doi:10.1109/TAC.2023.3331667engSebastián, EduardoMontijano, EduardoSagüés, CarlosECO-DKF: Event-Triggered and Certifiable Optimal Distributed Kalman Filter Under Unknown CorrelationsART-2023-135894This paper presents ECO-DKF, the first E vent-Triggered and C ertifiable O ptimal D istributed K alman F ilter. Our algorithm addresses two major issues inherent to Distributed Kalman Filters: (i) fully distributed and scalable optimal estimation and (ii) reduction of the communication bandwidth usage. The first requires to solve an NP-hard optimisation problem, forcing relaxations that lose optimality guarantees over the original problem. Using only information from one-hop neighbours, we propose a tight Semi-Definite 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. Additionally, ECO-DKF is a globally asymptotically stable estimator. To address the second issue, we propose an event-triggered scheme from the relaxed optimisation 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.2023http://zaguan.unizar.es/record/12963210.1109/TAC.2023.3331667http://zaguan.unizar.es/record/129632oai:zaguan.unizar.es:129632IEEE TRANSACTIONS ON AUTOMATIC CONTROL (2023), 1-8All rights reservedhttp://www.europeana.eu/rights/rr-f/info:eu-repo/semantics/openAccess