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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.G1,tr is then applied to one or more location coordinate triples (x.sub.G1, y.sub.G1, z.sub.G1) in GC1 to produce corresponding location coordinate triples (x.sub.L1, y.sub.L1, z.sub.L1) in LC1. The inverse transformation (T.sub.LC1,GC1).sup.-1 carries LC1 into GC1. The location coordinates in the global coordinate system GC1 can be determined using any suitable location determination system, such as GPS, GLONASS, Loran, Decca, Omega, Tacan or an FM subcarrier system.

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