Improving Algorithm to Compute Geodetic Coordinates

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 is fast, stable and sufficiently precise.