Inverse differential corrections for SATPS mobile stations

Claim 1

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 an SATPS reference station, having location coordinates that are known with high accuracy, the reference station having an SATPS signal antenna and associated SATPS signal receiver/processor for receiving and processing SATPS signals from a plurality of SATPS satellites to determine spatial location and clock bias coordinates for that station; providing an SATPS station that is mobile, having an SATPS signal antenna and associated SATPS signal receiver/processor for receiving and processing SATPS signals from a plurality of SATPS satellites to determine spatial location and clock bias coordinates for that station; providing the mobile station with a radiowave transmitter and providing the reference station with a radiowave receiver so that the mobile station can transmit signals at a selected frequency that are received by the reference station; causing each of the reference station and the mobile station to receive SATPS signals from a plurality of M SATPS satellites (M≧4) in common with each other, and to determine the pseudorange values PR(t;i;j) as a function of time t for that station, numbered i (i=reference, i=mobile), from the signals received from the M common SATPS satellites, numbered j=j1, j2, . . . , jM; causing the reference station to determine pseudorange corrections ΔPR(t;i;j) that, when added to the pseudorange values PR(t;i;j) measured at the reference station, produce spatial location and clock bias coordinates that agree with the known spatial location and clock bias coordinates for the reference station; providing the mobile station with the spatial location and clock bias coordinates of a nominal solution of the pseudorange equations {(x0(t)-x.sub.j (t)).sup.2 +(y0(t)-y.sub.j (t)).sup.2 +(z0(t)-z.sub.j (t)).sup.2 }.sup.1/2 +b0(t)=PR(t;i;j), where (x0(t),y0(t),z0(t)) are the spatial location coordinates and b0(t) is the clock bias for this nominal solution, and (x j (t),y j (t),z j (t)) are the location coordinates of satellite number j; determining the spatial location and clock bias coordinates (x',y',z',b') for the mobile station from the SATPS signals received at that station; forming a 4×1 matrix ΔW(t; mobile)={x'-x0 y'-y0 z'-z0 b'-b0} tr , having matrix entries that are offset from the mobile station coordinates values (x',y',z',b') by the nominal solution coordinates values (x0,y0,z0,b0); transmitting the entries of the matrix ΔW(timobile) to the reference station; providing at the reference station an M×4 matrix H(t) whose entries are defined by the relations H(t)=(h ji (t)), h j1 (t)=α j1 (t)=(x0-x j (t))/r 0j , h j2 (t)=α j2 (t)=(y0-y j (t))/r 0j , h j3 (t)=α j3 (t)=(z0-z j (t))/r 0j , h j4 (t)=1, (j=1, 2, 3, . . . , M) , r 0j (t)={(x0=x j (t)) 2 +(y0-y j (t)) 2 +(z0-z j (t)) 2 } 1/2 ; augmenting the matrix H(t) by adding M-4 columns of matrix entries to produce an augmented M×M matrix H*(t) for the reference station, where four columns of the matrix H*(t) are identical with four columns of the matrix H(t) and each of the columns of H*(t) forms an M×1 column matrix that is independent of the other M-1 column matrices of the matrix H*(t); forming an inverse matrix H*(t) -1 , determining an M×1 matrix ΔW* by the matrix equation ΔW*(t)=H*(t) -1 ΔPR(t), where ΔPR(t) is an M×1 matrix whose entries are the values ΔPR(t;i;j) (j=1, 2, . . . , M) for the reference station; interpreting four entries w 1 *(t), w 2 *(t), w 3 *(t), and w 4 *(t) of the matrix ΔW*(t) as corrections to the location coordinates and clock bias values (x',y',z',b') for the mobile station; and determining the corrected spatial location coordinates (x,y,z) and corrected clock bias b for the mobile station using the relations x(t)=x'(t)+w 1 *(t), y(t)=y'(t)+w 2 *(t), z(t)=z'(t)+w 3 *(t), b(t)=b'(t)+w 4 *(t).

