Computing satellite velocity using the broadcast ephemeris

Abstract

GPS has been used for applications where satellite velocities are needed as well as satellite positions. Traditionally, the position was determined from noisy code pseudoranges while the velocity came from delta carrier phase measurements. This motivates the need to have a velocity model to accompany the velocity data. With velocity data, the velocity states are directly observed in a Kalman filter. While processing can be carried out using either post-processed or predicted ephemerides from the international GPS service (IGS), it is convenient to use broadcast ephemerides for real-time applications. In this paper, a set of equations is derived which will allow one to compute the velocity vector for a GPS satellite using time derivatives of the Keplerian elements and correction terms broadcast from the GPS satellites, as described in the GPS interface control document (ICD-GPS-200). It will be assumed that the reader is familiar with the equations listed in this document for computing the X, Y, Z earth-centered, earth-fixed (ECEF) coordinates of a satellite (the reader may obtain a PDF version of the ICDGPS-200 from the US Coast Guard website at http:// www.navcen,uscg.gov/pubs/gps/icd200/default.htm). A complete main program written in C is included on the GPS Toolbox website (http://www.ngs.noaa.gov/gps-toolbox) to illustrate how these equations can be easily incorporated into source code to yield accurate velocity components. As a check, the velocity calculations were done numerically as well. Derivation of the velocity equations