A static event-triggered background-impulse Kalman filter for wireless sensor networks with non-Gaussian measurement noise

Event-triggered mechanisms (ETMs) have received increasing attention since they provide a way to reduce the communication burden by preventing sensors from transmitting unnecessary measurement values. This article focuses on the problem of a static ETM-based Kalman filter (static ET-KF) failing to work in the case of non-Gaussian measurement noise. To tackle this problem, we combine the static ETM with a background-impulse Kalman filter (BIKF) where the non-Gaussian noise is modeled as a Gaussian mixture model, composed of background noise and impulse noise. First, we make modifications to BIKF to facilitate its integration with the static ETM. Based on this, we propose a static event-triggered background-impulse Kalman filter (static ETBIKF) algorithm for a single sensor. Then we extend the static ETBIKF to the fusion form used for wireless sensor networks. The existing static ET-KF is a special case of our static ETBIKF. Simulations show that the proposed algorithms perform better than static ET-KF under non-Gaussian environments and the communication-saving can reach 45.64% at most. •Eliminate the model interaction part of background-impulse Kalman filter.•Model the non-Gaussian noise as a Gaussian Mixture Model.•Extend the static event-triggered mechanism to non-Gaussian noise case.•Propose fusion algorithm for wireless sensor networks with non-Gaussian noise.•The proposed algorithms shows good performance under non-Gaussian noise.