ) is the distance at the location fix time t f from a location given by the uncorrected spatial location coordinates (x'(t f ),y'(t f ),z'(t f )) for the mobile station to the location of SATPS satellite number j (j=1, 2, . . . , M); identifying the M pseudorange correction values PRC(t f ;j;mob) that would be computed at the mobile station with the respective M pseudorange correction values PRC(t f ;j;ref) computed for the reference station; forming an M×1 matrix PRC(t f ;ref) whose entries are the values PRC(t f ;j;ref) for j=1, 2, . . . , M; forming a 3×M matrix H(t f ;mob).sup.Λ that satisfies the relation H(t f ;mob).sup.Λ H(t f ;mob)=I, where I is the 3×3 identity matrix; forming a 3×1 matrix ΔW(t f ;mob) whose entries are given by the product H(t f ;mob).sup.Λ PRC(t f ;ref) of the matrices H(t f ;mob).sup.Λ and PRC(t f ;ref); interpreting three entries Δw 1 (t f ), Δw 2 (t f ) and Δw 3 (t f ) of the matrix ΔW(t f ;mob) as corrections to the location fix coordinates for the mobile station; and adding the location fix coordinate corrections Δw 1 (t f ), Δw 2 (t f ) and Δw 3 (t f ) to the respective location fix coordinates x'(t f ), y'(t f ) and z'(t f ) to produce corrected location fix coordinates x(t f ), y(t f ) and z(t f ) for the mobile station for the location fix time t=t f .
Claim 55
Independent Claim
625 words
A method for determining spatial location and clock bias coordinates with enhanced accuracy for a mobile user Satellite Positioning System (SATPS) station, the method comprising the steps of: providing pseudorange corrections PRC(t f ;j;ref) for uncorrected pseudorange values PR(t f ;j;ref), measured at an SATPS reference station that has location coordinates that are known with high accuracy and that receives SATPS signals at a selected location fix time t=t f from each of M SATPS satellites, numbered j=1, 2, . . . , M (M≧3), where the sums PR(t f ;j;ref)+PRC(t f ;j;ref) for j=1, 2, . . . , M provide corrected reference station pseudorange values PR(t f ;j;ref) cor that agree with known pseudorange values for the reference station for the M SATPS satellites for the location fix time t f ; providing an SATPS mobile station that has an SATPS signal antenna and associated SATPS signal receiver/processor, and causing the mobile station to receive and process SATPS signals from each of the M SATPS satellites and to determine uncorrected location fix coordinates, including uncorrected three-dimensional spatial location coordinates (x'(t f ),y'(t f ),z'(t f )), for the mobile station for the location fix time t f ; providing a supplemental data processor with the location fix time t f , with the mobile station uncorrected location fix coordinates (x'(t f ), y'(t f ), z'(t f )), with spatial coordinate values (x j (t f ), y j (t f ), z j (t f )) of SATPS satellite number j for a time corresponding to the location fix time t f , and with the reference station pseudorange corrections PRC(t f ;j;ref) for j=1, 2, . . . , M; computing at the supplemental data processor an M×3 matrix H(t f ;mob) that approximately expresses each of M pseudorange correction values PRC(t f ;j;mob) that would be computed at the mobile station as a linear combination of location fix coordinate differences (x'(t f )-x j (t f ))/r 0j (t f ), (y'(t f )-y j (t f ))/r 0j (t f ) and (z'(t f )-z j (t f ))/r 0j (t f ), where the quantity r 0j (t f ) is the distance at the location fix time t f from a location given by the uncorrected spatial location coordinates (x'(t f ),y'(t f ),z'(t f )) for the mobile station to the location of SATPS satellite number j (j=1, 2, . . . , M); identifying the M pseudorange correction values PRC(t f ;j;mob) that would be computed at the mobile station with the respective M pseudorange correction values PRC(t f ;j;ref) computed for the reference station; forming an M×1 matrix PRC(t f ;ref) whose entries are the values PRC(t f ;j;ref) for j=1, 2, . . . , M; forming a 3×M matrix H(t f ;mob).sup.Λ that satisfies the relation H(t f ;mob).sup.Λ H(t f ;mob)=I, where I is the 3×3 identity matrix; forming a 3×1 matrix ΔW(t f ;mob) whose entries are given by the product H(t f ;mob).sup.Λ PRC(t f ;ref) of the matrices H(t f ;mob).sup.Λ and PRC(t f ;ref); interpreting three entries Δw 1 (t f ), Δw 2 (t f ) and Δw 3 (t f ) of the matrix ΔW(t f ;mob) as corrections to the location fix coordinates for the mobile station; and adding the location fix coordinate corrections Δw 1 (t f ), Δw 2 (t f ) and Δw 3 (t f ) to the respective location fix coordinates x'(t f ), y'(t f ) and z'(t f ) to produce corrected location fix coordinates x(t f ), y(t f ) and z(t f ) for the mobile station for the location fix time t=t f .
