Interpolation of survey coordinate differences
First Claim
1. A method for improving the accuracy of a survey of a region, the method comprising the step of providing a computer that is programmed to perform the following:
- determining a grid of at least three survey reference points in a selected first coordinate system for a selected region;
providing a set of N survey control locations associated with the region;
for each grid point in the grid, identifying an associated survey control set of a selected number K (K≦
N) of survey control locations that are associated with the grid point, and determining a transformation T that has at least one adjustable parameter and that maps location coordinates in the first coordinate system into location coordinates in a selected second coordinate system;
for each grid point in the grid, determining a coordinate difference between at least a first coordinate of the grid point and a corresponding coordinate of the image of the grid point under the transformation T;
determining a difference interpolation function, defined on and continuous at all points in the selected region, which is approximately equal to the coordinate difference for each point on the grid; and
using the difference interpolation function to estimate and display a difference of at least one coordinate value between at least one selected survey location that is not among the K survey control locations in the first coordinate system and an image under the transformation T of the at least one selected survey location.
3 Assignments
0 Petitions
Accused Products
Abstract
A system for improving the accuracy of location coordinate determined in a survey of a chosen region, using a computer. A grid of spaced apart points is imposed on the region, and a set of survey control points is provided. A "near set" of nearest survey control points is associated with each grid point. For each grid point, a transformation T from a first (global) datum and coordinate system to a second (local) datum and coordinate system is determined that minimizes a collective difference between coordinates of each survey control point in the near set and the corresponding coordinates of that survey control point under the transformation T. For one, two or three coordinates of each grid point, a difference Δ between the coordinate(s) of the grid point in the near set and the corresponding coordinate(s) of that grid point under the transformation T is computed. An interpolation function is determined that approximately matches the coordinate(s) difference Δ at each grid point. The interpolation function provides a continuous datum-to-datum mapping between all points of the first and the second coordinate systems. Determination of location of each survey point may use GPS, GLONASS, modified LEO, LORAN or any other suitable location determination system.
36 Citations
25 Claims
-
1. A method for improving the accuracy of a survey of a region, the method comprising the step of providing a computer that is programmed to perform the following:
-
determining a grid of at least three survey reference points in a selected first coordinate system for a selected region; providing a set of N survey control locations associated with the region; for each grid point in the grid, identifying an associated survey control set of a selected number K (K≦
N) of survey control locations that are associated with the grid point, and determining a transformation T that has at least one adjustable parameter and that maps location coordinates in the first coordinate system into location coordinates in a selected second coordinate system;for each grid point in the grid, determining a coordinate difference between at least a first coordinate of the grid point and a corresponding coordinate of the image of the grid point under the transformation T; determining a difference interpolation function, defined on and continuous at all points in the selected region, which is approximately equal to the coordinate difference for each point on the grid; and using the difference interpolation function to estimate and display a difference of at least one coordinate value between at least one selected survey location that is not among the K survey control locations in the first coordinate system and an image under the transformation T of the at least one selected survey location. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17)
-
9. The method of claim 8, wherein said step of choosing said at least one adjustable parameter further comprises the step of selecting at least one of said adjustable coefficients hij to minimize said error sum ε
- p.
-
10. The method of claim 7, further comprising the step of choosing as said transformation T the transformation defined by (1) a rotation of the first coordinate system around a selected rotation axis by a selected angle θ
- 1, (2) multiplication of said coordinates resulting from the rotation by a selected real number scale factor L, and (3) translation of the resulting first and second location coordinates by selected translation distances Δ
x and Δ
y, respectively, where at least one of the coefficients θ
1, L, Δ
x and Δ
y is an adjustable parameter.
- 1, (2) multiplication of said coordinates resulting from the rotation by a selected real number scale factor L, and (3) translation of the resulting first and second location coordinates by selected translation distances Δ
-
11. The method of claim 7, further comprising the step of selecting said positive number p to be equal to 2 and choosing, each of said non-negative numbers ek and fk to be equal to a selected positive number.
