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

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... 1 times, given the time-horizon from = 0 to = . We also discuss how to extend the result to cases involving multiple power levels scheduling. Simulation examples are the provided to demonstrate the results. Index Terms-Kalman filter, packet-dropping networks, power scheduling, remote state estimation. I. INTRODUCTION Remote state estimation has gained much interest in the past decade, and is found in a growing number of applications including sensor networks, smart grid, smart transportation systems, etc. In many of these applications, the available resources such as the communication energy and network bandwidth are limited. Furthermore, information flow across the network may be unreliable, e.g., data packets could be randomly delayed or dropped. In this correspondence, we consider a remote state estimation problem subject to transmission energy constraint. A sensor measures the state of a process and sends its local state estimate or the measurement data over a packet-dropping network to a remote estimator. The sensor has limited communication energy and it decides whether to send the measurement data using a high transmission power or a low transmission power. We assume that using high transmission power leads to a higher packet arrival rate compared with using low transmission power. This assumption is motivated by two facts: most sensor nodes in the market have different transmission power to choose from [17], and higher transmission power leads to a higher signal-to-noise ratio at the remote estimator, which corresponds to a higher packet arrival rate [7]. Consider a time-horizon from k = 0to k = T and assume the sensor can only use the high transmission power m < T + 1 times due to the limited energy constraint. We are interested in how the sensor should Manuscript