Real-Time Determination of a BDS Satellite's Velocity Using the Broadcast Ephemeris

This paper studies the algorithms for determining a BDS satellite's velocity using the broadcast ephemeri. Firstly, by taking the time derivatives of the Kepler orbit elements and the correction terms, the algorithm comprises close-form analysis formulas and the processing steps for directly computing a BDS satellite's instant velocity using the broadcast ephemeris is derived, and its validity is verified by test. Further, it is discussed on how the size of the differential time step affects the accuracy of the velocity results computed using the position differential algorithm. To investigate the suitable magnitudes of the differential time step, a comprehensive test is performed. In this test, several BDS satellites with different types were specially chosen and the real broadcast ephemeris was used to determine the velocity vectors both by the position differential algorithm and the direct algorithm, and the results were compared. The 12hr comparison test illustrates that the differential time step magnitude suitable for computing a BDS GEO satellite's velocity is 1s and the max residual is less than 0.0001mm/s. The differential time step suitable for a BDS MEO/IGSO Satellite is 100ms and the max residual is less than 0.001mm/s.