Model-Free Neural State Estimation in Nonlinear Dynamical Systems: A Comparative Study of Neural Architectures and Classical Filters
This work addresses the problem of state estimation in control and decision-making for researchers and practitioners, showing neural models can be competitive without system models, but it is incremental as it builds on existing neural and classical methods.
The study compared model-free neural network architectures with classical filters for state estimation in nonlinear dynamical systems, finding that neural models, especially state-space models, approached the performance of strong nonlinear Kalman filters and outperformed weaker baselines while achieving higher inference throughput.
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.