In this paper, we consider the problem of sensor selection for parameterestimation with correlated measurement noise. We seek optimal sensoractivations by formulating an optimization problem, in which the estimationerror, given by the trace of the inverse of the Bayesian Fisher informationmatrix, is minimized subject to energy constraints. Fisher information has beenwidely used as an effective sensor selection criterion. However, existinginformation-based sensor selection methods are limited to the case ofuncorrelated noise or weakly correlated noise due to the use of approximatemetrics. By contrast, here we derive the closed form of the Fisher informationmatrix with respect to sensor selection variables that is valid for anyarbitrary noise correlation regime, and develop both a convex relaxationapproach and a greedy algorithm to find near-optimal solutions. We furtherextend our framework of sensor selection to solve the problem of sensorscheduling, where a greedy algorithm is proposed to determine non-myopic(multi-time step ahead) sensor schedules. Lastly, numerical results areprovided to illustrate the effectiveness of our approach, and to reveal theeffect of noise correlation on estimation performance.
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