A Bayesian Benchmarking of GBEES Applied to Outer Planet Orbiter Estimation

Gaussian 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 planetary moons. These complex trajectories may necessitate non-Gaussian filters for accurate estimation over realistic measurement cadences. To mitigate the inherent risk associated with testing novel navigation software, non-Gaussian 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, sufficiently addresses all these criteria when compared with the contemporary landscape of Gaussian and non-Gaussian filters. These qualities are demonstrated through 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, Gridbased, Bayesian Estimation Exploiting Sparsity outperforms the other non-Gaussian filters assessed in accuracy, though it comes at a nontrivial computational cost.