Robust filtering for continuous-time stochastic uncertain systems with relative entropy constraints

In this paper, we consider a filtering problem for stochastic uncertain systems. The uncertainty in the system is characterized in terms of an uncertain probability distribution on the noise input. This uncertainty is assumed to satisfy a certain relative entropy constraint. The solution to a specially parametrized risk-sensitive stochastic filtering problem is used to construct a filter for the uncertain system which guarantees a certain upper bound on the filtering error. This solution is obtained by solving a pair of algebraic Riccati equations. The corresponding filtering error bound holds for all admissible uncertainties.