Cost-constrained D-optimum node activation for large-scale monitoring networks

Abstract

The aim of this contribution is to develop a simple and fast procedure to determine an optimal node activation policy in large-scale sensor networks whose measurements are supposed to be used to estimate unknown parameters of the underlying spatiotemporal process model described by a partial differental equation. The problem consists in selecting gaged sites from among all available sites so that the determinant of the Fisher information matrix associated with the estimated parameters be maximal. In addition to that, given a spatially-varying cost of taking measurements, the resulting total cost of the experiment must not exceed a fixed budget. The technique adopted here to circumvent the inherent combinatorial nature of the sensor selection problem amounts to operating on the spatial density of sensors, rather than on the specific sensor locations. A linear separability characterization of optimal solutions is derived and then simplicial decomposition is applied to obtain numerical solutions resulting in a simple computational scheme.