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By using the Newton–Raphson method to solve a quartic equation of the Lagrange parameter, we propose a new iterative algorithm for the transformation from Cartesian to geodetic coordinates. Numerical experiments show that the new method is sufficiently precise and free from singularity and non-convergency, except within 50km of the geocentre. After one iteration, the maximum error of latitude is less...
An improved algorithm for computing geodetic coordinates from Cartesian coordinates is presented. The algorithm solves a quartic equation of the Lagrange parameter using Newton-Raphson (NR) method. A initial guess is given weightily that works rigorously for most points except in a small near-geocenter region. Numerical experiments and comparisons with some other methods show that the new algorithm...
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