Claim 56
Independent Claim
637 words
A method for determining spatial location and clock bias coordinates with enhanced accuracy for a mobile user Satellite Positioning System (SATPS) station, the method comprising the steps of: providing pseudorange corrections PRC(t f ;j;ref) for uncorrected pseudorange values PR(t f ;j;ref), measured at an SATPS reference station that has location coordinates that are known with high accuracy and that receives SATPS signals at a selected location fix time t=t f from each of M SATPS satellites, numbered j=1, 2, . . . , M (M≧3), where the sums PR(t f ;j;ref)+PRC(t f ;j;ref) for j=1, 2, . . . , M provide corrected reference station pseudorange values PR(t f ;j;ref) cor that agree with known pseudorange values for the reference station for the M SATPS satellites for the location fix time t f ; providing an SATPS mobile station that has an SATPS signal antenna and associated SATPS signal receiver/processor, and causing the mobile station to receive and process SATPS signals from each of the M SATPS satellites and to determine uncorrected location fix coordinates, including uncorrected three-dimensional spatial location coordinates (x'(t f ),y'(t f ),z'(t f )), for the mobile station for the location fix time t f ; providing a supplemental data processor with the location fix time t f , with the mobile station uncorrected location fix coordinates (x'(t f ), y'(t f ), z'(t f )), with spatial coordinate values (x j (t f ), y j (t f ), z j (t f )) of SATPS satellite number j for a time corresponding to the location fix time t f , and with the reference station pseudorange corrections PRC(t f ;j;ref) for j=1, 2, . . . , M; computing at the supplemental data processor an M×3 matrix H(t f ;mob) that approximately expresses each of M pseudorange correction values PRC(t f ;j;mob) that would be computed at the mobile station as a linear combination of location fix coordinate differences (x'(t f )-x j (t f ))/r 0j (t f ), (y'(t f )-y j (t f ))/r 0j (t f ) and (z'(t f )-z j (t f ))/r 0j (t f ), where the quantity r 0j (t f ) is the distance at the location fix time t f from a location given by the uncorrected spatial location coordinates (x'(t f ),y'(t f ),z'(t f )) for the mobile station to the location of SATPS satellite number j (j=1, 2, . . . , M); identifying the M pseudorange correction values PRC(t f ;j;mob) that would be computed at the mobile station with the respective M pseudorange correction values PRC(t f ;j;ref) computed for the reference station; forming an M×1 matrix PRC(t f ;ref) whose entries are the values PRC(t f ;j;ref) for j=1, 2, . . . , M; forming a 3×M matrix H(t f ;mob).sup.Λ that satisfies the relation H(t f ;mob).sup.Λ H(t f ;mob)=I, where I is the 3×3 identity matrix; forming a 3×1 matrix ΔW(t f ;mob) whose entries are given by the product H(t f ;mob).sup.Λ PRC(t f ;ref) of the matrices H(t f ;mob).sup.Λ and PRC(t f ;ref); interpreting four entries Δw 1 (t f ), Δw 2 (t f ) and Δw 3 (t f ) of the matrix ΔW(t f ;mob) as corrections to the location fix coordinates for the mobile station; and adding the location fix coordinate corrections Δw 1 (t f ) and Δw 2 (t f ) to the respective location fix coordinates x'(t f ) and y'(t f ) to produce corrected location fix coordinates x(t f ) and y(t f ) and defining z(t f )=z'(t f ) for the corrected location fix coordinates x'(t f ), y'(t f ) and z'(t f ) for the mobile station for the location fix time t=t f .
