2024/02/07 by Tobias M. Wolff, Wolff, Tobias M., Victor G. Lopez +3
Computer Science · Engineering · #Advanced Measurement and Detection Methods #FOS: Electrical engineering #Inertial Sensor and Navigation #Systems and Control (eess.SY) #Target Tracking and Data Fusion in Sensor Networks #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2402.04665
openalex publication_date 2024/02/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
In this paper, we propose a novel Gaussian process-based moving horizon estimation (MHE) framework for unknown nonlinear systems. On the one hand, we approximate the system dynamics by the posterior means of the learned Gaussian processes (GPs). On the other hand, we exploit the posterior variances of the Gaussian processes to design the weighting matrices in the MHE cost function and account for the uncertainty in the learned system dynamics. The data collection and the tuning of the hyperparameters are done offline. We prove robust stability of the GP-based MHE scheme using a Lyapunov-based proof technique. Furthermore, as additional contribution, we derive a sufficient condition under which incremental input/output-to-state stability (a nonlinear detectability notion) is preserved when approximating the system dynamics using, e.g., machine learning techniques. Finally, we illustrate the performance of the GP-based MHE scheme in two simulation case studies and show how the chosen weighting matrices can lead to an improved performance compared to standard cost functions.