On geometric upper bounds for positioning algorithms in wireless sensor networks
2015 (English)In: Signal Processing, ISSN 0165-1684, E-ISSN 1872-7557, Vol. 111, 179-193 p.Article in journal (Refereed) Published
This paper studies the possibility of upper bounding the position error for range-based positioning algorithms in wireless sensor networks. In this study, we argue that in certain situations when the measured distances between sensor nodes have positive errors, e.g., in non-line-of-sight (NLOS) conditions, the target node is confined to a closed bounded convex set (a feasible set) which can be derived from the measurements. Then, we formulate two classes of geometric upper bounds with respect to the feasible set. If an estimate is available, either feasible or infeasible, the position error can be upper bounded as the maximum distance between the estimate and any point in the feasible set (the first bound). Alternatively, if an estimate given by a positioning algorithm is always feasible, the maximum length of the feasible set is an upper bound on position error (the second bound). These bounds are formulated as nonconvex optimization problems. To progress, we relax the nonconvex problems and obtain convex problems, which can be efficiently solved. Simulation results show that the proposed bounds are reasonably tight in many situations, especially for NLOS conditions.
Place, publisher, year, edition, pages
2015. Vol. 111, 179-193 p.
Wireless sensor networks, Positioning problem, Projection onto convex set, Convex feasibility problem, Semidefinite relaxation, Quadratic programming, Position error, Worst-case position error, Non-line-of-sight
IdentifiersURN: urn:nbn:se:kth:diva-163940DOI: 10.1016/j.sigpro.2014.12.015ISI: 000350524800018ScopusID: 2-s2.0-84921056804OAI: oai:DiVA.org:kth-163940DiVA: diva2:808016
QC 201504272015-04-272015-04-132015-04-27Bibliographically approved