Tobit Kalman filtering for two-dimensional systems subject to stochastic nonlinearity under round-robin protocol

This paper focuses on the recursive filtering issue for a category of discrete two-dimensional (2D) shift-varying systems subject to measurement censoring and stochastic nonlinearity. The round-robin mechanism is applied to manage the transmission of signal sequences, aiming to save network resources and relieve network burden. The conditional mathematical expectation and variance of the censored measurement with respect to the system state are derived innovatively for the 2D systems. Subsequently, a two-step recursive filter is established, which could provide an unbiased estimation for the discussed 2D system. Furthermore, by utilising some matrix inequalities and stochastic analysis methods, the minimal upper bound for the filtering error variance is achieved. Finally, we analyse how the censoring threshold influences the proposed filtering behaviour, indicating that an increased censoring threshold tends to degrade the filtering performance. A numerical simulation is also presented to demonstrate feasibility of the developed filtering scheme in the presence of the censored measurement outputs.