  In this paper, we propose a robust Kalman filtering framework for systems
with probabilistic uncertainty in system parameters. We consider two cases,
namely discrete time systems, and continuous time systems with discrete
measurements. The uncertainty, characterized by mean and variance of the
states, is propagated using conditional expectations and polynomial chaos
expansion framework. The results obtained using the proposed filter are
compared with existing robust filters in the literature. The proposed filter
demonstrates better performance in terms of root mean squared error and rate of
convergence.
