  In this paper, we study a generalized Kalman-Bucy filtering problem under
uncertainty. The drift uncertainty for both signal process and observation
process is considered and the attitude to uncertainty is characterized by a
convex operator (convex risk measure). The optimal filter or the minimum mean
square estimator (MMSE) is calculated by solving the minimum mean square
estimation problem under a convex operator. In the first part of this paper,
this estimation problem is studied under g-expectation which is a special
convex operator. For this case, we prove that there exists a worst-case prior.
Based on this worst-case prior we obtained the Kalman-Bucy filtering equation
under g-expectation. In the second part of this paper, we study the minimum
mean square estimation problem under general convex operators. The existence
and uniqueness results of the MMSE are deduced.
