Bayesian filtering for high-dimensional nonlinear stochastic dynamical systems is a fundamental yet challenging problem in many fields of science and engineering. Existing methods face significant obstacles: Gaussian-based filters struggle with non-Gaussian distributions, sequential Monte Carlo methods are computationally intensive and prone to particle degeneracy in high dimensions, and deep learning approaches often fail to balance accuracy and efficiency in complex filtering tasks. To address these challenges, we propose a flow-based Bayesian filter (FBF) that integrates normalizing flows to construct a latent linear state-space model with Gaussian filtering distributions. This framework enables efficient density estimation and sampling through invertible transformations provided by normalizing flows, which can be learned directly from data, thereby eliminating the need for prior knowledge of system dynamics or observation models. Numerical experiments demonstrate the advantages of FBF in terms of both accuracy and efficiency.

翻译：高维非线性随机动力系统的贝叶斯滤波是科学与工程众多领域中的一个基础性且具有挑战性的问题。现有方法面临显著障碍：基于高斯分布的滤波器难以处理非高斯分布，序列蒙特卡洛方法计算量大且在高维情况下易受粒子退化影响，而深度学习方法在复杂滤波任务中往往难以平衡精度与效率。为应对这些挑战，我们提出了一种基于流的贝叶斯滤波器，该滤波器集成标准化流以构建具有高斯滤波分布的潜在线性状态空间模型。该框架通过标准化流提供的可逆变换，实现了高效的密度估计与采样，这些变换可直接从数据中学习，从而无需系统动力学或观测模型的先验知识。数值实验证明了该滤波器在精度和效率方面的优势。