| We consider the sensor scheduling problem for the purpose of parameter estimation. There are multiple parameters and multiple sensors. Sensors are activated one at a time by a central controller to take a measurement of a parameter
and transmit the observation data back to the the
controller. Each activation incurs a cost (e.g., sensing and communication costs). Sensors' observation data are combined at the controller to generate estimates on the parameters. This
process continues till a certain criterion is satisfied, e.g., when the total estimation error is sufficiently small, when available sensors are exhausted, when the time period of interest has elapsed, etc. Assuming that sensors may be of different quality (i.e. they may have different signal to noise ratios) and the activation of
different sensors may incur different cost, our scheduling problem is to determine the sequence of sensors to be activated and the corresponding sequence of parameters to be measured so as to minimize the sum of the total terminal
estimation error(how accurate the measurement is) and total estimation cost (how energy efficient the measurement is).
After introducing a quantitative measure of the &096;&096;goodness'' of a sensors, which combines both its sensing quality and sensing cost, we decouple the sequential decision problem into two subproblems.
The first one is to determine the sequence of the sensors to be used, which is independendt of the parameter selection, and the second one is to determine the sequence of parameters to be measured for a given sensor sequence. We present a greedy algorithm
and give a sufficient conditions under which this algorithm is optimal.
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