Expectation–Maximization-Based Remote State Estimation Under State-Dependent Packet Dropouts: From Maximum A Posteriori Perspective

This article is concerned with the problem of remote state estimation for linear discrete-time systems with packet dropouts. The packet dropouts are state dependent, which occur only when the real-time target state enters specific observation-denied regions. At the remote estimator, the batch and iterative expectation–maximization (EM) algorithms are proposed for computing the optimal estimation in the maximum a posteriori (MAP) sense. It is shown that the iterative estimator exhibits a structure similar to that of an information-like type filter. The convergence of the EM algorithm for MAP estimation is investigated, and it is proven that the sequence of estimates converges to a local optimal solution. The computational complexities of both the batch and iterative algorithms are analyzed. Furthermore, a posterior Cramér–Rao lower bound is derived to provide an offline performance bound for the proposed estimator. Finally, the effectiveness of the proposed estimator is demonstrated through an illustrative example.