Claim 2

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 an SATPS reference station, having location coordinates that are known with high accuracy, the reference station having an SATPS signal antenna and associated SATPS signal receiver/processor for receiving and processing SATPS signals from a plurality of SATPS satellites to determine spatial location and clock bias coordinates for that station; providing an SATPS station that is mobile, having an SATPS signal antenna and associated SATPS signal receiver/processor for receiving and processing SATPS signals from a plurality of SATPS satellites to determine spatial location and clock bias coordinates for that station; providing the mobile station with a radiowave transmitter and providing the reference station with a radiowave receiver so that the mobile station can transmit signals at a selected frequency that are received by the reference station; causing each of the reference station and the mobile station to receive SATPS signals from a plurality of M SATPS satellites (M≧4) in common with each other, and to determine the pseudorange values PR(t;i;j) as a function of time t for that station, numbered i (i=reference, i=mobile), from the signals received from the M common SATPS satellites, numbered j=j1, j2, . . . , jM; causing the reference station to determine pseudorange corrections ΔPR(t;i;j) that, when added to the pseudorange values PR(t;i;j) measured at the reference station, produce spatial location and clock bias coordinates that agree with the known spatial location and clock bias coordinates for the reference station; providing the mobile station with the spatial location and clock bias coordinates of a nominal solution of the pseudorange equations {(x0(t)-x.sub.j (t)).sup.2 +(y0(t)-y.sub.j (t)).sup.2 +(z0(t)-z.sub.j (t)).sup.2 }.sup.1/2 +b0(t)=PR(t;i;j), where (x0(t),y0(t),z0(t)) are the spatial location coordinates and b0(t) is the clock bias for this nominal solution, and (x j (t),y j (t),z j (t)) are the location coordinates of satellite number j; determining the spatial location and clock bias coordinates (x',y',z',b') for the mobile station from the SATPS signals received at that station; forming a 4×1 matrix ΔW(t; mobile)={x'-x0 y'-y0 z'-z0 b'-b0} tr , having matrix entries that are offset from the mobile station coordinates values (x',y',z',b') by the nominal solution coordinates values (x0,y0,z0,b0); transmitting the entries of the matrix ΔW(timobile) to the reference station; providing at the reference station an M×4 matrix H(t) whose entries are defined by the relations H(t)=(h ji (t)), h j1 (t)=α j1 (t)=(x0-x j (t))/r 0j , h j2 (t)=α j2 (t)=(y0-y j (t))/r 0j , h j3 (t)=α j3 (t)=(z0-z j (t))/r 0j , h j4 (t)=1, (j=1, 2, 3, . . . , M) , r 0j (t)={(x0=x j (t)) 2 +(y0-y j (t)) 2 +(z0-z j (t)) 2 } 1/2 ; augmenting the matrix H(t) by adding M-4 columns of matrix entries to produce an augmented M×M matrix H*(t) for the reference station, where four columns of the matrix H*(t) are identical with four columns of the matrix H(t) and each of the columns of H*(t) forms an M×1 column matrix that is independent of the other M-1 column matrices of the matrix H*(t); forming an inverse matrix H*(t) -1 , determining an M×1 matrix ΔW* by the matrix equation ΔW*(t)=H*(t) -1 ΔPR(t), where ΔPR(t) is an M×1 matrix whose entries are the values ΔPR(t;i;j) (j=1, 2, . . . , M) for the reference station; interpreting four entries w 1 *(t), w 2 *(t), w 3 *(t), and w 4 *(t) of the matrix ΔW*(t) as corrections to the location coordinates and clock bias values (x',y',z',b') for the mobile station; and determining the corrected spatial location coordinates (x,y,z) and corrected clock bias b for the mobile station using the relations x(t)=x'(t)+w 1 *(t), y(t)=y'(t)+w 2 *(t), z(t)=z'(t)+w 3 *(t), b(t)=b'(t)+w 4 *(t).

