An event-based scheduling solution for remote state estimation of two LTI systems under bandwidth constraint

Bandwidth constraint is commonly encountered when scheduling many sensors over one channel. In this paper we consider scheduling two sensors communicating with one remote estimator. Each of them independently monitors the state of one linear discrete time-invariant system. Each sensor collects observation data, computes the local state estimate, and transmits it to the remote central estimator over the channel of which the capacity only allows one sensor to use at each time. In the meanwhile, the remote estimator computes its own estimate of the state for each system at each time. Our objective is to minimize the sum of the average estimation error covariance of each system over an infinite horizon. On top of the optimal offline schedule, we introduce a novel event-based schedule that utilizes the real-time information. By selecting the appropriate threshold for the event, we show that the proposed online schedule outperforms the optimal offline one.