X射线脉冲星自主导航的卫星运动方程

基于X射线脉冲星的卫星自主导航模型中, 无论从理论上还是从测量精度方面考虑, 光子到达时间测量方程(观测方程)和卫星运动方程(状态方程)应在同一参考系中讨论. 在DSX体系中太阳系质心系是惯性系, 可以使用现行时间测量方程, 但卫星摄动加速度中除了地球多极矩、日月引力摄动和太阳光压三项外, 还应考虑相对论修正项, 计算表明该修正项导致卫星位置误差在10m量级. 而地心系是非惯性系, 在此系中卫星运动方程中的相对论效应导致卫星误差在10 cm量级, 因而可以忽略, 但要将BCRS的时间测量方程转换到GCRS中. 在此基础上建立的导航模型较为精确和完整. 

Motion Equation of Satellite in XNAV

In X-ray pulsar-based navigation model for satellite autonomous position determination, whether in theory or in view of measurement precision, the equations of time-of-arrival measurement and satellite's motion, observation equation and state equation must all base on same reference system. In the solar system Barycentric Reference Systems (BCRS), that is an inertial frame in DSX system, current time measurement equation can be used, but the perturbing acceleration of satellite consists not only the multipole of Earth, gravitation perturbation of Sun and Moon and radiation pressure of Sun, but also relativistic effect. Because the satellite's position error caused by relativistic effect is about 10 meter in quantity order. In the Geocentric Reference Systems (GCRS), that is a non-inertial frame, the relativistic effect term can be neglected in the motion equation of satellite. Because the error caused by this effect is about 10 centimeter. But time measurement equation in BCRS must transform to GCRS. As a result of the above, the navigation model can be more precision and complete.