ECO-DKF: Event-Triggered and Certifiable Optimal Distributed Kalman Filter Under Unknown Correlations

This article presents ECO-DKF, the first Event-Triggered and Certifiable Optimal Distributed Kalman Filter. Our algorithm addresses two major issues inherent to distributed Kalman filters: fully distributed and scalable optimal estimation and reduction of the communication bandwidth usage. The first requires to solve an NP-hard optimization problem, forcing relaxations that lose optimality guarantees over the original problem. Using only information from one-hop neighbors, we propose a tight semidefinite programming relaxation that allows to certify locally and online if the relaxed solution is the optimum of the original NP-hard problem. In that case, ECO-DKF is optimal in the square error sense under scalability and event-triggered one-hop communications restrictions. In addition, ECO-DKF is a globally asymptotically stable estimator. To address the second issue, we propose an event-triggered scheme from the relaxed optimization output. The consequence is a broadcasting-based algorithm that saves communication bandwidth, avoids individual communication links and multiple information exchanges within instants, and preserves the optimality and stability properties of the filter.