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

Zhuochen Liu, Hans Walker, Rahul Jain

TL;DR

The paper investigates whether model-free neural estimators can match principled filtering in nonlinear dynamical systems. It conducts a controlled, large-scale comparison across Transformer-based, recurrent, and state-space neural models against EKF, UKF, EnKF, and PF in five nonlinear scenarios, using long-horizon RMSE and robustness metrics. The results show that state-space neural models (e.g., Mamba and Mamba-2) achieve competitive accuracy, closely approaching strong nonlinear filters while delivering substantially higher inference throughput, demonstrating filtering-like behavior learned from data. These findings suggest neural architectures can serve as viable, high-throughput alternatives to classical filters when system models are unavailable, while highlighting data and calibration considerations for uncertainty quantification. The work provides benchmarked evidence and practical insights for integrating neural estimators into real-time state estimation tasks.

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.

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

TL;DR

The paper investigates whether model-free neural estimators can match principled filtering in nonlinear dynamical systems. It conducts a controlled, large-scale comparison across Transformer-based, recurrent, and state-space neural models against EKF, UKF, EnKF, and PF in five nonlinear scenarios, using long-horizon RMSE and robustness metrics. The results show that state-space neural models (e.g., Mamba and Mamba-2) achieve competitive accuracy, closely approaching strong nonlinear filters while delivering substantially higher inference throughput, demonstrating filtering-like behavior learned from data. These findings suggest neural architectures can serve as viable, high-throughput alternatives to classical filters when system models are unavailable, while highlighting data and calibration considerations for uncertainty quantification. The work provides benchmarked evidence and practical insights for integrating neural estimators into real-time state estimation tasks.

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.
Paper Structure (20 sections, 11 equations, 2 figures, 12 tables)

This paper contains 20 sections, 11 equations, 2 figures, 12 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Preliminaries
  4. Nonlinear Dynamical Systems
  5. Bayesian Filtering
  6. Approximate Nonlinear Filtering
  7. Experiment Setup
  8. Scenarios
  9. Models
  10. Training Setup
  11. Evaluation Setup
  12. Evaluation Metrics
  13. Results
  14. RMSE over Time
  15. Aggregated Performance Metrics
  16. ...and 5 more sections

Figures (2)

  • Figure 1: RMSE as a function of timestep across the five scenarios. Curves show median error across runs, with shaded regions indicating interquartile ranges. A shared legend is shown in the bottom-right panel. EnKF is omitted from the Bearings-Only Tracking scenario due to divergence.
  • Figure 2: RMSE under varying observation noise levels across the five scenarios. EnKF is omitted from the Bearings-Only Tracking scenario due to divergence.