Conversion between Cartesian and geodetic coordinates on a rotational ellipsoid by solving a system of nonlinear equations

By M. Ligas, Piotr Banasik. 2011

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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 coordi- nates 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 ( ' < 0.0004") and height ( 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.

Subfields: Mechanical Engineering, Numerical Analysis, Oceanography

View Paper: https://www.semanticscholar.org/paper/53602257bcab3e87543a319fd92367b7f700005b