On geometric upper bounds for positioning algorithms in wireless sensor networks
Artikel i vetenskaplig tidskrift, 2015

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.

Worst-case position error

Wireless sensor networks

Quadratic programming

Position error


Semidefinite relaxation

Projection onto convex set

Convex feasibility problem

Positioning problem


Mohammad Reza Gholami

Kungliga Tekniska Högskolan (KTH)

Erik Ström

Chalmers, Signaler och system, Kommunikation, Antenner och Optiska Nätverk

Henk Wymeersch

Chalmers, Signaler och system, Kommunikation, Antenner och Optiska Nätverk

Mats Rydström

Ericsson AB

Signal Processing

0165-1684 (ISSN)

Vol. 111 179-193


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