Normalizing Flow-based Differentiable Particle Filters

2024-03-03

IEEE Transactions on Signal Processing

AI Summary

Existing differentiable particle filters for nonlinear, non-Gaussian state-space models are constrained by prespecified distribution families (e.g., Gaussians) or the bootstrap framework, limiting their capacity to capture complex, multimodal posterior densities. To address this, we propose the first end-to-end differentiable particle filtering framework based on conditional normalizing flows. Our method uniformly integrates conditional flows into all key components—state dynamics propagation, proposal distribution design, and observation likelihood modeling—enabling flexible approximation of arbitrarily complex posterior densities and joint sequential state inference and model learning. We provide theoretical guarantees on filter consistency and gradient unbiasedness. Experiments demonstrate substantial improvements in estimation accuracy and robustness over state-of-the-art baselines, particularly in highly nonlinear and multimodal settings.

Technology Category

• Intelligent Robots: State Estimation
• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Probabilistic Circuits and Graphical Models

Application Category

• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• Develops differentiable particle filters using normalizing flows
• Enables adaptive learning without predefined distribution constraints
• Performs sequential state estimation in complex non-linear systems

Innovation

• Normalizing flows for dynamic and proposal models
• Adaptive learning without predefined distribution families
• Differentiable particle filters with valid density estimation