Normalizing Flow-based Differentiable Particle Filters

TL;DR

This paper introduces a novel differentiable particle filter framework that employs normalizing flows to model dynamic, proposal, and measurement distributions, enabling flexible, density-estimating, and adaptive state estimation in complex environments.

Contribution

It proposes a new differentiable particle filter using normalizing flows, allowing density estimation and flexible learning beyond predefined distribution families.

Findings

Outperforms traditional methods in complex scenarios

Enables density estimation for all models

Demonstrates theoretical properties and practical effectiveness

Abstract

Recently, there has been a surge of interest in incorporating neural networks into particle filters, e.g. differentiable particle filters, to perform joint sequential state estimation and model learning for non-linear non-Gaussian state-space models in complex environments. Existing differentiable particle filters are mostly constructed with vanilla neural networks that do not allow density estimation. As a result, they are either restricted to a bootstrap particle filtering framework or employ predefined distribution families (e.g. Gaussian distributions), limiting their performance in more complex real-world scenarios. In this paper we present a differentiable particle filtering framework that uses (conditional) normalizing flows to build its dynamic model, proposal distribution, and measurement model. This not only enables valid probability densities but also allows the proposed method to adaptively learn these modules in a flexible way, without being restricted to predefined distribution families. We derive the theoretical properties of the proposed filters and evaluate the proposed normalizing flow-based differentiable particle filters' performance through a series of numerical experiments.