Geometric Projection Particle Filtering under Model Uncertainty

2026-07-20

AI Summary

This work addresses bias, inconsistency, and particle degeneracy in nonlinear state estimation arising from model structural uncertainty by proposing the Geometric Projection Filter (GPF). The method uniquely integrates observation geometry explicitly into the state propagation process, introducing geometric costate variables and a measure transformation within a continuous-time framework to construct an observation-driven proposal mechanism. This projects the nominal dynamics onto a subspace consistent with the observations, thereby reducing model–observation mismatch prior to particle weighting. Experimental results demonstrate that GPF significantly mitigates particle degeneracy in model-mismatch scenarios such as lunar descent navigation, maintains a high effective sample size, ensures bounded estimation error, and achieves nearly an order-of-magnitude improvement in accuracy over standard particle filters, thereby preserving Bayesian posterior consistency and robustness.

Abstract

Nonlinear state estimation under structural model uncertainty remains a central challenge in autonomous Guidance, Navigation, and Control (GNC) systems. Classical estimators propagate states using assumed dynamics and incorporate measurements through posterior correction, which under mismatch leads to biased innovations, estimator inconsistency, and particle degeneracy due to proposal--likelihood mismatch. This paper presents the \emph{Geometric Projection Particle Filter (GPF)}, a measurement-informed framework in which observation geometry directly influences state propagation. The method projects nominal drift dynamics onto the measurement-consistent subspace, enforcing local compatibility between dynamics and observations. This yields a geometry-consistent proposal process that reduces effective mismatch prior to weighting while preserving the Bayesian posterior via a change-of-measure formulation. A continuous-time formulation is developed, introducing a geometric co-state variable that characterizes mismatch-induced inconsistency and has zero conditional mean under correct modeling. It is shown that filtering error is governed by the component of mismatch orthogonal to the measurement-consistent subspace, and particle consistency is established with convergence at the standard Monte Carlo rate. The approach is evaluated on lunar descent navigation scenarios with partial observability and persistent mismatch. Results demonstrate significant reduction in particle degeneracy, sustained effective sample size, and bounded estimation error in regimes where standard particle filters diverge, achieving up to an order-of-magnitude improvement in accuracy. These findings show that enforcing geometric compatibility during propagation provides a principled mechanism for improving robustness and consistency in nonlinear particle filtering under model uncertainty.

Problem

• model uncertainty
• nonlinear state estimation
• particle degeneracy
• estimator inconsistency
• Guidance, Navigation, and Control

Innovation

• Geometric Projection Particle Filter
• model uncertainty
• measurement-consistent subspace
• particle degeneracy
• nonlinear state estimation