On the characterization of distributed observability from first principles

In this paper, we derive the distributed observable state from first principles. In particular, we extend the estimation setup to a distributed framework where in addition to the state and sensing, we also have communication among the sensors. We consider that each sensor estimates the entire state-vector to recover its unobservability. Combining the estimates at all of the sensors we arrive at the networked estimator, which subsequently results into the corresponding networked dynamics. We show that the networked dynamics are not just a mere extension of the original dynamics repeated (block-diagonally) to accommodate for each sensor, but belongs to a large class of systems that naturally defines the allowable collaboration among the sensors. Using the redefined distributed estimator (networked dynamics and estimate), we cast the distributed observability and the corresponding estimator.