Claim 6

A method for determining two-dimensional spatial location coordinates and clock bias with enhanced accuracy for a mobile user Satellite Positioning System (SATPS) station, the method comprising the steps of: providing an SATPS reference station, having location coordinates that are known with high accuracy, the reference station having an SATPS signal antenna and associated SATPS signal receiver/processor for receiving and processing SATPS signals from a plurality of SATPS satellites to determine spatial location and clock bias coordinates for that station; providing an SATPS station that is mobile, having an SATPS signal antenna and associated SATPS signal receiver/processor for receiving and processing SATPS signals from a plurality of SATPS satellites to determine spatial location and clock bias coordinates for that station; providing the mobile station with a radiowave transmitter and providing the reference station with a radiowave receiver so that the mobile station can transmit signals at a selected frequency that are received by the reference station; causing each of the reference station and the mobile station to receive SATPS signals from a plurality of M SATPS satellites (M≧3) in common with each other, and to determine the pseudorange values PR(t;i;j) as a function of time t for that station, numbered i (i=reference, i=mobile), from the signals received from the M common SATPS satellites numbered j=j1, j2, . . . , jM; causing the reference station to determine pseudorange corrections ΔPR(t;i;j) that, when added to the pseudorange values PR(t;i;j) measured at the reference station, produce spatial location and clock bias coordinates that agree with the known spatial location and clock bias coordinates for the reference station; providing the mobile station with the spatial location and clock bias coordinates of a nominal solution of the pseudorange equations {(x0(t)-x.sub.j (t)).sup.2 +(y0(t)-y.sub.j (t)).sup.2 }.sup.1/2 +b0(t)=PR(t;i;j), where (x0(t),y0(t)) are the spatial location coordinates and b0(t) is the clock bias for this nominal solution, and (xj(t),yj(t)) are the location coordinates of satellite number j; determining the spatial location and clock bias coordinates (x',y',b') for the mobile station from the SATPS signals received at that station; forming a 3×1 matrix ΔW(t; mobile)={x'-x0 y'-y0 b'-b0} tr , having matrix entries that are offset from the mobile station coordinates values (x',y',b') by the nominal solution coordinates values (x0,y0,b0); transmitting the entries of the matrix ΔW(t;mobile) to the reference station; providing at the reference station an M×3 matrix H(t) whose entries are defined by the relations H(t)=(h ji (t)), h j1 (t)=α j1 (t)=(x0-x j (t))/r 0j , h j2 (t)=α j2 (t)=(y0-y j (t))/r 0j , h j3 (t)=1, (j=1, 2, 3, . . . , M) , r 0j (t)={(x0-x j (t)) 2 +(y0-y j (t)) 2 } 1/2 ; augmenting the matrix H(t) by adding M-3 rows of matrix entries to produce an augmented M×M matrix H*(t) for the reference station, where three columns of the matrix H*(t) are identical with three columns of the matrix H(t) and each of the columns of H*(t) forms a 1×M column matrix that is independent of the other M-1 column matrices of the matrix H*(t); forming an inverse matrix H*(t) -1 , determining an M×1 matrix ΔW* by the matrix equation ΔW*(t)=H*(t) -1 ΔPR(t), where ΔPR(t) is an M×1 matrix whose entries are the values ΔPR(t;i;j) (j=1, 2, . . . , M) for the reference station; interpreting three entries w 1 *(t), w 2 *(t) and w 3 *(t) of the matrix ΔW*(t) as corrections to the location coordinates and clock bias values (x',y',b') for the mobile station; and determining the corrected location coordinates (x,y) and corrected clock bias coordinate b for the mobile station using the relations x(t)=x'(t)+w 1 *(t), y(t)=y'(t)+w 2 *(t), b(t)=b'(t)+w 3 *(t).

