Robust State Estimator Design for Systems with Unknown Exogenous Inputs: A Risk-Sensitive Approach

In this paper, a robust state estimation problem for discrete-time systems with unknown exogenous inputs is investigated utilizing a risk-sensitive filtering approach. By proposing a Radon-Nikodym derivative, we introduce a reference measure under which the measurement and system state become independent. Based on this independent property and by treating the unknown inputs as a process modeled by a non-informative prior, we derive the reformulated risk-sensitive cost criterion under the reference measure and further propose a recursive algorithm for the risk-sensitive state estimate. A simulation example is provided to validate the theoretical results, where the proposed estimator is shown to outperform the MMSE estimator for unknown input case under the scenario subject to system parameter uncertainties.