Higher-Order Tensor-Based Deferral of Gaussian Splitting for Orbit Uncertainty Propagation
G. Andrew Siciliano, Keith A. LeGrand, Jackson Kulik
TL;DR
This work tackles the challenge of propagating orbital uncertainty through nonlinear dynamics by introducing hotdogs, a deferred Gaussian-splitting algorithm that couples with higher-order splitting to maintain accuracy while reducing computational cost. By leveraging flow-map compositions and second-order moment propagation, the method reuses precomputed derivatives (stm and stt) and defers splits until nonlinearities exceed a tolerance, yielding substantial runtime savings without sacrificing fidelity across diverse orbital regimes. The approach is evaluated on GEO, LEO, Molniya, and Earth–Moon L1 halo scenarios, showing that DS-2/DS-3 variants closely match immediate splitting in accuracy while delivering large speedups, and that second-order propagation consistently improves moment accuracy, especially in strongly nonlinear cases. Overall, this framework advances efficient and accurate orbit uncertainty propagation, enabling more scalable space-domain awareness analyses.
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 four representative test cases, including a low Earth orbit, a geostationary orbit, a Molniya orbit, and a multi-body cislunar orbit.