Optimal robust Kalman-type recursive filter for uncertain systems with finite-step autocorrelated process noises and missing measurements

In this paper, the problem of optimal robust Kalman-type recursive filter design is studied for a class of uncertain systems with finite-step autocorrelated process noises and missing measurements. The system model and measurement model under consideration are both subject to stochastic uncertainties or multiplicative noises. The finite-step autocorrelated process noises are characterized by the covariances between different time instant. The missing measurements are described by a binary switching sequence that obeys a conditional probability distribution. A robust Kalman-type recursive filter is developed in this paper. The proposed robust Kalman-type recursive filter is optimal in the minimum variance sense. Finally, simulation results show the effectiveness of the proposed method.