无需似然函数，用耦合结构实现非线性非高斯滤波的精准逼近。
Coupling-Informed Transport Maps for Bayesian Filtering in Nonlinear Dynamical Systems
- 利用状态与观测的耦合结构设计分块三角运输映射。
- 通过梯度流实现无训练优化，避免粒子坍缩且后验逼近精度高。
- 适用于高维系统，适合复杂非线性动态系统的贝叶斯滤波场景。
提出一种无需似然函数的运输滤波方法，基于状态与观测变量间的耦合关系。通过在运输映射中引入分块三角结构，将滤波的分析步骤重构成真实联合测度与其基于运输的近似之间最大均值差异（MMD）的最小化问题。为克服MMD优化中的非凸性，采用梯度流构造无训练运输滤波器，得到解析形式的运输映射，其对应于MMD的最速下降方向。该方法能准确逼近非高斯滤波后验分布，避免粒子坍缩。提供了近似后验与真实后验间期望MMD的收敛性分析。最后，通过域局部化扩展至高维问题。数值实验表明，在非线性、非高斯场景下，该方法显著优于传统滤波方法。
原文摘要 · Abstract (English)
A likelihood-free transport filtering method is proposed based on the couplings between state and observation variables. By exploiting a block-triangular structure in the transport map, the analysis step of filtering is reformulated as the minimization of the maximum mean discrepancy (MMD) between the true joint measure and its transport-based approximation. To circumvent the non-convexity in the MMD optimization, we introduce a training-free transport filter method via gradient flows, which leads to an analytic computation for the transport map that implies the steepest descent direction of the MMD. The proposed approach accurately approximates non-Gaussian filtering posteriors and avoids particle collapse. We provide a convergence analysis for the expectation of the MMD between the approximated posterior and the truth posterior. Finally, we extend the method to high-dimensional problems through domain localization. Numerical examples demonstrate the superior performance of our approach over conventional filtering methods in nonlinear, non-Gaussian scenarios.
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