Differential correction of orbits by Kepler versus Cartesian parameters

Numerical integration of orbits of near Earth satellites is usually carried out in a Cartesian Coordinate System. When performing the differential correction of an initial orbit to match observations, the parameters of the solution are sometimes the corrections to the position and velocity vector of the satellite at epoch. At the Naval Surface Weapons Center, however, the parameters chosen are Kepler parameters modified to avoid singularity for circular orbits. The rate of convergence for a sample case was not found to be significantly different for the two parameterizations, but a significant gain in numerical accuracy was obtained with the set of Kepler parameters.