An Optimal Scanning Sensor Activation Policy for Parameter Estimation of Distributed Systems

Abstract

A technique is proposed to solve an optimal node activation problem in sensor networks whose measurements are supposed to be used to estimate unknown parameters of the underlying process model in the form of a partial differential equation. Given a partition of the observation horizon into a finite number of consecutive intervals, the problem is set up to select nodes which will be active over each interval while the others will remain dormant such that the log-determinant of the resulting Fisher information matrix associated with the estimated parameters is maximized. The search for the optimal solution is performed using the branch-and-bound method in which an extremely simple and efficient technique is employed to produce an upper bound to the maximum objective function. Its idea consists in solving a relaxed problem through the application of a simplicial decomposition algorithm in which the restricted master problem is solved using a multiplicative algorithm for D-optimal design. The performance evaluation of the technique is additionally presented by means of simulations.