Sensor Selection with Nonsmooth Design Criteria Based on Semi-Infinite Programming

Abstract

A problem of optimal node activation in large-scale sensor networks is considered. The resulting measurements are supposed to be used to estimate unknown parameters of a spatiotemporal process described by a partial differential equation. In this setting, the sensor subset selection problem may quickly become computationally intractable when an excessively complex sensor location algorithm is employed. The is even more pronounced when the design criterion is nondifferentiable. A vital example of this criterion is the sum of an arbitrary number of smallest eigenvalues of the Fisher information matrix, being a generalization of the well-known E-optimality criterion. A simple branch-and-bound algorithm is exposed here to maximize this criterion. Its key component to produce upper bounds to the maximum of the objective function implements a relaxation procedure for solving semi-infinite programming problems. It alternates between solving a linear programming subproblem and evaluation of the eigenvalues and eigenvectors of the current information matrix, which makes it extremely easy to implement. The paper is complemented with a numerical example of computing actual sensor locations.