Optimal sensor power scheduling for state estimation of Gauss-Markov systems over a packet-dropping network

We consider sensor power scheduling for estimating the state of a general high-order Gauss-Markov system. A sensor decides whether to use a high or low transmission power to communicate its local state estimate or raw measurement data with a remote estimator over a packet-dropping network. We construct the optimal sensor power schedule which minimizes the expected terminal estimation error covariance at the remote estimator under the constraint that the high transmission power can only be used m < T + 1 times, given the time-horizon from k = 0 to k = T. We also discuss how to extend the result to cases involving multiple power levels scheduling. Simulation examples are the provided to demonstrate the results.