Sliding mode mean-module filtering for linear stochastic systems

This paper addresses the mean-module filtering problem for a linear system with Gaussian white noises. The obtained solution contains a sliding mode term, signum of the innovations process. It is shown that the designed sliding mode filter generates the mean-module estimate, which yields a better value of the mean-module criterion in comparison to the mean-square Kalman-Bucy filter. To the best of our knowledge, this is the first designed sliding mode filter that is optimal with respect to the mean-module criterion. The theoretical result is complemented with an illustrative example verifying performance of the designed filter, which is compared to the conventional Kalman-Bucy filter. The simulation results confirm an advantage in favor of the designed sliding mode filter.