Claim 57
Independent Claim
637 words
A method for determining spatial location and clock bias coordinates with enhanced accuracy for a mobile user Satellite Positioning System (SATPS) station, the method comprising the steps of: providing pseudorange corrections PRC(t f ;j;ref) for uncorrected pseudorange values PR(t f ;j;ref), measured at an SATPS reference station that has location coordinates that are known with high accuracy and that receives SATPS signals at a selected location fix time t=t f from each of M SATPS satellites, numbered j=1, 2, . . . , M (M≧3), where the sums PR(t f ;j;ref)+PRC(t f ;j;ref) for j=1, 2, . . . , M provide corrected reference station pseudorange values PR(t f ;j;ref) cor that agree with known pseudorange values for the reference station for the M SATPS satellites for the location fix time t f ; providing an SATPS mobile station that has an SATPS signal antenna and associated SATPS signal receiver/processor, and causing the mobile station to receive and process SATPS signals from each of the M SATPS satellites and to determine uncorrected location fix coordinates, including uncorrected three-dimensional spatial location coordinates (x'(t f ),y'(t f ),z'(t f )), for the mobile station for the location fix time t f ; providing a supplemental data processor with the location fix time t f , with the mobile station uncorrected location fix coordinates (x'(t f ), y'(t f ), z'(t f )), with spatial coordinate values (x j (t f ), y j (t f ), z j (t f )) of SATPS satellite number j for a time corresponding to the location fix time t f , and with the reference station pseudorange corrections PRC(t f ;j;ref) for j=1, 2, . . . , M; computing at the supplemental data processor an M×3 matrix H(t f ;mob) that approximately expresses each of M pseudorange correction values PRC(t f ;j;mob) that would be computed at the mobile station as a linear combination of location fix coordinate differences (x'(t f )-x j (t f ))/r 0j (t f ), (y'(t f )-y j (t f ))/r 0j (t f ) and (z'(t f )-z j (t f ))/r 0j (t f ), where the quantity r 0j (t f ) is the distance at the location fix time t f from a location given by the uncorrected spatial location coordinates (x'(t f ),y'(t f ),z'(t f )) for the mobile station to the location of SATPS satellite number j (j=1, 2, . . . , M); identifying the M pseudorange correction values PRC(t f ;j;mob) that would be computed at the mobile station with the respective M pseudorange correction values PRC(t f ;j;ref) computed for the reference station; forming an M×1 matrix PRC(t f ;ref) whose entries are the values PRC(t f ;j;ref) for j=1, 2, . . . , M; forming a 3×M matrix H(t f ;mob).sup.Λ that satisfies the relation H(t f ;mob).sup.Λ H(t f ;mob)=I, where I is the 3×3 identity matrix; forming a 3×1 matrix ΔW(t f ;mob) whose entries are given by the product H(t f ;mob).sup.Λ PRC(t f ;ref) of the matrices H(t f ;mob).sup.Λ and PRC(t f ;ref); interpreting four entries Δw 1 (t f ), Δw 2 (t f ) and Δw 3 (t f ) of the matrix ΔW(t f ;mob) as corrections to the location fix coordinates for the mobile station; and adding the location fix coordinate corrections Δw 1 (t f ) and Δw 2 (t f ) to the respective location fix coordinates x'(t f ) and y'(t f ) to produce corrected location fix coordinates x(t f ) and y(t f ) and defining z(t f )=z'(t f ) for the corrected location fix coordinates x'(t f ), y'(t f ) and z'(t f ) for the mobile station for the location fix time t=t f .
References Cited (Backward Citations)
USPTO Annuity & Maintenance Windows
| Annuity Stage | Window Opens | Payment Deadline | Surcharge Period Until | Estimated Fee | Status |
|---|---|---|---|---|---|
| 3.5 Years (Year 4) | 2000-10-20 | 2001-04-21 | 2001-10-21 | $2000.00 | Window Closed / Lapsed |
| 7.5 Years (Year 8) | 2004-10-20 | 2005-04-21 | 2005-10-21 | $3760.00 | Window Closed / Lapsed |
| 11.5 Years (Year 12) | 2008-10-20 | 2009-04-21 | 2009-10-21 | $7700.00 | Window Closed / Lapsed |