A sparsity-enforcing method for optimal node activation in parameter estimation of spatiotemporal processes
Maciej Patan, Dariusz Uciński · 2017
The purpose of this study is to develop a simple computational scheme to determine a minimum-support 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. The problem consists in selecting gaged sites from among all available sites so that a convex design criterion defined on the Fisher information matrix associated with the estimated parameters be minimal. 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 solution to this problem is not unique and we are primarily interested in sparse solutions, i.e., solutions with as many components equal to zero as possible. As an efficient alternative to the multiobjective optimization, we propose an approach based on postprocessing a nonsparse optimal solution, which heavily exploits a separability form of optimality conditions. Then, approximate solutions are obtained by solving a sequence of separable concave minimization problem using a branch-and-bound algorithm.