A 3D Procrustean Approach to Transform WGS84 Coordinates to Ghana War Office 1926 Reference Datum

Abstract

Abstract

Satellite positioning technique such as Global Positioning System (GPS) is available to all countries for geospatial positioning. The availability of such positioning technique has revolutionised surveying in Ghana. The GPS operates on a global reference frame to fix control points for surveying and mapping purposes. There is therefore the need to transform coordinates from the satellite-based datum to the Ghana War Office 1926 datum. Several iterative methods have been proposed over the years for coordinate transformation and have been found to exhibit good transformation accuracy. However, these iterative methods always demand the linearisation of the transformation model equations and initial approximation values of the yet to be determined transformation parameters. These computational processes further enhance the computational complexity of the iterative methods and longer convergence time. As alternative solution, the Procrustes method has been proposed and applied to solve coordinate transformation problems in different geodetic reference networks. Review of previous studies indicates that the Procrustes method is direct, simple to use and produce satisfactory transformation accuracy. This method, however, is yet to be applied to ascertain its efficiency in the Ghana geodetic reference network. Therefore, this study utilised the 3D Procrustean approach to transform coordinates from World Geodetic System 1984 (WGS84) to Ghana War Office 1926 reference datum. The technique produced Root Mean Square Horizontal Error (RMSHE), Arithmetic Mean of the Horizontal Error (AMHE) and Standard Deviation (SD) values of 1.003 m, 0.901 m and 0.452 m, respectively. This study is serving as an extension to the ongoing research works to determine optimal transformation model for Ghana geodetic reference network.

Keywords: Procrustean Approach, Coordinate Transformation, Conformal Model, Satellite Positioning