Geometric utilization of exact solutions of the pseudorange equations
First Claim
1. A method for determining the location of a location determination (LD) station, the method comprising the steps of:
- receiving LD signals from a plurality of LD signal sources at an LD station and determining a pseudorange value between the LD station and each LD signal source, where the number of LD signal sources is less than the number of location fix coordinates for the LD station to be determined;
processing the pseudorange values to produce at least one exact linear relation relating at least first and second location fix coordinates for the LD station without iteration; and
using the at least one linear relation together with at least one pseudorange value to obtain at least one exact non-linear relation relating the at least first and second location fix coordinates without iteration.
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Accused Products
Abstract
Method and apparatus for determining non-iterative exact solutions for two, three or four location fix coordinates x, y, z and/or time offset b from pseudorange measurements from a plurality of location determination (LD) signals received at a GPS or GLONASS station. If M location fix coordinates are to be determined from N pseudorange measurements, the solution is exact if N=M. If N=M-1, the solution for two of the location fix coordinates lies at a point, on an ellipse or on an hyperbola. If N≧M+1, a solution lies at the center of a sphere in M-dimensional space or in the interior of the sphere, according as N=M+1 or N≧M+2.
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Citations
35 Claims
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1. A method for determining the location of a location determination (LD) station, the method comprising the steps of:
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receiving LD signals from a plurality of LD signal sources at an LD station and determining a pseudorange value between the LD station and each LD signal source, where the number of LD signal sources is less than the number of location fix coordinates for the LD station to be determined; processing the pseudorange values to produce at least one exact linear relation relating at least first and second location fix coordinates for the LD station without iteration; and using the at least one linear relation together with at least one pseudorange value to obtain at least one exact non-linear relation relating the at least first and second location fix coordinates without iteration. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15)
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16. A method for determining the location of a location determination (LD) station, the method comprising the steps of:
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receiving LD signals from N LD signal sources (N≧
2) at an LD station and determining a pseudorange value between the LD station and each LD signal source, where the number of LD signal sources is greater than the number of location fix coordinates, M, for the LD station to be determined;processing the pseudorange values to produce at least one exact M relations relating location fix coordinates for the LD station; and using the at least M linear relations together with at least one pseudorange value to obtain at least one exact non-linear relation relating at least first and second location fix coordinates; and using the at least one nonlinear relation to relate the first location fix coordinate to the second location fix coordinate without iteration. - View Dependent Claims (17, 18, 19, 20)
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21. A method for determining the location of a location determination (LD) station, the method comprising the steps of:
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(1) receiving and processing LD signals at an LD station from N LD signal sources, numbered n=1, 2, . . . , N (N≧
2) and spaced apart from the LD unit, where the LD station can determine the location of the LD station from the LD signals received and where the number of LD signal sources is less than the number M of location fix coordinates for the LD station to be determined;(2) measuring a pseudorange value PR(t=tr,n ;
ts,n ;
n) associated with an LD signal transmitted by LD source number n (n=1, 2, . . . , N) at a selected time t=ts,n and received at the LD station at a selected receive time t=tr,n, where the receive times tr,n (n=1, 2, . . . , N) are approximately equal, where the pseudorange value for an LD signal received from LD signal source number n at the time t=tr,n is represented approximately by a pseudorange equation of the form
space="preserve" listing-type="equation">PR(t=t.sub.r,n ;
t.sub.s,n ;
n)+b=d.sub.n ={(x-x.sub.n).sup.2 +(y-y.sub.n).sup.2 +(z-z.sub.n).sup.2 }.sup.1/2 ==b-χ
(t.sub.r,n ;
t.sub.s,n ;
n),that relates a distance dn from the LD signal source number n, having approximately known spatial location coordinates (xn,yn,zn)=(xn (ts,n)yn (ts,n),zn (ts,n)) at the selected time t=ts,n, to the LD unit, which has initially unknown spatial location coordinates (x,y,z), where b/c=Δ
tr,n is an initially unknown error in the clock coordinate of the LD signal station, where χ
(tr,n ;
ts,n ;
n) is a selected term with a known value that is determined from the measured pseudorange value for a signal transmitted from LD signal source number n and that compensates for at least one of (i) time delay, Ir,s,n, for propagation of an LD signal in the ionosphere, (ii) time delay, Tr,s,n, for LD signal propagation in the troposphere, and (iii) clock error Δ
