Robust sensor localization with locally-computed, global H∞-design

This paper considers sensor localization in ℝm, i.e. the problem to find the positions of an arbitrary number of sensor nodes in the presence of at least m+1 anchor nodes, given only the inter-node distances. Assuming that the sensors lie in the convex hull of the anchors, we provide a linear, continuous-time update at each sensor that uses barycentric coordinates and Cayley-Menger determinants. In this paper, we consider design enhancements by adding a dynamic controller in the feed-forward loop of the location estimator at each sensor. We show that the dynamic controller has the ability to both speed-up the convergence and improve the transient behavior, while ensuring a certain disturbance rejection that could be introduced by inter-node communication. The design of the local controllers is based on the input-output approach, H∞ design and does not require the knowledge of global parameters. Simulations illustrates the concepts described in the paper.