Converting GNSS satellite orbit segments to GPS-compatible format

An algorithm to convert a GNSS satellite track segment into the generalised Kepler parameter format used in GPS ephemerides messages is presented. A track segment is a sequence of 3D positions in Cartesian coordinates, such as is produced by orbit prediction software for self-assistance, where the format conversion is an essential post-processing step to reduce storage and for compatibility with GPS software and equipment. In this work the conversion task is formulated as a nonlinear curve fitting problem that is solved using the Levenberg-Marquardt algorithm. The algorithm is tested using orbit predictions for GPS and GLONASS satellites and using actual orbits obtained from precise ephemerides. The median error for a two-hour fitting interval is less than 10 cm; for a four-hour fitting interval the median error is less than 40 cm.