To realize GPS orbit determination for low earth arbit satellites, a navigationalgorithm called sequential UD covariance factorization algorithm is proposed inthis paper. Formulas of UD algorithm are given completely, and state equationsand measurement equations are derived in detail in the paper. Mathematical modelof the navigation system is built, which is composed of nine state vectors and eightobservation vectors. Finally, numerical simulation experiments are conducted. Simulation results indicate that UD algorithm can not only provide high positioningprecision but also be fit for computers onboard low earth orbit satellites.