Claim 7

A method for determining two-dimensional spatial location coordinates and clock bias with enhanced accuracy for a mobile user Satellite Positioning System (SATPS) station, the method comprising the steps of: providing an SATPS reference station, having location coordinates that are known with high accuracy, the reference station having an SATPS signal antenna and associated SATPS signal receiver/processor for receiving and processing SATPS signals from a plurality of SATPS satellites to determine spatial location and clock bias coordinates for that station; providing an SATPS station that is mobile, having an SATPS signal antenna and associated SATPS signal receiver/processor for receiving and processing SATPS signals from a plurality of SATPS satellites to determine spatial location and clock bias coordinates for that station; providing the mobile station with a radiowave transmitter and providing the reference station with a radiowave receiver so that the mobile station can transmit signals at a selected frequency that are received by the reference station; causing each of the reference station and the mobile station to receive SATPS signals from a plurality of M SATPS satellites (M≧3) in common with each other, and to determine the pseudorange values PR(t;i;j) as a function of time t for that station, numbered i (i=reference, i=mobile), from the signals received from the M common SATPS satellites numbered j=j1, j2, . . . , jM; causing the reference station to determine pseudorange corrections ΔPR(t;i;j) that, when added to the pseudorange values PR(t;i;j) measured at the reference station, produce spatial location and clock bias coordinates that agree with the known spatial location and clock bias coordinates for the reference station; providing the mobile station with the spatial location and clock bias coordinates of a nominal solution of the pseudorange equations {(x0(t)-x.sub.j (t)).sup.2 +(y0(t)-y.sub.j (t)).sup.2 }.sup.1/2 +b0(t)=PR(t;i;j), where (x0(t),y0(t)) are the spatial location coordinates and b0(t) is the clock bias for this nominal solution, and (xj(t),yj(t)) are the location coordinates of satellite number j; determining the spatial location and clock bias coordinates (x',y',b') for the mobile station from the SATPS signals received at that station; forming a 3×1 matrix ΔW(t; mobile)={x'-x0 y'-y0 b'-b0} tr , having matrix entries that are offset from the mobile station coordinates values (x',y',b') by the nominal solution coordinates values (x0,y0,b0); transmitting the entries of the matrix ΔW(t;mobile) to the reference station; providing at the reference station an M×3 matrix H(t) whose entries are defined by the relations H(t)=(h ji (t)), h j1 (t)=α j1 (t)=(x0-x j (t))/r 0j , h j2 (t)=α j2 (t)=(y0-y j (t))/r 0j , h j3 (t)=1, (j=1, 2, 3, . . . , M) , r 0j (t)={(x0-x j (t)) 2 +(y0-y j (t)) 2 } 1/2 ; augmenting the matrix H(t) by adding M-3 rows of matrix entries to produce an augmented M×M matrix H*(t) for the reference station, where three columns of the matrix H*(t) are identical with three columns of the matrix H(t) and each of the columns of H*(t) forms a 1×M column matrix that is independent of the other M-1 column matrices of the matrix H*(t); forming an inverse matrix H*(t) -1 , determining an M×1 matrix ΔW* by the matrix equation ΔW*(t)=H*(t) -1 ΔPR(t), where ΔPR(t) is an M×1 matrix whose entries are the values ΔPR(t;i;j) (j=1, 2, . . . , M) for the reference station; interpreting three entries w 1 *(t), w 2 *(t) and w 3 *(t) of the matrix ΔW*(t) as corrections to the location coordinates and clock bias values (x',y',b') for the mobile station; and determining the corrected location coordinates (x,y) and corrected clock bias coordinate b for the mobile station using the relations x(t)=x'(t)+w 1 *(t), y(t)=y'(t)+w 2 *(t), b(t)=b'(t)+w 3 *(t).

