Low Earth orbit satellites with satellite navigation receiver use onboard navigation filters for filtering measurement signals and for orbit prediction under signal loss. Precision satellite dynamic models, core of the navigation filter, are studied and a computation program is developed. Gravity acceleration, precision coordinate transform, third-body gravity, atmospheric drag, and solar radiation pressure models are combined into an orbit prediction algorithm, and a proven precision orbit determination software is used to validate the program. Orbit prediction accuracy is analyzed with simulated and flight orbit data. The program meets an accuracy level for onboard real-time navigation filter.