A quaternion-based geodetic datum transformation algorithm

This paper briefly introduces quaternions to represent rotation parameters and then derives the formulae to compute quaternion, translation and scale parameters in the Bursa-Wolf geodetic datum transformation model from two sets of co-located 3D coordinates. The main advantage of this representation is that linearization and iteration are not needed for the computation of the datum transformation parameters. We further extend the formulae to compute quaternion-based datum transformation parameters under constraints such as the distance between two fixed stations, and develop the corresponding iteration algorithm. Finally, two numerical case studies are presented to demonstrate the applications of the derived formulae.