3,218 research outputs found
On geometric upper bounds for positioning algorithms in wireless sensor networks
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
Robust Localization from Incomplete Local Information
We consider the problem of localizing wireless devices in an ad-hoc network
embedded in a d-dimensional Euclidean space. Obtaining a good estimation of
where wireless devices are located is crucial in wireless network applications
including environment monitoring, geographic routing and topology control. When
the positions of the devices are unknown and only local distance information is
given, we need to infer the positions from these local distance measurements.
This problem is particularly challenging when we only have access to
measurements that have limited accuracy and are incomplete. We consider the
extreme case of this limitation on the available information, namely only the
connectivity information is available, i.e., we only know whether a pair of
nodes is within a fixed detection range of each other or not, and no
information is known about how far apart they are. Further, to account for
detection failures, we assume that even if a pair of devices is within the
detection range, it fails to detect the presence of one another with some
probability and this probability of failure depends on how far apart those
devices are. Given this limited information, we investigate the performance of
a centralized positioning algorithm MDS-MAP introduced by Shang et al., and a
distributed positioning algorithm, introduced by Savarese et al., called
HOP-TERRAIN. In particular, for a network consisting of n devices positioned
randomly, we provide a bound on the resulting error for both algorithms. We
show that the error is bounded, decreasing at a rate that is proportional to
R/Rc, where Rc is the critical detection range when the resulting random
network starts to be connected, and R is the detection range of each device.Comment: 40 pages, 13 figure
Upper bounds on position error of a single location estimate in wireless sensor networks
This 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. © 2014 Gholami et al.; licensee Springer
Positioning and Scheduling of Wireless Sensor Networks - Models, Complexity, and Scalable Algorithms
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