A discontinuous mean-square filter for stochastic differential systems

This paper presents a mean-square filter for Lipschitz stochastic differential systems, which contains a discontinuous innovations term in the form of unit control. It is demonstrated that the designed filter yields the ultimate boundedness of the estimation error variance. The developed algorithm is then applied to a third degree polynomial system and compared to the extended Kalman-Bucy filter. The simulation results show the faster convergence and better approximation properties of the proposed filter.