Optimization of survey coordinate transformations
First Claim
1. A method for determining location coordinates for a plurality of surveyed locations, the method comprising the steps of:
- providing a location determination (LD) receiver having an LD signal antenna and an LD signal receiver/processor to receive and process LD signals transmitted from three or more LD signal sources, which are spaced apart from the LD receiver, and to use these LD signals to determine three-dimensional location coordinates for the LD signal antenna;
using the LD signals received at the LD receiver to determine a first set of three-dimensional location coordinates (x'"'"'n,1,y'"'"'n,1,z'"'"'n,1) for N selected presently-surveyed locations, numbered n=1, 2, . . . , N (N≧
3) in a first coordinate system G1;
providing a second set of three-dimensional location coordinates (x'"'"'m,2, y'"'"'m,2, z'"'"'m,2) for M previously-surveyed locations, numbered m=1, 2, . . . , M (M≦
N), where each previously-surveyed location number m=k is coincident with the presently-surveyed location number n=k for k=1, 2, . . . , M;
providing a three-dimensional coordinate transformation T(G2;
G1) of the first coordinate system G1 onto a second three-dimensional coordinate system G2, under which the location coordinates (x'"'"'n,1, y'"'"'n,1, z'"'"'n,1) for each of the N presently-surveyed locations in G1 are transformed into location coordinates (x"n,2, y"n,2, z"n,2) in G2 (n=1, 2, . . . , N);
choosing the transformation T(G2;
G1) so that the error sum ##EQU19## is minimized, where p is a selected positive number and em,fm and gm are selected non-negative weight coefficients; and
determining the location coordinates (x"n,2, y"n,2, z"n,2) for at least one of the presently surveyed locations (n=1, 2, . . . , N) under the transformation T(G2;
G1), and displaying these location coordinates by a visually perceptible or audibly perceptible image.
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Accused Products
Abstract
A system for selecting an optimal transformation T(G2;G1) between a first ellipsoid E1 (e.g., WGS 84) in a first global coordinate system G1, relative to which the survey measurements are made, and a second ellipsoid E2 in a second global coordinate system G2. A set of location coordinates (x'"'"'m,2, y'"'"'m,2,z'"'"'m,2) for M previously-surveyed locations, numbered m=1, . . . , M, and a set of location coordinates (x'"'"'n,1, y'"'"'n,1,z'"'"'n,1) for N presently-surveyed locations, numbered n=1, . . . , N (M≦N) are provided, where the first M presently-surveyed locations coincide with the M previously-surveyed locations. The transformation is chosen so that the images of the location coordinates (x'"'"'n,1,y'"'"'n,1, z'"'"'n,1) for n=1, . . . , M under T(G2;G1) are as close as possible to the corresponding location coordinates (x'"'"'m,2,y'"'"'m,2, z'"'"'m,2) for m=1, . . . , M. Given an ellipsoid and a selected survey plane τ0 that is tangent to the ellipsoid at a selected location, a set of selected locations can be surveyed with reference to the ellipsoid, and the location coordinates of each such surveyed location can be mapped into a corresponding "survey location," defined by reference to a local coordinate system that uses the survey plane τ0 as its base. These transformations and projections are determined and optimized in real time, while a surveyor is measuring the presently-surveyed locations in the field. The instruments used for surveying may be part of a location determination system, such as a Global Positioning System, a Global Orbiting Navigational Satellite System or Loran.
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Citations
15 Claims
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1. A method for determining location coordinates for a plurality of surveyed locations, the method comprising the steps of:
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providing a location determination (LD) receiver having an LD signal antenna and an LD signal receiver/processor to receive and process LD signals transmitted from three or more LD signal sources, which are spaced apart from the LD receiver, and to use these LD signals to determine three-dimensional location coordinates for the LD signal antenna; using the LD signals received at the LD receiver to determine a first set of three-dimensional location coordinates (x'"'"'n,1,y'"'"'n,1,z'"'"'n,1) for N selected presently-surveyed locations, numbered n=1, 2, . . . , N (N≧
3) in a first coordinate system G1;providing a second set of three-dimensional location coordinates (x'"'"'m,2, y'"'"'m,2, z'"'"'m,2) for M previously-surveyed locations, numbered m=1, 2, . . . , M (M≦
N), where each previously-surveyed location number m=k is coincident with the presently-surveyed location number n=k for k=1, 2, . . . , M;providing a three-dimensional coordinate transformation T(G2;
G1) of the first coordinate system G1 onto a second three-dimensional coordinate system G2, under which the location coordinates (x'"'"'n,1, y'"'"'n,1, z'"'"'n,1) for each of the N presently-surveyed locations in G1 are transformed into location coordinates (x"n,2, y"n,2, z"n,2) in G2 (n=1, 2, . . . , N);choosing the transformation T(G2;
G1) so that the error sum ##EQU19## is minimized, where p is a selected positive number and em,fm and gm are selected non-negative weight coefficients; anddetermining the location coordinates (x"n,2, y"n,2, z"n,2) for at least one of the presently surveyed locations (n=1, 2, . . . , N) under the transformation T(G2;
G1), and displaying these location coordinates by a visually perceptible or audibly perceptible image. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8)
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9. A method for determining location coordinates for a plurality of surveyed locations, the method comprising the steps of:
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providing a location determination (LD) receiver having an LD signal antenna and an LD signal receiver/processor to receive and process LD signals transmitted from two or more LD signal sources, which are spaced apart from the LD receiver, and to use these LD signals to determine two-dimensional location coordinates for the LD signal antenna; using the LD signals received at the LD receiver to determine a first set of two-dimensional location coordinates (x'"'"'n,1, y'"'"'n,1) for N selected presently-surveyed locations, numbered n=1, 2, . . . , N (N≧
3) in a first coordinate system G1;providing a second set of two-dimensional location coordinates (x'"'"'m,2, y'"'"'m,2) for M previously-surveyed locations, numbered m=1, 2, . . . , M (M≦
N), where each previously-surveyed location number m=k is coincident with the presently-surveyed location number n=k for k=1, 2, . . . , M;providing a two-dimensional coordinate transformation T(G2;
G1) of the first coordinate system G1 onto a second two-dimensional coordinate system G2, under which the location coordinates (x'"'"'n,1, y'"'"'n,1) for each of the N presently-surveyed locations in G1 are transformed into location coordinates (x"n,2, y"n,2) in G2 (n=1, 2, . . . , N);choosing the transformation T(G2;
G1) so that the error sum ##EQU22## is minimized, where p is a selected positive number and em and fm are selected non-negative weight coefficients; anddetermining the location coordinates (x"n,2, y"n,2) for at least one of the presently surveyed locations (n=1, 2, . . . , N) under the transformation T(G2;
G1) ,and displaying these location coordinates by a visually perceptible or audibly perceptible image. - View Dependent Claims (10, 11, 12, 13, 14, 15)
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Specification