In this presentation, first I would like to give some introduction for the background of numerical satellite orbit propagation, and the implementations of orbit prediction for GNSS satellites on mobile devices. Secondly, explain the algorithms to correct GNSS satellites' initial states for orbit prediction with Broadcast Ephemeris. This will mention the details of initial states correction for GlONASS orbits, and how to extract Earth Orientation Parameters (EOP) and correct initial states for GPS orbits. Finally, introduce some other positioning projects of our research group.