This analysis explores error bounds in state reconstruction within uncertain dynamical systems, suggesting improvements in estimators.
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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Kunisch et al. (2025) studied this question.
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