Event-Based Distributed Filtering with Multiplicative Measurement Noise and Correlated Additive Noises

Distributed filtering problem with event-based transmissions and uncorrelated additive noises has been extensively studied in the literature. However, in many practical applications, the sensor node measurements are corrupted with multiplicative noise along with additive noise. Furthermore, the additive noises (of the process and sensor) are also correlated. Hence, the filter’s performance may not be optimal if the above two additional conditions are not considered while designing the filter. Therefore, in this work, we consider the distributed filtering problem for a linear discrete-time system with event-based transmissions, multiplicative measurement noise, and correlated additive noises. To design an optimal distributed filter for such a system, we first derive the upper bound of the estimation error covariance matrix to show that the mean square error of the distributed filter is convergent. We then derive the filter gain matrix by minimizing the trace of the upper bound of the estimation error covariance matrix to compute the state estimates of the considered system. Finally, a numerical example is presented to validate the derived distributed filtering algorithm.