综合无奇点根数和坐标旋转的广播星历拟合及其性能评估

The Broadcast Ephemeris Fitting Algorithm Combining No Singularity Orbital Elements with Coordinate Rotation and Its Performance Evaluation

将无奇点根数和坐标旋转方法综合运用到地球静止轨道(geostationary earth orbit,GEO)卫星的18参数星历拟合,解决GEO卫星的小偏心率奇点和小倾角奇点问题。基于5颗北斗在轨GEO卫星1a的轨道数据,分析全年星历拟合精度和稳定性,对卫星进出地影的拟合精度进行定量分析,针对Δn参数超限问题,比较绕X轴旋转5°和55°的Δn参数变化范围。结果表明,2~4h的拟合弧长5颗GEO卫星的星历拟合精度最大为3cm,迭代次数最多为5次;拟合弧长越长,拟合精度越低,迭代次数更少;当拟合弧段包含进出地影轨道时,拟合精度降低;旋转55°比旋转5°Δn参数的变化范围减少一个数量级,Δn参数全年无超限现象。

No singularity orbital elements combination with coordinate rotation is applied to 18-parameter ephemeris fitting model for GEO satellites in this article, which synchronously solve the singularity problem caused by small eccentricity and small inclination. Based on one year data of five Beidou GEO satellites in or- bit, the fitting accuracy and stability are analyzed, and during the eclipse the fitting accuracy is quantitatively analyzed. Finally aiming at parameter＇s exceeding limitation, the range of variation of parameters between 55° and 5° rotation with X axis is compared. The results show that in 2-4 h fitting arc the maximum fitting error for five GEO satellites is of only 3 cm, and the number of iterations is up to 5 times. The longer the fitting arc the worse the accuracy, and the longer the fitting are the fewer iterations. During the eclipse, the fitting accu- racy gets worse. The range of variation of parameters of 55° rotation with X axis is reduced by one order of magnitude compared with 5° rotation with X axis. There are no parameters exceeding limitation in the overall year.