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A singularity-free perturbation solution is presented for inverting the Cartesian to Geodetic transformation. Geocentric latitude is used to model the satellite ground track position vector. A natural geometric perturbation variable is identified as the ratio of the major and minor Earth ellipse radii minus one. A rapidly converging perturbation solution is developed by expanding the satellite height above the Earth and the geocentric latitude as a perturbation power series in the geometric perturbation variable. The solution avoids the classical problem encountered of having to deal with highly nonlinear solutions for quartic equations. Simulation results are presented that compare the solution accuracy and algorithm performance for applications spanning the LEO-to-GEO range of missions

A Simple Perturbation Algorithm for Inverting the Cartesian to Geodetic Transformation