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This paper proposes a new method of deriving 9-parameter affine 3D datum transformations by ordinary least-squares. Unlike previous methods, it covers all versions of the transformation. Initially, an ‘average’ scale factor is computed by distance analysis. Removing the scaling effect, the ‘RIGOPT’ subroutine is applied to optimise the rigid transformation that consists of 3 translations and 3 rotations. Using an equivalent enlargement hypothesis, the number of scale factors is increased to 3 by a short series of single-search-direction optimisations. The minimisation of residuals is verified by enclosing-interval analysis. The case studies cover datasets in Western Australia, Great Britain and Sweden.

Derivation of 9-parameter affine 3D geodetic datum transformations