Autonomous satellite orbit prediction

A method to predict satellite orbits in a GPS device without a network connection is presented. The motivation for this work was to reduce time to first fix when assistance data is not available. The orbit of a satellite is predicted by numerically integrating the differential equation that models its motion. The initial position and velocity values used in prediction correspond to those received from the broadcast when the device was last operated. These initial values are given in the Earth centered, Earth fixed reference frame and have to be transformed into an inertial reference frame prior to substitution into the equation of motion and subsequent integration. For this purpose, one needs to predict the movement of Earth’s rotation axis with respect to both space (nutation and precession) and to the Earth’s crust (polar motion). Using precise ephemeris as the initial condition, we found that this kind of model gave quite accurate prediction results. However, the results were worse when initial conditions were computed from the less accurate broadcast ephemeris which, unfortunately, is the only ephemeris available to the navigation device without a network connection. In addition, we were not able to find a model that would be able to predict Earth’s polar motion with sufficient accuracy within the assumed lifetime of the device. Without the polar motion parameters, one cannot do the transformation from ECEF to an inertial reference frame. In this paper we will present a method to improve the accuracy of the initial velocity of the satellite computed from the broadcast and simultaneously solve the unknown polar motion parameters. Tests of our algorithm show that in 95%of the cases the error in satellite’s predicted position stays under 21 meters for one day and under 94 meters for three days.