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On geometric upper bounds for positioning algorithms in wireless sensor networks

Mohammad Reza Gholami ; Erik G. Ström (Institutionen för signaler och system, Kommunikationssystem) ; Henk Wymeersch (Institutionen för signaler och system, Kommunikationssystem) ; Mats Rydström
Signal Processing (0165-1684). Vol. 111 (2015), p. 179-193.
[Artikel, refereegranskad vetenskaplig]

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.

Nyckelord: 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

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Denna post skapades 2015-04-16. Senast ändrad 2016-12-06.
CPL Pubid: 215278


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Institutionen för signaler och system, Kommunikationssystem (1900-2017)


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