Gholami, M. R.Ström, E. G.Wymeersch, H.Gezici, Sinan2016-02-082016-02-0820141687-6172http://hdl.handle.net/11693/26644This paper studies upper bounds on the position error for a single estimate of an unknown target node position based on distance estimates in wireless sensor networks. In this study, we investigate a number of approaches to confine the target node position to bounded sets for different scenarios. Firstly, if at least one distance estimate error is positive, we derive a simple, but potentially loose upper bound, which is always valid. In addition assuming that the probability density of measurement noise is nonzero for positive values and a sufficiently large number of distance estimates are available, we propose an upper bound, which is valid with high probability. Secondly, if a reasonable lower bound on negative measurement errors is known a priori, we manipulate the distance estimates to obtain a new set with positive measurement errors. In general, we formulate bounds as nonconvex optimization problems. To solve the problems, we employ a relaxation technique and obtain semidefinite programs. We also propose a simple approach to find the bounds in closed forms. Simulation results show reasonable tightness for different bounds in various situations.EnglishConvex feasibility problemPosition errorPositioning problemProjection onto convex setSemidefinite relaxationWireless sensor networksWorst-case position errorMeasurement errorsOptimizationProbability density functionSensor nodesWireless sensor networksConvex feasibility problemArticle10.1186/1687-6180-2014-4