Satellite onboard orbit propagation using Deprit’s radial intermediary

Abstract

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.

Intermediary LEO propagation including higher order zonal harmonics

“…Output: time t i+1 and state vector (r(t i+1 ), θ (t i+1 ), ν(t i+1 ), R(t i+1 ),Θ (t i+1 ), N 0 ) 21: end while applications to onboard orbit propagation. Therefore, we assume the same scenario as in Gurfil and Lara (2014), in which the Cowell integration is carried out with a fourth-order R-K integration using a constant step-size of one second.…”

On J2 short-term orbit predictions in terms of KS elements

“…Garfinkel [7] and Aksnes [1] employed the use of intermediary orbit to obtain a solution in terms of Delaunay's variables. Deprit's Radial Intermediary [5] is a particular canonical transformation theory of Lie type to remove the parallactic factors by the elimination of parallax, which was utilized to produce a viable alternative for the onboard orbit propagators [8]. The classical Newtonian equations, being unstable, are not very ideal choice for numerical integration as well as for development of analytical theories.…”

Constant, Radial Low-Thrust Problem Including First-Order Effects of J2

“…Since the dynamics of the J 2 problem are non-integrable (except for equatorial motion), the only possible closed-form solutions are obtained by approximating or averaging the full J 2 gravitational potential [15]. Among the many possibilities to approximate the J 2 problem, the concept of intermediary orbits is particularly useful.…”