Optimal filtering for systems with finite-step autocorrelated noises and multiple packet dropouts

This paper addresses the optimal filtering problem for a class of uncertain dynamical systems with multiple packet dropouts and finite-step correlated observation noises. By rearranging the stochastic terms in the transmission and measurement matrices of the dynamical system into the noises directly, the process noises and observation noises in resulted system depend on the state as well as the stochastic uncertain perturbations, and are not only autocorrelated respectively but also cross-correlated. For this complicated dynamical system, instead of designing a Kalman-type filter, a globally optimal filtering in the minimum mean square error sense is developed by exploiting sufficiently the statistical properties of correlated noises. Numerical simulation is provided to demonstrate the performance of the proposed filter.