Event‐based optimal filter for a networked system with multiplicative and auto/cross‐correlated process and measurement noise

Summary This article presents an event triggered based optimal filter for a networked system with multiplicative noise in state and measurement matrices. The process and measurement noise are auto/cross‐correlated, which is described as a moving average process. The network in both sensor to estimator (S‐E) and controller to actuator (C‐A) channel is affected by random sensor delay and packet dropouts. These effects are modeled using two random variables for both the S‐E and C‐A channels. Sensor data are transmitted to the estimator through the S‐E channel using an event‐based mechanism. It depends on a time varying threshold to improve trade‐off between tracking performance and utilization of network bandwidth. The process and measurement noise are two‐step auto/cross‐correlated. A comprehensive augmented stochastic model is developed for the networked system by combining the effects of event triggering, network constraints and noise correlation. The filter is designed using an innovation analysis approach based on orthogonal projection. The solution of the filter is given in terms of a Lyapunov and a Riccati equation. An algorithm is presented for the implementation of developed filter. The stability properties of the proposed optimal filter are analyzed. The effectiveness of the proposed filter is shown in the simulation platform and accumulated mean square error performance is evaluated based on Monte Carlo simulation.