Optimal Filtered and Smoothed Estimators for Discrete-Time Linear Systems With Multiple Packet Dropouts Under Markovian Communication Constraints

This paper concentrates on the linear least mean square (LLMS) filtered and smoothed estimators for networked linear stochastic systems. Multiple packet losses, Markovian communication constraints, and superposed process noise are considered simultaneously. In order to reduce the channel load during communication, at every step, just one transmission node is permitted to send data packets. Hence, a Markovian communication protocol is utilized to arrange the packets of these transmission nodes. Moreover, multiple data packet dropouts occur during transmission due to an imperfect communication channel. Therefore, the global observation information cannot be obtained by the state estimator. The real state of Markov chain is assumed to be unknown to the estimator except the transition probability matrix. By means of the innovation analysis approach and orthogonal projection principle, we design Kalman-like estimators in a recursive form. Finally, through simulation experiments, we verify the effectiveness and superiority of the designed algorithm.