北斗GEO卫星实时求速算法研究

An Algorithm for Realtime Computing of the Velocity of BDS GEO Satellites

以北斗系统空间信号接口控制文件中规定的卫星位置计算标准算法为基础,研究了采用北斗广播星历实时计算北斗GEO(Geostationary Earth Orbit,地球静止轨道)卫星速度的算法。首先,通过将开普勒参数和摄动改正项对时间求导,给出了计算北斗GEO卫星瞬时速度的直接求速算法并进行了验证测试。接着,探讨了微分步长对北斗GEO卫星位置微分求速精度的影响。进一步,采集真实北斗GEO卫星广播星历数据,选择代表卫星,采取不同微分步长,分别按照位置微分与直接求速计算卫星速度,并进行了比对测试。验证测试结果证明了北斗GEO卫星直接求速算法的理论正确性,该算法可作为计算GEO卫星瞬时速度的标准算法;比对测试结果则表明适用于北斗GEO卫星位置微分求速的合理微分步长应为1s。

Based on the standard algorithm for computing a satellite＇s position described in the BDS （BeiDou System） ICD （Interface Control Document）, an algorithm for computing the velocity vector of a BDS GEO （Geostationary Earth Orbit） satellite in real time using ephemeris broadcast by BDS is studied. First, an algorithm for direct com- puting of a BDS GEO satellite＇s instant velocity vector using the broadcast ephemeris was derived by the way of time derivatives of the Kepler elements and perturbation correction terms, and its validation was done through testing. Then, discussions are given on how the differential time step affects the accuracy of a BeiDou GEO satellite＇s velocity computed using the position differential algorithm. Furthermore, the velocity vectors of representative BeiDou GEO satellites were computed and compared using both the position differential algorithm with different time steps and the direct algorithm. Validation test shows that the direct algorithm is theoretically correct and can be used as the standard algorithm for computing a BDS GEO satellite＇s instant velocity. As shown by the comparison and test results, the applicable differential time step for computing a BeiDou GEO satellite＇s velocity is 1 s.