A filtering problem with uncertainty in observation

This paper is concerned with a generalized Kalman-Bucy filtering model and corresponding robust problem under model uncertainty. We find that this robust problem is equivalent to considering an estimate problem under some sublinear operator. Therefore, we turn to obtaining the minimum mean square estimator under a sublinear operator. By Girsanov theorem and minimax theorem, we obtain the optimal estimator $\hat{x}_{t}$ of the signal process $x_{t}$ for given time $t\in\lbrack0,T]$.