Discrete-time Linear Time-invariant Distributed Minimum Energy Estimator

Proper monitoring of large complex spatially critical infrastructures often requires a sensor network capable of inferring the state of the system. Such networks enable the design of distributed estimators considering only local (partial) measurements, local communication capabilities with nearby sensors, as well as the system model. Solutions often assume perfect knowledge of the system model, and white process and measurement noise, which are limiting in engineering settings. In this paper, we consider the minimum energy setting where the model uncertainty and process and measurement noises are bounded but unknown. We provide the first distributed minimum energy estimator for discrete-time linear time-invariant systems, and we show that the error dynamics is input-to-state stable. Lastly, we illustrate the performance in some pedagogical examples, and compare the performance with respect to the centralized implementation of the minimum energy estimator.