Inverse and Compound Datum/Frame Transformations

Abstract

Transformations between local datums/frames have provided an indispensable method for expressing coordinates in the same datum. The advent of space-based geodetic techniques propelled the homogenization of national networks through the definition of conventional earth-centered, earth-fixed datums globally accessible through satellite observations. On the other hand, datum transformations enhanced mapping applications by using different realizations of the conventional reference frames. Realization of conventional datums/frames also led to investigations determining the transformation parameters between conventional terrestrial frames, and local datums rather than between local datums themselves. In this context, both inverse and sequential transformations are needed to express the coordinates of one local datum into another. Obtaining the transformation parameters through a “compound transformation” rather than transforming coordinates in a sequential scheme has several advantages. In this study, avenues to rigorously compute compound datum transformation parameters given two independent sets of transformation parameters are examined and compact analytical equations free of any matrix inversion are derived. New linear equations are presented both in compact matrix notation and in its expanded form to facilitate the propagation of errors from individual sets of transformation parameters to those of the compound datum transformation.