Tight 2-Dimensional Outer-approximations of Feasible Sets in Wireless Sensor Networks

Finding a tight ellipsoid that contains the intersection of a finite number of ellipsoids is of interest in positioning applications for wireless sensor networks (WSNs). To this end, we propose a novel geometrical method in 2-dimensional (2-D) space. Specifically, we first find a tight polygon which contains the desired region and then obtain the tightest ellipse containing the polygon by solving a convex optimization problem. For demonstrating the usefulness of this method, we employ it in a distributed algorithm for elliptical outer-approximation of feasible sets in cooperative WSNs. Through simulations, we show that the proposed method gives a tighter bounding ellipse than conventional methods, while having similar computational cost. Keywords—Computational geometry, localization, non-line-ofsight, optimization.