Hybridized centroid technique for 3D Molodensky-Badekas coordinate transformation in the Ghana geodetic reference network using total least squares approach

Abstract

The Molodensky-Badekas model is one of the similarity transformation models used in Ghana for transferring Global Positioning System (GPS) coordinates from the geocentric World Geodetic System 1984 (WGS 84) ellipsoid to the local non-geocentric coordinate system, and vice versa. The objective of the Molodensky-Badekas model is to introduce a centroid to cater for the correlation that exists between the parameters when used over a small portion on the earth surface. However, the Molodensky-Badekas model performance depends on a particular centroid method adopted and the adjustment technique used. By virtue of literature covered, it was realised that the arithmetic mean centroid has been the most widely used. In view of this, the present study developed and tested two new hybrid centroid techniques known as the harmonic-quadratic mean and arithmetic-quadratic mean centroids. The proposed hybrid approaches were compared with the geometric mean, harmonic mean, median, quadratic mean and arithmetic mean. In addition, the Total Least Squares (TLS) technique was used to compute the transformation parameters with varying centroid techniques to investigate and assess their accuracies in precise GPS datum transformation parameters estimation within the Ghana Geodetic Reference Network. Statistical indicators such as Mean Error (ME), Mean Squared Error (MSE), Standard Deviation (SD), and Mean Horizontal Position Error (MHPE) were used to assess the centroid techniques performance. The results attained show that the Harmonic-Quadratic Mean produced reliable coordinate transformation results within the Ghana geodetic reference network and thus could serve as practical alternative technique to the frequently used arithmetic mean.

Keywords: Coordinate transformation, Molodensky-Badekas model, Centroid, Total Least Squares