Non-Gaussian Recursive Bayesian Filtering for Outer Planetary Orbilander Navigation

Gaussian estimation filters have successfully aided spacecraft navigation for decades. However, future missions are set to venture into deep-space regimes with significant round-trip light-time telecommunication delays, operate in unstable, quasiperiodic 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 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.

数十年来，高斯估计滤波器（Gaussian estimation filters）已成功助力航天器导航任务。然而，未来深空探测任务将迈入存在显著往返光时通信延迟的深空环境，需在不稳定的准周期轨道（quasiperiodic orbits）上运行，并对外行星卫星开展高精度低空飞越探测。此类复杂轨迹可能需要采用非高斯滤波器（non-Gaussian filters），以在实际测量时序下实现精准估计。为降低新型导航软件测试过程中的固有风险，非高斯滤波器需兼具精准性、高效性与鲁棒性。基于网格的稀疏性贝叶斯估计（Grid-based Bayesian Estimation Exploiting Sparsity）是一种高维Godunov型有限体积法（Godunov-type finite volume method），可高效传播完整的d维概率分布函数（d-dimensional probability distribution function）；相较于当前主流的非高斯滤波器方案，该方法充分满足了前述所有要求。通过一项贝叶斯验证研究可验证上述优势：该研究对土星-土卫二远距顺行轨道（Saturn-Enceladus Distant Prograde Orbit）的状态不确定性进行传播，并融入了非频繁的非线性测量更新环节。