Sparsity-promoting sensor selection for nonlinear measurement models

Abstract—The problem of choosing the best subset of sensors that guarantees a certain estimation performance is referred to as sensor selection. In this paper, we focus on observations that are related to a general non-linear model. The proposed framework is valid as long as the observations are independent, and its likelihood satisfies the regularity conditions. We use several functions of the Cramér–Rao bound (CRB) as a performance measure. We formu-late the sensor selection problem as the design of a sparse vector, which in its original form is a nonconvex-(quasi) norm optimiza-tion problem. We present relaxed sensor selection solvers that can be efficiently solved in polynomial time. The proposed solvers re-sult in sparse sensing techniques. We also propose a projected sub-gradient algorithm that is attractive for large-scale problems. The developed theory is applied to sensor placement for localization. Index Terms—Convex optimization, Cramér–Rao bound, non-linear models, projected subgradient algorithm, sensor networks