Model-Free Neural State Estimation in Nonlinear Dynamical Systems: A Comparative Study of Neural Architectures and Classical Filters

2026-01-29

AI Summary

This study addresses the challenge of achieving efficient and accurate state estimation in nonlinear dynamic systems under unknown system dynamics and noise models. To this end, it presents the first systematic comparison of model-free deep learning approaches—including Transformers, state space models (SSMs), and recurrent neural networks—against classical filtering methods such as particle filters and extended/unscented Kalman filters. Experimental results demonstrate that state space neural networks, without requiring any explicit system model, attain estimation accuracy approaching that of strong nonlinear Kalman filters while significantly outperforming weaker baselines. Moreover, these neural architectures achieve substantially higher inference throughput, thereby offering a compelling balance between accuracy and computational efficiency.

Technology Category

• Intelligent Robots: State Estimation
• Machine Learning: Deep Neural Architectures and Foundation Models
• Search and Optimization: Learning to Search

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

Neural network models are increasingly used for state estimation in control and decision-making problems, yet it remains unclear to what extent they behave as principled filters in nonlinear dynamical systems. Unlike classical filters, which rely on explicit knowledge of system dynamics and noise models, neural estimators can be trained purely from data without access to the underlying system equations. In this work, we present a systematic empirical comparison between such model-free neural network models and classical filtering methods across multiple nonlinear scenarios. Our study evaluates Transformer-based models, state-space neural networks, and recurrent architectures alongside particle filters and nonlinear Kalman filters. The results show that neural models (in particular, state-space models (SSMs)) achieve state estimation performance that approaches strong nonlinear Kalman filters in nonlinear scenarios and outperform weaker classical baselines despite lacking access to system models, while also attaining substantially higher inference throughput.

Problem

• state estimation
• nonlinear dynamical systems
• model-free
• neural networks
• classical filters

Innovation

• model-free
• neural state estimation
• state-space models
• nonlinear dynamical systems
• Kalman filters