Thomas Dearing, ARKA Group; Isaiah Owsley, ARKA Group; Piyush Mehta, West Virginia University
Keywords: Astrodynamics, Unscented Transform, Constraints, Unscented Kalman Filtering
Abstract:
This work examines a novel approach for accurately propagating orbit estimates whose uncertainty distributions intersect implicit model or domain constraints. This approach addresses practical challenges for tracking small debris in LEO where position uncertainty expands below the altitude floor of popular gravity and atmospheric drag models during periods of poor observability. To accurately and feasibly estimate these distributions, our approach actively adjusts the sampling pattern (sigma points) of the Unscented Transform (UT) to constrain propagated trajectories to the feasible ranges of each force model. This Model-Constrained Unscented Transform (MCUT) offers several advantages over traditional linearization and projection approaches applied in constrained Kalman Filtering. Firstly, by ensuring that the representative trajectories for each distribution remain strictly feasible under each force model, the MCUT avoids approximation errors from extrapolating those models (potentially nonphysically) beyond the constraint boundary while maintaining the nonlinear estimation capabilities of the classic UT. Additionally, the MCUT enables the definition of probabilistic dismissal criteria, allowing for the potential recovery of classically infeasible orbit estimates when new observations are acquired. To evaluate the accuracy, robustness, and numerical cost of this approach, the MCUT is compared against prevalent estimation approaches for an example LEO orbit intersecting a variable altitude floor constraint. This comparison yields the following key conclusions: (1) the MCUT successfully propagates all test distributions whose mean remains feasible, (2) the estimation error of the MCUT is bounded between that of the linear (state-transition-matrix) projection and the (unconstrained) UT, and (3) the estimation error of the MCUT increases as the distribution mean approaches the constraint boundary. These results form a compelling argument for the application of the MCUT in LEO debris tracking applications.
Date of Conference: September 16-19, 2025
Track: Astrodynamics