Risk averse deterministic Kalman filters for uncertain dynamical systems

TL;DR

This paper extends the Kalman-Bucy filter to uncertain deterministic systems, focusing on risk-averse designs that minimize large errors, with theoretical error bounds and numerical comparisons.

Contribution

It introduces risk-averse deterministic Kalman filters for systems with parametric uncertainties, providing theoretical error bounds and practical implementation insights.

Findings

Risk-averse filters reduce large reconstruction errors.

Theoretical error bounds depend on uncertainty variance.

Numerical examples compare risk-neutral and risk-averse estimators.

Abstract

Taking a deterministic viewpoint this work investigates extensions of the Kalman-Bucy filter for state reconstruction to systems containing parametric uncertainty in the state operator. The emphasis lies on risk averse designs reducing the probability of large reconstruction errors. 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 examples allowing for a comparison of risk neutral and risk averse estimators.