On Geometric Upper Bounds for Positioning Algorithms in Wireless Sensor Networks
This paper studies the possibility of upper bounding the position error of an estimate for range based positioning algorithms in wireless sensor networks. In this paper, the authors argue that in certain situations when the measured distances between sensor nodes are positively biased, e.g., in non-line-of-sight conditions, the target node is confined to a closed bounded convex set (a feasible set) which can be derived from the measurements. Then, they formulate two classes of geometric upper bounds with respect to the feasible set. If an estimate is available, either feasible or infeasible, the worst-case position error can be defined as the maximum distance between the estimate and any point in the feasible set (the first bound).