Claim 11

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 an SATPS reference station, having location coordinates that are known with high accuracy, the reference station having an SATPS signal antenna and associated SATPS signal receiver/processor for receiving and processing SATPS signals from a plurality of SATPS satellites to determine spatial location and clock bias coordinates for that station; providing an SATPS station that is mobile, having an SATPS signal antenna and associated SATPS signal receiver/processor for receiving and processing SATPS signals from a plurality of SATPS satellites to determine spatial location and clock bias coordinates for that station; providing the mobile station with a radiowave transmitter and providing the reference station with a radiowave receiver so that the mobile station can transmit signals at a selected frequency that are received by the reference station; causing each of the reference station and the mobile station to receive SATPS signals from a plurality of M SATPS satellites (M≧3) in common with each other, and to determine the pseudorange values PR(t;i;j) as a function of time t for that station, numbered i (i=reference, i=mobile), from the signals received from the M common SATPS satellites numbered j=j1, j2, . . . , jM; causing the reference station to determine pseudorange corrections ΔPR(t;i;j) that, when added to the pseudorange values PR(t;i;j) measured at the reference station, produce spatial location and clock bias coordinates that agree with the known spatial location and clock bias coordinates for the reference station; providing the mobile station with the spatial location and clock bias coordinates of a nominal solution of the pseudorange equations {(x0(t)-x.sub.j (t)).sup.2 +(y0(t)-y.sub.j (t)).sup.2 +(z0(t)-z.sub.j (t)).sup.2 }.sup.1/2 =PR(t;i;j), where (x0(t),y0(t),z0(t)) are the spatial location coordinates for this nominal solution, and (x j (t),y j (t),z j (t)) are the location coordinates of satellite number j; determining the spatial location coordinates (x',y',z') for the mobile station from the SATPS signals received at that station; forming a 3×1matrix ΔW(t; mobile)={x'-x0 y'-y0 z'-z0 } tr , having matrix entries that are offset from the mobile station coordinates values (x',y',z') by the nominal solution coordinates values (x0,y0,z0); transmitting the entries of the matrix ΔW(t;mobile) to the reference station; providing at the reference station an M×3 matrix H(t) whose entries are defined by the relations H(t)=(h ji (t)), h j1 (t)=α j1 (t)=(x0-x j (t))/r 0j , h j2 (t)=α j2 (t)=(y0-y j (t))/r 0j , h j3 (t)=α j3 (t)=(z0-z j (t))/r 0j , r 0j (t)={(x0-x j (t)) 2 +(y0-y j (t)) 2 +(z0-zj(t)) 2 } 1/2 ; augmenting the matrix H(t) by adding M-3 columns of matrix entries to produce an augmented M×M matrix H*(t) for the reference station, where three columns of the matrix H*(t) are identical with three columns of the matrix H(t) and each of the columns of H*(t) forms an M×1 column matrix that is independent of the other M×1 column matrices of the matrix H*(t); forming an inverse matrix H*(t) -1 , determining an M×1 matrix ΔW* by the matrix equation ΔW*(t)=H*(t) -1 ΔPR(t), where ΔPR(t) is an M×1 matrix whose entries are the values ΔPR(t;i;j) (j=1, 2, . . . , M) for the reference station; interpreting three entries w 1 *(t), w 2 *(t) and w 3 *(t) of the matrix ΔW*(t) as corrections to the location coordinates (x',y',z') for the :mobile station; and determining the corrected location coordinates (x,y,z) for the mobile station using the relations x(t)=x'(t)+w 1 *(t), y(t)=y'(t)+w 2 *(t), z(t)=z'(t)+w 3 *(t).

