LOBEFIT: LEO satellite broadcast ephemeris fitting open-source software based on automatic differentiation technique

LEO (Low Earth Orbit)-based PNT (Positioning, Navigation and Timing) has become a research topic of much interest and a focus of development. As LEO satellites for PNT are expected to independently provide space-time references in the future, similar to Global Navigation Satellite System (GNSS) satellites, the accurate determination of their broadcast ephemerides becomes crucial. This paper proposes the open-source software LOBEFIT (LeO satellite Broadcast Ephemeris Fitting), which utilizes the automatic differentiation technique to fit LEO satellite broadcast ephemeris parameters. The primary advantage of this software lies in its ability to allow users to focus on implementing various broadcast ephemeris models without the need to manually derive complex partial derivatives with respect to broadcast ephemeris parameters. Centimeter-level fitting accuracy can be achieved by selecting appropriate broadcast models for different LEO satellites using this software. The paper provides the description, use and impact of the LOBEFIT software in satellite navigation.