Abstract: A system for improving the accuracy of location coordinate determined in a survey of a chosen region. 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, and the number of elements in this new set may vary with the grid point. Definition of a near set can vary from one grid point to the next. For each grid point, a transformation T from a first coordinate system to a second 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, the difference(s) 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 are computed.

Abstract: Methods for providing a representation of location coordinates for a collection of survey points with enhanced accuracy. An obliquely oriented cylindrical surface, rather than a tangent plane, is determined and used as the projection surface at or near a survey base point, with the angular orientation and radius of the cylinder being chosen to optimize the accuracy of the projection. A scale factor that corrects for distances of locations projected onto the cylindrical surface is optionally determined and applied. A three-dimensional transformation of survey location coordinates, optimized to provide a best fit for a selected set of fiducial survey locations, is determined that provides a correspondence between a globally determined height coordinate and a locally determined elevation coordinate.

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 (e.g., NAD 27) in a second global coordinate system G2. Location coordinates (x'.sub.m,2,y'.sub.m,2,z'.sub.m,2) for M previously-surveyed locations, numbered m=1, . . . , M (M>1) in the second system, and location coordinates (x'.sub.n,1,y'.sub.n,1,z'.sub.n,1) for N presently-surveyed locations, numbered n=1, . . . , N (M<N), in the first system are provided, where M presently-surveyed locations coincide with the M previously-surveyed locations. The transformation is chose.sub.n so that the images of previously-surveyed locations in the first system under the transformation T are as close as possible to the corresponding [previously-surveyed] locations in the second system. Give.sub.n an ellipsoid and a selected survey plane .tau.

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 .DELTA. 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 .DELTA. at each grid point.

Abstract: Method and apparatus for optimally transforming location coordinates from a global system GC1 of survey coordinates to a local system LC1 of coordinates in a location survey. Linear translation transformations T.sub.G1 and T.sub.L1 are determined that translate the GC1 coordinates and the LC1 coordinates new coordinates in coordinate systems LC1' and GC2 having a corresponding origin. A rotation transformation R(.phi.,.theta.), having a selected azimuthal rotation angle .phi. and a selected polar rotation angle .theta., that transforms the coordinate system LC1' into another coordinate system LC2 so that a coordinate plane or coordinate axes in LC2 are aligned with a coordinate plane or coordinate axes in GC2. An optimized invertible transformation T.sub.LC2,GC2 is found that minimizes a selected functional and carries GC2 into LC2. The optimal transformation of GC1 into LC1,T.sub.LC1,GC1 =(T.sub.L1,tr).sup.-1 R(.phi.,.theta.).sup.-1 T.sub.LC2,GC2 T.sub.

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'.sub.m,2, y'.sub.m,2,z'.sub.m,2) for M previously-surveyed locations, numbered m=1, . . . , M, and a set of location coordinates (x'.sub.n,1, y'.sub.n,1,z'.sub.n,1) for N presently-surveyed locations, numbered n=1, . . . , N (M.ltoreq.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'.sub.n,1,y'.sub.n,1, z'.sub.n,1) for n=1, . . . , M under T(G2;G1) are as close as possible to the corresponding location coordinates (x'.sub.m,2,y'.sub.m,2, z'.sub.m,2) for m=1, . . . , M. Given an ellipsoid and a selected survey plane .tau.