Geometric Projection Particle Filtering under Model Uncertainty

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.