-
12. The method of claim 1, further comprising the step of selecting said first coordinate system and said second coordinate system to have a spatial dimension 3, with said location coordinates (x, y, z).
-
13. The method of claim 12, wherein said step of choosing, said at least one adjustable parameter comprises the steps of:
-
obtaining a first set of K coordinate triples {(xk, yk, zk)}(k=1, . . . , K;
K≧
2) for said survey control locations in said first coordinate system and applying said transformation T to each coordinate triple in the first set to determine an image under T of the coordinate triple in said second coordinate system
space="preserve" listing-type="equation">T (x.sub.k, y.sub.k, z.sub.k)=(x'"'"'.sub.k, y'"'"'.sub.k, z'"'"'.sub.k);choosing said at least one adjustable parameter for said transformation T so that an error sum ε
p defined by ##EQU18## is minimized, where p is a selected positive number and ek, fk and gk are selected non-negative numbers, not all zero.
-
- 14. The method of claim 13, further comprising the step of choosing as said transformation T the linear transformation defined by
- space="preserve" listing-type="equation">x'"'"'=h.sub.11 x+h.sub.12 y+h.sub.13 z+h.sub.14,
space="preserve" listing-type="equation">y'"'"'=h.sub.21 x+h.sub.22 y+h.sub.23 z+h.sub.24,
space="preserve" listing-type="equation">z'"'"'=h.sub.31 x+h.sub.32 y+h.sub.33 z+h.sub.34,where at least one of the coefficients hij (i=1,2,3;
j=1,2,3,4) is an adjustable parameter.
-
-
15. The method of claim 14, wherein said step of choosing said at least one adjustable parameter further comprises the step of selecting at least one of said adjustable coefficients hij to minimize said error sum ε
- p.
-
16. The method of claim 13, further comprising the step of choosing as said transformation T the transformation defined by (1) a first rotation of the first coordinate system around a selected first rotation axis by a selected first angle θ
- 1, (2) a second rotation of the first coordinate system around a selected second rotation axis, which differs from the selected first rotation axis, by a selected second angle θ
2, (3) a third rotation of the first coordinate system around a selected third rotation axis, which differs from the selected second rotation axis, by a selected second angle θ
3, (4) multiplication of said coordinates resulting from the first, second and third rotations by a selected real number scale factor L, and (5) translation of the resulting first, second and third location coordinates by selected translation distances Δ
x, Δ
y and Δ
z, respectively, where at least one of the coefficients θ
1, θ
2, θ
3, L, Δ
x, Δ
y and Δ
z is an adjustable parameter.
- 1, (2) a second rotation of the first coordinate system around a selected second rotation axis, which differs from the selected first rotation axis, by a selected second angle θ
-
17. The method of claim 13, further comprising the step of selecting said positive number p to be equal to 2 and choosing each of said non-negative numbers ek, fk and gk to be equal to a selected positive number.
-
18. Apparatus for transforming coordinates for at least one location, surveyed in a first coordinate system, into location coordinates in a second coordinate system, the apparatus comprising a computer that is programmed to:
-
obtain location coordinates for a selected set of survey control locations (K≧
2) in a first coordinate system, and to obtain a subset of K selected survey control locations (K≧
2) that are closer to a selected location than any other survey control location in the selected set;obtain location coordinates for the set of survey control locations, expressed in a selected second coordinate system; determine a coordinate transformation T, having at least one adjustable parameter, of the first coordinate system onto the second coordinate system to minimize a selected generalized sum of distances between each survey control location in the selected subset of K survey control locations and the corresponding image under the transformation T, by choice of at least one adjustable parameter; determine an interpolation function that estimates the difference between at least one coordinate of a selected location in the first coordinate system and the corresponding coordinate of the image under T of the selected location; and use the difference interpolation function to estimate and display a difference of at least one coordinate value between at least one of the N survey control locations in the first coordinate system and an image under the transformation T of the at least one of the N survey control locations. - View Dependent Claims (19, 20, 21, 22, 23, 24, 25)
-
Specification