Claim 12

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 an SATPS reference station, having location coordinates that are known with high accuracy, the reference station having an SATPS signal antenna and associated SATPS signal receiver/processor for receiving and processing SATPS signals from a plurality of SATPS satellites to determine spatial location and clock bias coordinates for that station; providing an SATPS station that is mobile, having an SATPS signal antenna and associated SATPS signal receiver/processor for receiving and processing SATPS signals from a plurality of SATPS satellites to determine spatial location and clock bias coordinates for that station; providing the mobile station with a radiowave transmitter and providing the reference station with a radiowave receiver so that the mobile station can transmit signals at a selected frequency that are received by the reference station; causing each of the reference station and the mobile station to receive SATPS signals from a plurality of M SATPS satellites (M≧3) in common with each other, and to determine the pseudorange values PR(t;i;j) as a function of time t for that station, numbered i (i=reference, i=mobile), from the signals received from the M common SATPS satellites numbered j=j1, j2, . . . , jM; causing the reference station to determine pseudorange corrections ΔPR(t;i;j) that, when added to the pseudorange values PR(t;i;j) measured at the reference station, produce spatial location and clock bias coordinates that agree with the known spatial location and clock bias coordinates for the reference station; providing the mobile station with the spatial location and clock bias coordinates of a nominal solution of the pseudorange equations {(x0(t)-x.sub.j (t)).sup.2 +(y0(t)-y.sub.j (t)).sup.2 +(z0(t)-z.sub.j (t)).sup.2 }.sup.1/2 =PR(t;i;j), where (x0(t),y0(t),z0(t)) are the spatial location coordinates for this nominal solution, and (x j (t),y j (t),z j (t)) are the location coordinates of satellite number j; determining the spatial location coordinates (x',y',z') for the mobile station from the SATPS signals received at that station; forming a 3×1matrix ΔW(t; mobile)={x'-x0 y'-y0 z'-z0 } tr , having matrix entries that are offset from the mobile station coordinates values (x',y',z') by the nominal solution coordinates values (x0,y0,z0); transmitting the entries of the matrix ΔW(t;mobile) to the reference station; providing at the reference station an M×3 matrix H(t) whose entries are defined by the relations H(t)=(h ji (t)), h j1 (t)=α j1 (t)=(x0-x j (t))/r 0j , h j2 (t)=α j2 (t)=(y0-y j (t))/r 0j , h j3 (t)=α j3 (t)=(z0-z j (t))/r 0j , r 0j (t)={(x0-x j (t)) 2 +(y0-y j (t)) 2 +(z0-zj(t)) 2 } 1/2 ; augmenting the matrix H(t) by adding M-3 columns of matrix entries to produce an augmented M×M matrix H*(t) for the reference station, where three columns of the matrix H*(t) are identical with three columns of the matrix H(t) and each of the columns of H*(t) forms an M×1 column matrix that is independent of the other M×1 column matrices of the matrix H*(t); forming an inverse matrix H*(t) -1 , determining an M×1 matrix ΔW* by the matrix equation ΔW*(t)=H*(t) -1 ΔPR(t), where ΔPR(t) is an M×1 matrix whose entries are the values ΔPR(t;i;j) (j=1, 2, . . . , M) for the reference station; interpreting three entries w 1 *(t), w 2 *(t) and w 3 *(t) of the matrix ΔW*(t) as corrections to the location coordinates (x',y',z') for the :mobile station; and determining the corrected location coordinates (x,y,z) for the mobile station using the relations x(t)=x'(t)+w 1 *(t), y(t)=y'(t)+w 2 *(t), z(t)=z'(t)+w 3 *(t).

Claim 16

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 an SATPS reference station, having location coordinates that are known with high accuracy, the reference station having an SATPS signal antenna and associated SATPS signal receiver/processor for receiving and processing SATPS signals from a plurality of SATPS satellites to determine spatial location and clock bias coordinates for that station; providing an SATPS station that is mobile, having an SATPS signal antenna and associated SATPS signal receiver/processor for receiving and processing SATPS signals from a plurality of SATPS satellites to determine spatial location and clock bias coordinates for that station; providing the mobile station with a radiowave transmitter and providing the reference station with a radiowave receiver so that the mobile station can transmit signals at a selected frequency that are received by the reference station; causing each of the reference station and the mobile station to receive SATPS signals from a plurality of M SATPS satellites (M≧5) in common with each other, and to determine the pseudorange values PR(t;i;j) as a function of time t for that station, numbered i (i=reference, or i=mobile), from the signals received from the M common SATPS satellites, numbered j=j1, j2, . . . , jM, where the satellites j=j1, j2, j3, j4 form a fundamental set of SATPS satellites used for determination of the location of the mobile station; determining spatial location and clock bias coordinates (x',y',z',b') for the mobile station from the SATPS signals received at that station; causing the reference station to determine pseudorange corrections ΔPR(t;ref;j) that, when added to the pseudorange values PR(t;ref;j) measured at the reference station, produce spatial location and clock bias coordinates that agree with the known spatial location and clock bias coordinates for the reference station; providing at the reference and mobile stations an M×4 matrix H(t;ref), determined from the reference station location coordinates, whose entries are defined by the relations H(t;ref)=(h ji (t)), h j1 (t)=α j1 (t)=(x0-x j (t))/r 0j , h j2 (t)=α j2 (t)=(y0-y j (t))/r 0j , h j3 (t)=α j3 (t)=(z0-z j (t))/r 0j , h j4 (t)=1, (j=1, 2, 3, . . . , M), r 0j (t)={(x0-x j (t)) 2 +(y0-y j (t)) 2 +(z0-z j (t)) 2 } 1/2 ; decomposing the matrix H(t;ref) 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;mobile) at the mobile station, where PR(t;mobile) is an M×1 vector whose ordered entries are the pseudorange values PR(t;mobile;j) (j=j1, j2, . . . , jM); decomposing the matrix v into a 4×1 column matrix v f , consisting of the first four entries of the matrix v, and an (M-4)×1 column matrix v nf , consisting of the last M-4 entries of the matrix v; transmitting the M-4 entries of the matrix v nf and the mobile station coordinates (x',y',z',b') to the reference station; constructing at the reference station the 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 } tr at the reference station as a concatenation of the vectors v f and v nf ; reconstructing the matrix of pseudorange values PR(t;mobile) from the vector v at the reference station; adding the pseudorange corrections ΔPR(t;ref;j) to the pseudorange values PR(t;mobile;j) for the fundamental set (j=j1, j2, j3, j4) to form corrected pseudorange values PR(t;mobile;j) cor for the fundamental set; and determining corrected spatial location and clock bias coordinates for the mobile station, using the corrected pseudorange values PR(t;mobile;j) cor for the fundamental set.

