Multi-Element Trajectory Models for Satellite Tour Missions

摘要

Polynomial chaos expansions (PCEs) are useful for improving tractability and reducing computational cost when propagating uncertainty through nonlinear system dynamics. However, global PCEs may fail when applied to systems that exhibit non-smooth, multi-modal, or discontinuous behavior. Multi-element expansion models can achieve better performance for such systems by decomposing the random input space and generating individual PCEs for each component element. This study uses an adaptive approach to generating multi-element PCEs for the modeling of uncertainty propagation both for a spacecraft in a Molniya orbit about the Earth and for a spacecraft conducting a double-flyby during a satellite tour at an outer planet. It is shown that, in these applications, the multi-element models can achieve much more rapid convergence in the final state statistics compared to a Monte Carlo simulation and 1-2 orders of magnitude improvement in accuracy over a global PCE.