Orbit and uncertainty propagation: a comparison of Gauss–Legendre-, Dormand–Prince-, and Chebyshev–Picard-based approaches

Abstract

We present a new variable-step Gauss–Legendre implicit-Runge–Kutta-based approach for orbit and uncertainty propagation, VGL-IRK, which includes adaptive step-size error control and which collectively, rather than individually, propagates nearby sigma points or states. The performance of VGL-IRK is compared to a professional (variable-step) implementation of Dormand–Prince 8(7) (DP8) and to a fixed-step, optimally-tuned, implementation of modified Chebyshev–Picard iteration (MCPI). Both nearly-circular and highly-elliptic orbits are considered using high-fidelity gravity models and realistic integration tolerances. VGL-IRK is shown to be up to eleven times faster than DP8 and up to 45 times faster than MCPI (for the same accuracy), in a serial computing environment. Parallelization of VGL-IRK and MCPI is also discussed.