An event-triggered approach to robust recursive filtering for stochastic discrete time-varying spatial-temporal systems

In this paper, the robust recursive filtering problem is investigated for a class of uncertain stochastic discrete time-varying spatial-temporal systems with an event-based communication mechanism. The system under consideration includes a set of sensors located at specified points where each sensor can only receive the measurement output from the system at corresponding position. In order to reduce the communication cost, an event-triggered mechanism is utilized to decide when a certain measurement output should be transmitted from sensors to the centralized filter. By re-organizing the state variables, the uncertain spatial-temporal system is first transformed into an ordinary uncertain difference dynamic system. The aim of this paper is to design a filter such that, for all possible parameter uncertainties, the filtering error covariance is guaranteed to have an upper bound which is then minimized at each time-instant under the event-triggered mechanism. By using the matrix derivation approach, the desired filter gain is obtained in terms of the solution to certain Riccati-like difference equations. Finally, a numerical example is employed to demonstrate the effectiveness of the filtering scheme proposed.