Generalized Simplicial Decomposition for Optimal Sensor Selection in Parameter Estimation of Spatiotemporal Processes

Abstract

We propose an algorithm based on general sim-plicial decomposition for optimal node activation in large-scale sensor networks. The resulting measurements are to be used to estimate unknown parameters of a spatiotemporal process described by a partial differential equation under some nondifferentiable metrics of estimation accuracy. In this setting, continuous relaxations of the sensor subset selection problem quickly become computationally intractable for extraordinarily large numbers of sensors. We show how generalized simplicial decomposition, which is a recent extension of the classical simplicial decomposition to nondifferentiable optimization, can be employed to drastically reduce the dimensionality of the design problem. Computationally, the resulting algorithm alternates between solving a linear programming subproblem which has an explicit solution and a convex programming subproblem whose dimensionality is typically moderate. A simple separability characterization of optimal solutions is provided and illustrated with a numerical example.