Investigation into the Accuracy and Practicality of Methods for Transforming Coordinates between Geodetic Datums

This thesis is a study of methods of transforming coordinates between geodetic datums, the methods being generally known as datum transformations. Direct methods are described and categorised as conformal, near-conformal and non-conformal. New variations on all three types are included in the direct methods: SMITSWAM (which avoids changes of coordinate-type), generalisations of Standard & Abridged Molodensky, and normalised generalisations of multiple regression equations (5 types). Reverse transformations are extensively covered, as are methods of derivation. In both cases, new algorithms are included. Direct methods, with the exception of multiple regression equations, do not capture distortions in datum transformations. The thesis therefore includes a review of composite methods which extract a trend model and apply a surface-fitting technique (SFT) to the residuals. Sometimes the SFT is used as a gridding method, producing regularly-spaced data that can be interpolated as a final stage of the composite process. The SFTs selected for detailed study include new variations on inverse-distance-to-a-power weighting and nearest-neighbour interpolation. These are called HIPFEAD and LIVONN respectively. In both cases, the variations are shown to have advantages in terms of accuracy of fit. Least-squares collocation and radial basis functions are shown to produce reusable vectors - described here as “revamped signals” – that enable interpolation without gridding. Where the composite methods are used for gridding, it is shown that geodetic coordinates can be used, avoiding the need for projected grid coordinates. The interpolation options applied are piecewise-bilinear and piecewise-bicubic, the latter being an algorithm (believed to be new) that uses up to 12 “grid” points. Case studies were considered using 6 datasets, two for Great Britain, one each for Western Australia, Ghana, Sweden and Slovenia. These showed beneficial properties of the new methods, both in the direct and composite categories. They also enabled comparisons of transformation methods generally