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.