An iterative algorithm to compute geodetic coordinates

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 50 km of the geocentre. After one iteration, the maximum error of latitude is less than 10−8 arc-sec and the relative height error is less than 10−15 over the range of geodetic heights from −106 to 1012 m. Comparisons of the complexity and performance with some other well-known methods indicate that the algorithm is efficient and accurate.