Distributed Tobit Kalman filtering for random parameter 2-D system: Dealing with amplify-and-forward relay and stochastic communication protocol

This article is devoted to dealing with the distributed Tobit Kalman filtering issue for a class of random parameter two-dimensional systems over sensor networks. To enhance the signal quality after long-distance transmission, an amplify-and-forward (AF) relay node is deployed between each sensor and its corresponding remote filter. Additionally, the stochastic communication protocol (SCP) is utilized to regulate the data transmission order, which could effectively mitigate the potential network congestion and overload. Firstly, considering the presence of measurement censoring, the conditional expectation and variance of the censored measurement regarding the system state are calculated under AF relay and SCP framework. Subsequently, the distributed Tobit Kalman filter (TKF) is established, where each local filter could acquire data from its own node and the neighboring ones under a known network topology. Finally, upper bound of the filtering error variance is derived and further locally minimized in the trace sense by adopting the mathematical induction method and some matrix analysis techniques. The simulation results are also provided to show validity of the proposed distributed TKF.