Distortion modelling of the coordinate transformation between Ghana War Office 1926 and WGS84 datum’s using Polynomial Interpolation method

Abstract

Transforming points from one coordinate system to another can be accomplished by a number of transformation models including but not limited to conformal, affine and projective. This study aimed at using polynomial regression technique to assess distortions in existing Bursa-Wolf and 12 parameter linear affine coordinates within Ghana geodetic reference network. In all, nineteen known control points were utilised; fourteen as training sets and five points were used for testing analysis. An ordinary least square approach was used to derive the unknown polynomial coefficients based on the training sets. The obtained polynomial models were then used to predict a new set of coordinates (test points). Subsequently, the distortions were assessed by subtracting the predicted from the existing local coordinates. In order to ascertain the polynomial model performance, the Mean Square Error (MSE) was calculated. It was finally observed from the obtained results that, even though both data set thus, Bursa-Wolf and 12 parameter linear affine coordinates have some level of inherent distortions, comparatively, the 12 parameter linear affine data proved better.