Token-Bucket-Protocol-Based Recursive Remote State Estimation for Complex Networks under Amplify-and-Forward Relays

This article is concerned with a recursive remote estimation problem for a class of nonlinear complex networks subject to the token bucket protocol (TBP) and amplify-and-forward (AF) relays. The influence of the TBP is considered, for the first time, in the context of networked state estimation, where the token consumptions are modeled in a stochastic manner, so as to describe the potential size variability of transmitted measurement signals. Once processed by the TBP, the signals, with stochastic channel coefficients, are transmitted to the remote estimator via AF relays, where a failure in transmission under the TBP may occur due to insufficient tokens in the bucket. An extended-Kalman-filter-based novel recursive estimator is proposed, and by solving Riccati-like difference equations, an upper bound of prediction/estimation error covariance is determined and further minimized through the design of an appropriate estimator gain. The impact of the TBP on estimation performance is also investigated. Some numerical simulations are presented to demonstrate the effectiveness of the proposed estimator and the effects of the TBP.