Deterministic Kalman filters for uncertain dynamical systems
Dynamical Systems
2025-06-03 v1 Optimization and Control
Probability
Abstract
The Kalman(-Bucy) filter is the natural choice for the state reconstruction of disturbed, linear dynamical systems based on flawed and incomplete measurements. Taking a deterministic viewpoint this work investigates possible extensions of the concept to systems with uncertain dynamics and noise covariances. In a theoretical analysis error bounds in terms of the variance of the uncertainties are derived. The article concludes with a numerical implementation of two example systems allowing for a comparison of the estimators.
Cite
@article{arxiv.2506.00463,
title = {Deterministic Kalman filters for uncertain dynamical systems},
author = {Karl Kunisch and Jesper Schröder},
journal= {arXiv preprint arXiv:2506.00463},
year = {2025}
}