Sensor Scheduling for Multiple Parameters Estimation under Energy Constraint

We consider a sensor scheduling problem for estimating Gaussian random variables under an energy constraint. The sensors are described by a linear observation model, and the observation noise is Gaussian. We formulate this problem as a stochastic sequential decision problem. Due to the Gaussian assumption and the linear observation model, the stochastic sequential decision problem is equivalent to a deterministic one. We present a greedy algorithm for this problem, and discover conditions sufficient to guarantee the optimality of the greedy algorithm. Furthermore, we present two special cases of the original scheduling problem where the greedy algorithm is optimal under weaker conditions. We illustrate our result through numerical examples.