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Inverse differential corrections for SATPS mobile stations

  • US 5,495,257 A
  • Filed: 07/19/1994
  • Issued: 02/27/1996
  • Est. Priority Date: 07/19/1994
  • Status: Expired due to Fees
First Claim
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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 Δ

    PR(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
    
    
    space="preserve" listing-type="equation">{(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 (xj (t),yj (t),zj (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 Δ

    W(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 Δ

    W(timobile) to the reference station;

    providing at the reference station an M×

    4 matrix H(t) whose entries are defined by the relationsH(t)=(hji (t)),hj1 (t)=α

    j1 (t)=(x0-xj (t))/r0j,hj2 (t)=α

    j2 (t)=(y0-yj (t))/r0j,hj3 (t)=α

    j3 (t)=(z0-zj (t))/r0j,hj4 (t)=1, (j=1, 2, 3, . . . , M) ,r0j (t)={(x0=xj (t))2 +(y0-yj (t))2 +(z0-zj (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 Δ

    W* by the matrix equation Δ

    W*(t)=H*(t)-1 Δ

    PR(t), where Δ

    PR(t) is an M×

    1 matrix whose entries are the values Δ

    PR(t;

    i;

    j) (j=1, 2, . . . , M) for the reference station;

    interpreting four entries w1 *(t), w2 *(t), w3 *(t), and w4 *(t) of the matrix Δ

    W*(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 relationsx(t)=x'"'"'(t)+w1 *(t),y(t)=y'"'"'(t)+w2 *(t),z(t)=z'"'"'(t)+w3 *(t),b(t)=b'"'"'(t)+w4 *(t).

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