ts,n associated with LD signal source number n, and where x, y, z and b are location solution coordinates to be determined;(3) processing the pseudorange equations for the pseudorange values PR(t=tr,n ;
ts,n ;
n) to produce at least N-1 exact linear relations relating selected combinations of location fix coordinates x, y, z and b for the LD station, where the coefficients of these N-1 linear relations are determinable from values of selected terms χ
(tr,n ;
ts,n ;
n) and are independent of the values of the location fix coordinates;(4) using the N-1 linear relations relating the location fix coordinates, together with at least one of the pseudorange representation equations for the pseudorange values PR(t=tr,n ;
ts,n ;
n), to obtain at least one relation that is nonlinear in the unknown values for selected first and second location fix coordinates and that does not depend on the values of other location solution coordinates;(5) determining values for the selected first and second location fix coordinates that approximately satisfy the nonlinear relation for the selected first and second location fix coordinates, and using the selected first and second location fix coordinate values together with the N-1 linear relations relating the selected combinations of location fix coordinates to determine values of other location fix coordinates; and (6) interpreting the N values determined for the location fix coordinates as location fix coordinates for the LD station at the time t=tr,n. - View Dependent Claims (22, 23, 24, 25, 26, 27, 28)
- 28. The method of claim 21, wherein said integer M=3, further comprising the step of expressing said at least three linear relations relating said solution location coordinates in the form
- space="preserve" listing-type="equation">H.sub.11 x+H.sub.12 y=A'"'"'.sub.1,2 -B.sub.1,2 b,
space="preserve" listing-type="equation">H.sub.21 x+H.sub.22 y=A'"'"'.sub.1,3 -B.sub.1,3 b,where the coefficients Hij (i=1,2;
j=1,2) are determined by said spatial location coordinates (xn,yn) of said LD signal sources at said selected times t=ts,n, and the coefficients A'"'"'1,i (i=2,3) and B1,i (i=2,3) are determined by said selected terms χ
(tr,n ;
ts,n ;
n).
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29. A method for determining the location of a location determination (LD) station, the method comprising the steps of:
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receiving LD signals from N LD signal sources (N≧
2) at an LD station and determining a pseudorange value between the LD station and each LD signal source, where the number of LD signal sources is greater than the number of location fix coordinates, M, for the LD station to be determined;processing the pseudorange values to produce at least M exact linear relations relating location fix coordinates for the LD station; using the at least M linear relations together with at least one pseudorange value to obtain at least one exact non-linear relation relating at least first and second location fix coordinates; and using the at least M linear relations and the at least one nonlinear relation to estimate at least M+1 location fix coordinate M-tuples. - View Dependent Claims (30, 31, 32)
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33. A method for determining the location of a location determination (LD) station, the method comprising the steps of:
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receiving LD signals from N LD signal sources (N≧
2) at an LD station and determining a pseudorange value between the LD station and each LD signal source, where the number of LD signal sources is greater than the number of location fix coordinates, M, for the LD station to be determined;processing the pseudorange values to produce at least M-1 exact linear relations relating location fix coordinates for the LD station; providing a selected sum of squares of the at least M-1 exact linear relations plus a square of a difference between the at least one selected pseudorange value and a selected one of the location fix coordinates; processing the selected sum to obtain at least one additional linear relation relating the selected location fix coordinate to the at least M-1 location fix coordinates; and solving the at least M-1 linear relations plus the at least one additional linear relation to obtain values for the M location fix coordinates.
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34. A method for determining the location of a location determination (LD) station, the method comprising the steps of:
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receiving LD signals from N LD signal sources (N≧
2) at an LD station and determining a pseudorange value between the LD station and each LD signal source, where the number of LD signal sources is less than the number of location fix coordinates, M, for the LD station to be determined;processing the pseudorange values to produce at least N-1 exact linear relations relating location fix coordinates for the LD station; using the at least N-1 linear relations together with at least one pseudorange value to obtain at least one exact non-linear relation relating at least first and second location fix coordinates; and using the at least one nonlinear relation to relate a first location fix coordinate to a second location fix coordinate. - View Dependent Claims (35)
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Specification