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.

翻译：基于状态与观测变量之间的耦合关系，提出一种无似然传输滤波方法。通过利用传输映射中的块三角结构，将滤波分析步骤重构为真实联合测度与其基于传输的近似之间最大均值差异的最小化问题。为规避MMD优化中的非凸性，引入一种基于梯度流的无训练传输滤波方法，该方法可实现传输映射的解析计算，该映射隐含了MMD的最速下降方向。所提方法能精确逼近非高斯滤波后验分布，并避免粒子崩塌。我们给出了近似后验与真实后验之间MMD期望的收敛性分析。最后，通过区域局域化将该方法推广至高维问题。数值实验表明，在非线性非高斯场景下，本方法优于传统滤波方法。