Derivation of rigorously-conformal 7-parameter 3D geodetic datum transformations

Abstract

This paper proposes a new method of deriving rigorously-conformal 7-parameter 3D coordinate transformations between geodetic datums. The problem of linearisation is reduced by distance analysis which provides an estimate of scale-change. The resulting 6-parameter transformation is linearised to enable an initial least-squares estimate of the rotation parameters. The 6-parameter transformation is then re-linearised to obtain a least-squares estimate of the corrections to the rotations. The validity of the scale-change estimate can be tested and is verified in almost all cases. The exception is transformations covering very small areas where short distances maximise the impact of measurement errors in the control data. Even there, the method can be adapted to optimise the transformation. The method can also be used to obtain pseudo-optimal conformal transformations that provide a closest fit to published Bursa-Wolf transformations.