Claim 17

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 an SATPS reference station, having location coordinates that are known with high accuracy, the reference station having an SATPS signal antenna and associated SATPS signal receiver/processor for receiving and processing SATPS signals from a plurality of SATPS satellites to determine spatial location and clock bias coordinates for that station; providing an SATPS station that is mobile, having an SATPS signal antenna and associated SATPS signal receiver/processor for receiving and processing SATPS signals from a plurality of SATPS satellites to determine spatial location and clock bias coordinates for that station; providing the mobile station with a radiowave transmitter and providing the reference station with a radiowave receiver so that the mobile station can transmit signals at a selected frequency that are received by the reference station; causing each of the reference station and the mobile station to receive SATPS signals from a plurality of M SATPS satellites (M≧5) in common with each other, and to determine the pseudorange values PR(t;i;j) as a function of time t for that station, numbered i (i=reference, or i=mobile), from the signals received from the M common SATPS satellites, numbered j=j1, j2, . . . , jM, where the satellites j=j1, j2, j3, j4 form a fundamental set of SATPS satellites used for determination of the location of the mobile station; determining spatial location and clock bias coordinates (x',y',z',b') for the mobile station from the SATPS signals received at that station; causing the reference station to determine pseudorange corrections ΔPR(t;ref;j) that, when added to the pseudorange values PR(t;ref;j) measured at the reference station, produce spatial location and clock bias coordinates that agree with the known spatial location and clock bias coordinates for the reference station; providing at the reference and mobile stations an M×4 matrix H(t;ref), determined from the reference station location coordinates, whose entries are defined by the relations H(t;ref)=(h ji (t)), h j1 (t)=α j1 (t)=(x0-x j (t))/r 0j , h j2 (t)=α j2 (t)=(y0-y j (t))/r 0j , h j3 (t)=α j3 (t)=(z0-z j (t))/r 0j , h j4 (t)=1, (j=1, 2, 3, . . . , M), r 0j (t)={(x0-x j (t)) 2 +(y0-y j (t)) 2 +(z0-z j (t)) 2 } 1/2 ; decomposing the matrix H(t;ref) 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;mobile) at the mobile station, where PR(t;mobile) is an M×1 vector whose ordered entries are the pseudorange values PR(t;mobile;j) (j=j1, j2, . . . , jM); decomposing the matrix v into a 4×1 column matrix v f , consisting of the first four entries of the matrix v, and an (M-4)×1 column matrix v nf , consisting of the last M-4 entries of the matrix v; transmitting the M-4 entries of the matrix v nf and the mobile station coordinates (x',y',z',b') to the reference station; constructing at the reference station the 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 } tr at the reference station as a concatenation of the vectors v f and v nf ; reconstructing the matrix of pseudorange values PR(t;mobile) from the vector v at the reference station; adding the pseudorange corrections ΔPR(t;ref;j) to the pseudorange values PR(t;mobile;j) for the fundamental set (j=j1, j2, j3, j4) to form corrected pseudorange values PR(t;mobile;j) cor for the fundamental set; and determining corrected spatial location and clock bias coordinates for the mobile station, using the corrected pseudorange values PR(t;mobile;j) cor for the fundamental set.