Flow-based Bayesian filtering for high-dimensional nonlinear stochastic dynamical systems

TL;DR

This paper introduces a flow-based Bayesian filter that leverages normalizing flows to efficiently perform filtering in high-dimensional, nonlinear stochastic systems, overcoming limitations of traditional methods.

Contribution

The paper proposes a novel flow-based Bayesian filtering framework that constructs a latent linear state-space model using normalizing flows, enabling efficient and data-driven filtering without prior system knowledge.

Findings

Demonstrates superior accuracy over existing methods.

Shows improved computational efficiency.

Validates effectiveness through numerical experiments.

Abstract

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.