RCUKF

Abstract

Accurate modeling is crucial in many engineering and scientific applications, yet obtaining a reliable process model for complex systems is often challenging. To address this challenge, we propose a novel framework, reservoir computing with unscented Kalman filtering (RCUKF), which integrates data-driven modeling via reservoir computing (RC) with Bayesian estimation through the unscented Kalman filter (UKF). The RC component learns the nonlinear system dynamics directly from data, serving as a surrogate process model in the UKF prediction step to generate state estimates in high-dimensional or chaotic regimes where nominal mathematical models may fail. Meanwhile, the UKF measurement update integrates real-time sensor data to correct potential drift in the data-driven model. We demonstrate RCUKF effectiveness on well-known benchmark problems and a real-time vehicle trajectory estimation task in a high-fidelity simulation environment.

Model Architecture

RCUKF architecture

Results

Standard RC vs RCUKF trajectories for next-state prediction of Lorenz System on 700 data points

Standard RC vs RCUKF trajectories for next-state prediction of Rössler System on 700 data points

Standard RC vs RCUKF trajectories for next-state prediction of Mackey–Glass Time Series on 700 data points

Real-time Lissajous tracking of a car in the MIT FlightGoggles simulation environment

Citation

@misc{anurag2025rcukfdatadrivenmodelingmeets,
      title={RCUKF: Data-Driven Modeling Meets Bayesian Estimation}, 
      author={Kumar Anurag and Kasra Azizi and Francesco Sorrentino and Wenbin Wan},
      year={2025},
      eprint={2508.04985},
      archivePrefix={arXiv},
      primaryClass={cs.LG},
      url={https://arxiv.org/abs/2508.04985}, 
}