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

Euclidean distance geometry and applications

Euclidean distance geometry is the study of Euclidean geometry based on the concept of distance. This is useful in several applications where the input data consists of an incomplete set of distances, and the output is a set of points in Euclidean space that realizes the given distances. We survey some of the theory of Euclidean distance geometry and some of the most important applications: molecular conformation, localization of sensor networks and statics.Comment: 64 pages, 21 figure

Structures from Distances in Two and Three Dimensions using Stochastic Proximity Embedding

The point placement problem is to determine the locations of a set of distinct points uniquely (up to translation and reflection) by making the fewest possible pairwise distance queries of an adversary. Deterministic and randomized algorithms are available if distances are known exactly. In this thesis, we discuss a 1-round algorithm for approximate point placement in the plane in an adversarial model. The distance query graph presented to the adversary is chordal. The remaining distances are uniquely determined using the Stochastic Proximity Embedding (SPE) method due to Agrafiotis, and the layout of the points is also generated from SPE. We have also computed the distances uniquely using a distance matrix completion algorithm for chordal graphs, based on a result by Bakonyi and Johnson. The layout of the points is determined using the traditional Young- Householder approach. We compared the layout of both the method and discussed briefly inside. The modified version of SPE is proposed to overcome the highest translation embedding that the method faces when dealing with higher learning rates. We also discuss the computation of molecular structures in three-dimensional space, with only a subset of the pairwise atomic distances available. The subset of distances is obtained using the Philips model for creating artificial backbone chain of molecular structures. We have proposed the Degree of Freedom Approach to solve this problem and carried out our implementation using SPE and the Distance matrix completion Approac

Indoor Positioning for Monitoring Older Adults at Home: Wi-Fi and BLE Technologies in Real Scenarios

This paper presents our experience on a real case of applying an indoor localization system formonitoringolderadultsintheirownhomes. Sincethesystemisdesignedtobeusedbyrealusers, therearemanysituationsthatcannotbecontrolledbysystemdevelopersandcanbeasourceoferrors. This paper presents some of the problems that arise when real non-expert users use localization systems and discusses some strategies to deal with such situations. Two technologies were tested to provide indoor localization: Wi-Fi and Bluetooth Low Energy. The results shown in the paper suggest that the Bluetooth Low Energy based one is preferable in the proposed task