Recursive Bayesian Estimation for Discrete-Time Systems With State-Dependent Packet Dropouts: A Cross-Coupled Method

In this article, the recursive Bayesian estimation problem is investigated for a class of linear discrete-time systems subject to state-dependent packet dropouts. During the transmission to a remote estimator, the data packets carrying the local measurements might be dropped if the system state is located within certain occlusion region, and this gives rise to a nonstationary dropout process relying on real system states. In this scenario, due to the exponential growth of the computational cost, it is almost impossible to calculate the exact posterior distribution of the system state for the purpose of optimal state estimation. To address this issue, we propose a novel cross-coupled estimation framework consisting of two interactively working estimators, namely, a region-label estimator and a state estimator, where the former is utilized to obtain the optimal estimates of the region-label sequence in the maximum a posteriori sense, while the latter is adopted to achieve the optimal estimates of the system states in the minimum mean-square error sense. Moreover, a sufficient condition is obtained to ensure the mean-square boundedness of the resultant estimation error. The effectiveness of the proposed cross-coupled estimation framework is verified by a numerical simulation example.