Comparison and Analysis of Non-Linear Least Squares Methods for 3-D Coordinates Transformation

Abstract

Four different methods are evaluated by solving the Molodensky 3-D coordinate transformation problem. These methods are Steepest Descent, Trust region, Gauss Newton and Levenberg-Marquardt. Also, the problem has been solved using the traditional combined least-squares adjustment. The solutions of these methods are compared by the number of iterations required for the objective function to converge to its minimum value. Externally, the RMSE of the transformed check stations of the geodetic network (curvilinear coordinates) are compared to the RMSE obtained by transforming the same set of check stations using the transformation parameters recommended by the Egyptian Survey Authority.

Keywords:

• COORDINATE TRANSFORMATION
• OPTIMISATION PROCEDURES
• NATIONAL GEODETIC NETWORKS
• WGS84