第二类无奇点根数的北斗历书参数设计

为统一北斗三类卫星的历书拟合算法，提出基于第二类无奇点根数进行历书参数设计的方法，设计了以倾角向量变率作为摄动参数的历书参数模型，并给出新的历书模型的用户使用算法。利用覆盖2013年全年的实际在轨卫星的数值轨道进行了历书拟合试验。结果表明,地球静止轨道（GEO）和倾斜地球同步轨道（IGSO)卫星的拟合位置误差为2~4km，拟合用户距离误差（URE）约为1km，中圆地球轨道（MEO）卫星的拟合位置误差为1~2km，拟合URE约为500m。通过分析6个轨道根数和2个摄动参数全年的变化范围，对新历书模型进行量化单位和占用比特位的通信接口设计,定量分析量化单位对历书表达精度的影响。结果表明，参数截断后对位置误差的影响小于50m，对URE误差的影响小于5m。因此，历书量化误差对信号捕获以及首次定位时间带来的影响可以忽略不计。

Almanac Designing with Second Class of Nonsingular Orbital Elements for BeiDou Navigation Satellite System

In order to unify the almanac fitting algorithm for three kinds of the satellites of the BeiDou navigation satellite system, the method of designing the almanac parameters based on the second class of nonsingular orbital elements is proposed. The rate of the inclination vector is designed for the perturbation parameters and the user algorithm of the new almanac model is provided. The almanac fitting test is carried out based on the numerical orbits of the BeiDou satellites in orbit throughout 2013. The results show that the fitting position error for geostationary Earth orbit (GEO) and inclined geosynchronous satellite orbit(IGSO) is from 2 to 4km and the fitting user range error (URE) is about 1km. The fitting position error for medium Earth orbit(MEO) is from 1 to 2km and the fitting URE is about 0.5km. Through the analysis for the 6 orbital elements parameter variation range, the interface about scale factor and effective range are designed. The quantitative error for the almanac expression is analyzed, and the results show that the position error caused by the truncation is less than 50m, and the URE caused by the truncation is less than 5m. Therefore, the influence of the almanac quantitative error on signal capture and TTFF (Time to first fix)can be ignored.