Optimal Estimation for Discrete-Time Linear System with Communication Constraints and Measurement Quantization

This paper focuses on the linear minimum mean square estimator for a networked discrete time-varying linear system subject to data quantification and communication constraints. The communication limitation is that only one transmission node can get access to the shared communication channel at each time step, and that different transmission nodes in the networked systems are scheduled to transmit information according to a Markov protocol. Then the remote estimator completes the estimation with only partially available observations, which are quantified. Suppose that the Markov chain is unknown to the remote estimator. By using orthogonal projection principle and innovation analysis method, a Kalman type filter is designed in a recurrence form. It is shown that estimation performance depends on the transition probability matrix of the Markov chain, quantization error, and the shared channel weighting parameter. Finally, an illustrative example is given to show the effectiveness of the proposed method.