Event-based filtering for time-varying nonlinear systems subject to multiple missing measurements with uncertain missing probabilities

This paper is concerned with the recursive filtering problem for a class of time-varying nonlinear stochastic systems in the presence of event-triggered transmissions and multiple missing measurements with uncertain missing probabilities. The measurements from different sensors may undergo the missing phenomena, which are characterized by a set of mutually independent Bernoulli random variables and the missing probabilities could be uncertain. In addition, the event-triggered transmission mechanism is introduced to reduce the network communication burden, where the current measurement is transmitted to the remote filter only when it changes greatly compared with the previous one. The aim of this paper is to design a time-varying filter such that, in the presence of the multiple missing measurements, event-triggered transmission mechanism and stochastic nonlinearities, an upper bound of the filtering error covariance is obtained and then minimized by properly designing the filter gain. The explicit form of the filter gain is given in terms of the solutions to two recursive matrix equations. It is shown that the developed filtering scheme is of a recursive form applicable for the online computations. Finally, we provide two illustrative examples to demonstrate the feasibility and applicability of the developed event-triggered filtering scheme.