Robust filtering of stochastic uncertain systems on an infinite time horizon

In this paper, we consider a robust filtering problem for continuous time 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 parameterized risk-sensitive stochastic filtering problem is used to construct a filter for the original uncertain system which guarantees an optimal worst-case filtering error. The corresponding minimax optimal filter is obtained by solving a pair of algebraic Riccati equations.