Kalman Filtering with Probabilistic Uncertainty in System Parameters

Abstract: 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.