A Necessary and Sufficient Condition for State Omniscience of Linear Time-Invariant Distributed Estimators

The design of distributed estimators has been a growing interest to enable complex multi-sensor/multi-agent tasks. In such scenarios, it is important that each local estimator converges to the true global system state - a quality known as state omniscience. Most previous related work has focused on the design of such systems under varying assumptions on the graph topology with simplified information fusion schemes. Contrarily, this work focuses on characterizing state omniscience under generalized graph topologies and generalized information fusion schemes. State omniscience is discussed analogously to observability from classical control theory; and a necessary and sufficient condition for a distributed estimator to be state omniscient is presented.