Matrix analysis
Efficient Algorithms for Shortest Paths in Sparse Networks
Journal of the ACM (JACM)
The Cricket location-support system
MobiCom '00 Proceedings of the 6th annual international conference on Mobile computing and networking
Dynamic fine-grained localization in Ad-Hoc networks of sensors
Proceedings of the 7th annual international conference on Mobile computing and networking
Robust Positioning Algorithms for Distributed Ad-Hoc Wireless Sensor Networks
ATEC '02 Proceedings of the General Track of the annual conference on USENIX Annual Technical Conference
Localization from mere connectivity
Proceedings of the 4th ACM international symposium on Mobile ad hoc networking & computing
The n-hop multilateration primitive for node localization problems
Mobile Networks and Applications
Distributed localization in wireless sensor networks: a quantitative comparison
Computer Networks: The International Journal of Computer and Telecommunications Networking - Special issue: Wireless sensor networks
Semidefinite programming for ad hoc wireless sensor network localization
Proceedings of the 3rd international symposium on Information processing in sensor networks
Localization from Connectivity in Sensor Networks
IEEE Transactions on Parallel and Distributed Systems
The bin-covering technique for thresholding random geometric graph properties
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Wireless sensor network localization techniques
Computer Networks: The International Journal of Computer and Telecommunications Networking
Proceedings of the ACM SIGMETRICS international conference on Measurement and modeling of computer systems
Matrix Completion from Noisy Entries
The Journal of Machine Learning Research
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We consider the problem of localizing wireless devices in an ad hoc network embedded in a d-dimensional Euclidean space. Obtaining a good estimate 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. Furthermore, to account for detection failures, we assume that even if a pair of devices are within the detection range, they fail 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 HOP-TERRAIN introduced by Savarese et al. 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 RCritical/R, where RCritical is the critical detection range when the resulting random network starts to be connected, and R is the detection range of each device.