模型不确定性下的几何投影粒子滤波
Geometry-Consistent Bayesian Filtering under Structural Model Uncertainty: A Geometric Projection Particle Filter
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中文总结 AI 辅助
研究针对自主GNC系统中模型不确定性下的非线性状态估计问题，提出几何投影粒子滤波器，通过将动力学投影到测量一致子空间减少不匹配，在月球下降导航场景中评估，有效减少粒子退化，提高估计精度和鲁棒性。
中文摘要 AI 辅助
在自主制导、导航与控制（GNC）系统中，结构模型不确定性下的非线性状态估计仍是核心挑战。经典估计器按假设动力学传播状态并通过后验校正纳入测量值，模型不匹配时会导致创新偏差、估计器不一致及粒子退化。本文提出几何投影粒子滤波器（GPF），这是一个测量信息框架，观测几何直接影响状态传播。该方法将名义漂移动力学投影到测量一致子空间，强制动力学与观测局部兼容，产生几何一致的提议过程，在加权前减少有效不匹配并通过测度变换公式保留贝叶斯后验。开发了连续时间公式，引入几何共态变量表征不匹配引起的不一致，在正确建模下条件均值为零。结果表明滤波误差由与测量一致子空间正交的不匹配分量控制，粒子一致性以标准蒙特卡罗速率收敛。在部分可观测和持续不匹配的月球下降导航场景中评估该方法，结果显示粒子退化显著减少，有效样本量持续，在标准粒子滤波器发散的情况下估计误差有界，精度提高达一个数量级。这些发现表明，传播过程中强制几何兼容性为提高模型不确定性下非线性粒子滤波的鲁棒性和一致性提供了一种有原则的机制。
英文摘要
Nonlinear state estimation under structural model uncertainty remains a fundamental challenge in autonomous Guidance, Navigation, and Control (GNC) systems. Conventional Bayesian filtering separates state propagation from measurement correction, allowing model mismatch to accumulate during propagation, resulting in proposal--likelihood inconsistency, particle degeneracy, and degraded estimation accuracy. Existing approaches primarily improve proposal distributions or weighting strategies without explicitly incorporating measurement geometry into state propagation. This paper introduces a geometry-consistent Bayesian filtering framework that incorporates measurement geometry directly into the propagation process. The nominal drift is projected onto the measurement-consistent subspace, yielding a geometry-consistent proposal while preserving the Bayesian posterior through a rigorous change-of-measure formulation. A Geometric Projection Particle Filter (GPF) is developed together with a geometric co-state that quantifies instantaneous dynamics--measurement inconsistency. Theoretical analysis establishes existence and uniqueness of the projected dynamics, posterior preservation, standard Monte Carlo convergence of the particle approximation, and robustness under structural model uncertainty. The framework is validated using lunar descent navigation under partial observability and persistent model uncertainty. Compared with the bootstrap particle filter and conventional Gaussian filtering methods, GPF consistently achieves higher effective sample size and lower estimation error. These results demonstrate that geometry-consistent propagation provides a principled, computationally efficient, and theoretically grounded framework for robust nonlinear Bayesian filtering.
