Algorithm design for long-term GPS satellite orbit prediction

After GPS receivers being shot down for a long time, the time of booting may be too long due to the difficulty in obtaining the satellite´s position. In order to solve this problem and reduce the booting time, we use the GPS satellites positions prediction in this paper to extend the useable time of GPS ephemeris such that the GPS receivers can be maintained in the condition of hot start. Instead of the curve-fitting method, Newton´s equations of motion for the satellite is integrated to predict the position of the GPS satellites in a few days. Various effects, including that of the non-spherical Earth, the Solar-Lunar gravitational force, Solar radiation pressure, and attitude motion effect, are taken into account. The ephemeris data in the GPS receivers is in the frame of WGS-84, but the Newton´s equation is calculated in an inertial frame. Therefore, we have to adopt the appropriate coordinate transformation between the two frames by including the effect of the precession, the nutation, and the polor motion of the Earth. The forth-order Runge Kutta method is used to solve the Newton´s equation. From the numerical result, it is shown that the prediction error can be significantly reduced after those perturbations being included.