Higher-Order Tensor-Based Deferral of Gaussian Splitting for Orbit Uncertainty Propagation

Abstract: Accurate propagation of orbital uncertainty is essential for a range of applications within space domain awareness. Adaptive Gaussian mixture-based approaches offer tractable nonlinear uncertainty propagation through splitting mixands to increase resolution in areas of stronger nonlinearities, as well as by reducing mixands to prevent unnecessary computational effort. Recent work introduced principled heuristics that incorporate information from the system dynamics and initial uncertainty to determine optimal directions for splitting. This paper develops adaptive uncertainty propagation methods based on these robust splitting techniques. A deferred splitting algorithm tightly integrated with higher-order splitting techniques is proposed and shown to offer substantial gains in computational efficiency without sacrificing accuracy. Second-order propagation of mixand moments is also seen to improve accuracy while retaining significant computational savings from deferred splitting. Different immediate and deferred splitting methods are compared in three representative test cases, including a geostationary orbit, a Molniya orbit, and a periodic three-body orbit.