Bayesian Benchmarking of GBEES Applied to Outer Planet Orbiter Estimation

Abstract: Moment-based estimation filters have successfully aided spacecraft navigation for decades. However, future missions plan to venture into deep-space regimes with significant round-trip light-time telecommunication delays, operate in unstable, quasi-periodic orbits, and perform highly precise, low-altitude flybys of outer planet moons. These complex trajectories may necessitate ensemble-based filters for accurate estimation over realistic measurement cadences. To mitigate the inherent risk associated with testing novel navigation software, ensemble filters must be accurate, efficient, and robust. Grid-based, Bayesian Estimation Exploiting Sparsity, a high-dimensional Godunov-type finite volume method that efficiently propagates the full $d$-dimensional probability distribution function, demonstrates strong overall performance across all these criteria when compared with the contemporary landscape of filters. These qualities are exhibited via a Bayesian investigation in which the state uncertainty of a Saturn-Enceladus Distant Prograde Orbit is propagated, incorporating infrequent, nonlinear measurement updates. We use the Bhattacharyya coefficient, a non-normal metric for measuring the dissimilarity between distributions, to quantitatively ascertain that in this application, Grid-based, Bayesian Estimation Exploiting Sparsity outperforms the other ensemble filters assessed in accuracy, though it comes at a nontrivial computational cost.

Recommended citation: Hanson, B.L., Ely, T.A., Bewley, T.R., Rosengren, A.J.: Bayesian benchmarking of GBEES applied to outer planet orbiter estimation. Journal of Guidance, Control, and Dynamics 49(1), 240–246 (2026)
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