The particle filter (PF) and the ensemble Kalman filter (EnKF) are widely used for approximate inference in state-space models. From a Bayesian perspective, these algorithms represent the prior by an ensemble of particles and update it to the posterior with new observations over time. However, the PF often suffers from weight degeneracy in high-dimensional settings, whereas the EnKF relies on linear Gaussian assumptions that can introduce significant approximation errors. In this paper, we propose the Adversarial Transform Particle Filter (ATPF), a novel filtering framework that combines the strengths of the PF and the EnKF through adversarial learning. Specifically, importance sampling is used to ensure statistical consistency as in the PF, while adversarially learned transformations, such as neural networks, allow accurate posterior matching for nonlinear and non-Gaussian systems. In addition, we incorporate kernel methods to ease optimization and leverage regularization techniques based on optimal transport for better statistical properties and numerical stability. We provide theoretical guarantees, including generalization bounds for both the analysis and forecast steps of ATPF. Extensive experiments across various nonlinear and non-Gaussian scenarios demonstrate the effectiveness and practical advantages of our method.

翻译：粒子滤波器（PF）与集合卡尔曼滤波器（EnKF）被广泛用于状态空间模型中的近似推断。从贝叶斯视角看，这些算法通过粒子集合表示先验分布，并随时间利用新观测将其更新为后验分布。然而，PF在高维场景中常面临权值退化问题，而EnKF依赖于线性高斯假设，可能引入显著的近似误差。本文提出对抗变换粒子滤波器（ATPF），这是一种新颖的滤波框架，通过对抗学习结合了PF与EnKF的优势。具体而言，该方法采用重要性采样以保证如PF般的统计一致性，同时利用对抗学习得到的变换（如神经网络）实现对非线性非高斯系统的精确后验匹配。此外，我们引入核方法以简化优化过程，并基于最优传输的正则化技术来提升统计性质与数值稳定性。我们提供了理论保证，包括ATPF分析步骤与预报步骤的泛化误差界。在多种非线性非高斯场景下的大量实验证明了本方法的有效性与实用优势。