Sparsity-Promoting Sensor Selection for Non-Linear Measurement Models

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 formulate the sensor selection problem as the design of a sparse vector, which in its original form is a nonconvex ℓ₀-(quasi) norm optimization problem. We present relaxed sensor selection solvers that can be efficiently solved in polynomial time. The proposed solvers result in sparse sensing techniques. We also propose a projected subgradient algorithm that is attractive for large-scale problems. The developed theory is applied to sensor placement for localization.