Flow-based linear embedding for Bayesian filtering of nonlinear stochastic dynamical systems

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.