In this paper, we present a new ensemble-based filter method by reconstructing the analysis step of the particle filter through a transport map, which directly transports prior particles to posterior particles. The transport map is constructed through an optimization problem described by the Maximum Mean Discrepancy loss function, which matches the expectation information of the approximated posterior and reference posterior. The proposed method inherits the accurate estimation of the posterior distribution from particle filtering while gives an extension to high dimensional assimilation problems. To improve the robustness of Maximum Mean Discrepancy, a variance penalty term is used to guide the optimization. It prioritizes minimizing the discrepancy between the expectations of highly informative statistics for the reference posteriors. The penalty term significantly enhances the robustness of the proposed method and leads to a better approximation of the posterior. A few numerical examples are presented to illustrate the advantage of the proposed method over ensemble Kalman filter.

翻译：本文提出了一种新的基于集成的滤波方法，该方法通过传输映射重构粒子滤波的分析步骤，直接将先验粒子传输至后验粒子。该传输映射通过最大均值差异损失函数描述的优化问题构建，该函数匹配近似后验与参考后验的期望信息。所提方法继承了粒子滤波对后验分布的精确估计特性，同时可扩展至高维同化问题。为增强最大均值差异的鲁棒性，采用方差惩罚项引导优化过程，优先最小化参考后验高信息量统计量的期望差异。该惩罚项显著提升了方法的鲁棒性，并实现了更优的后验近似。通过若干数值算例，展示了所提方法相较于集成卡尔曼滤波的优势。