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, while sequential Monte Carlo methods are computationally intensive and prone to particle degeneracy in high dimensions. Although generative models in machine learning have made significant progress in modeling high-dimensional non-Gaussian distributions, their inefficiency in online updating limits their applicability to filtering problems. To address these challenges, we propose a flow-based Bayesian filter (FBF) that integrates normalizing flows to construct a novel latent linear state-space model with Gaussian filtering distributions. This framework facilitates efficient density estimation and sampling using invertible transformations provided by normalizing flows, and it enables the construction of filters in a data-driven manner, without requiring prior knowledge of system dynamics or observation models. Numerical experiments demonstrate the superior accuracy and efficiency of FBF.

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，而序列蒙特卡洛方法计算量大，在高维情况下容易发生粒子退化。尽管机器学习中的生成模型在高维非高斯分布建模方面取得了显著进展，但其在线更新效率低下，限制了它们在滤波问题中的应用。为解决这些挑战，我们提出了一种基于流的贝叶斯滤波器（FBF），它通过整合归一化流来构建一种新颖的潜在线性状态空间模型，该模型具有高斯滤波分布。该框架利用归一化流提供的可逆变换，实现了高效的密度估计与采样，并能以数据驱动的方式构建滤波器，无需预先了解系统动力学或观测模型。数值实验证明了FBF在精度和效率上的优越性。