Network design via modular set function optimization in localization problems

We consider the problem of selecting anchors for sensor network localization to optimize a metric of the error covariance of the position estimates. We show that an interesting metric is a modular set function, which allows a globally optimal selection to be obtained using a simple greedy algorithm. We also consider a separate but related problem of choosing a subset of distance measurements between pairs of sensors to optimize a metric of the error covariance. We utilize again modularity properties of an associated set function to construct networks with desirable algebraic rigidity properties. The results are illustrated via numerical examples, which scale to problems beyond the capabilities of current state-of-the-art convex relaxation techniques.