Satellite onboard orbit propagation using Deprit's radial intermediary

Short-term satellite onboard orbit propagation is required when GPS position measurements are unavailable due to an obstruction or a malfunction. In this paper, it is shown that natural intermediary orbits of the main problem provide a useful alternative for the implementation of short-term onboard orbit propagators instead of direct numerical integration. Among these intermediaries, Deprit's radial intermediary (DRI), obtained by the elimination of the parallax transformation, shows clear merits in terms of computational efficiency and accuracy. Indeed, this proposed analytical solution is free from elliptic integrals, as opposed to other intermediaries, thus speeding the evaluation of corresponding expressions. The only remaining equation to be solved by iterations is the Kepler equation, which in most of cases does not impact the total computation time. A comprehensive performance evaluation using Monte-Carlo simulations is performed for various orbital inclinations, showing that the analytical solution based on DRI outperforms a Dormand-Prince fixed-step Runge-Kutta integrator as the inclination grows.