A new method to transform from Cartesian to geodetic coordinates is presented. It is based on the solution of a system of nonlinear equations with respect to the coordinates of the point projected onto the ellipsoid along the normal. Newton’s method and a modification of Newton’s method were applied to give third-order convergence. The method developed was compared to some well known iterative techniques. All methods were tested on three ellipsoidal height ranges: namely, (-10 – 10 km) (terrestrial), (20 – 1000 km), and (1000 – 36000 km) (satellite). One iteration of the presented method, implemented with the third-order convergence modified Newton’s method, is necessary to obtain a satisfactory level of accuracy for the geodetic latitude ( σ φ < 0.0004”) and height ( σ h < 10 − 6 km, i.e. less than a millimetre) for all the heights tested. The method is slightly slower than the method of Fukushima (2006) and Fukushima’s (1999) fast implementation of Bowring’s (1976) method.

Land surveyors, photogrammetrists, remote sensing engineers and professionals in the Earth sciences are often faced with the task of transferring coordinates from one geodetic datum into another to serve their desired purpose. The essence is to create compatibility between data related to different geodetic reference frames for geospatial applications. Strictly speaking, conventional techniques of conformal, affine and projective transformation models are mostly used to accomplish such task. With developing countries like Ghana where there is no immediate plans to establish geocentric datum and still rely on the astro-geodetic datums as it national mapping reference surface, there is the urgent need to explore the suitability of other transformation methods. In this study, an effort has been made to explore the proficiency of the Extreme Learning Machine (ELM) as a novel alternative coordinate transformation method. The proposed ELM approach was applied to data found in the Ghana geodetic reference network. The ELM transformation result has been analysed and compared with benchmark methods of backpropagation neural network (BPNN), radial basis function neural network (RBFNN), two-dimensional (2D) affine and 2D conformal. The overall study results indicate that the ELM can produce comparable transformation results to the widely used BPNN and RBFNN, but better than the 2D affine and 2D conformal. The results produced by ELM has demonstrated it as a promising tool for coordinate transformation in Ghana.