A convex optimization approach to worst-case optimal sensor selection

This paper considers the problem of optimal sensor selection in a worst-case setup. Our objective is to estimate a given quantity based on noisy measurements, using no more than n sensors out of a total of N available, possibly subject to additional selection constraints. Contrary to most of the literature, we consider the case where the only information available about the noise is a deterministic set-membership description, the goal is to minimize the worst-case estimation error. While in principle this is a hard, combinatorial optimization problem, we show that tractable convex relaxations can be obtained by using recent results on polynomial optimization.