Deterministic Kalman filters for uncertain dynamical systems

TL;DR

This paper explores deterministic extensions of Kalman filters for linear systems with uncertain dynamics, deriving error bounds and comparing estimators through numerical examples.

Contribution

It introduces a deterministic approach to Kalman filtering for systems with uncertainties, providing theoretical error bounds and practical comparisons.

Findings

Derived error bounds based on uncertainty variance

Numerical comparison of different estimators

Extended Kalman filter variants for uncertain systems

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.