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arXiv · 2506.00463

Deterministic Kalman filters for uncertain dynamical systems

Karl Kunisch·Jesper Schröder
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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.

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Karl Kunisch, Jesper Schröder. 2025-05-31. Deterministic Kalman filters for uncertain dynamical systems. https://arxiv.org/abs/2506.00463

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