Conditions for unique graph realizations
SIAM Journal on Computing
Laplacian Eigenmaps for dimensionality reduction and data representation
Neural Computation
Semidefinite programming for ad hoc wireless sensor network localization
Proceedings of the 3rd international symposium on Information processing in sensor networks
Robust distributed network localization with noisy range measurements
SenSys '04 Proceedings of the 2nd international conference on Embedded networked sensor systems
Theory of semidefinite programming for sensor network localization
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Image deformation using moving least squares
ACM SIGGRAPH 2006 Papers
Semidefinite programming based algorithms for sensor network localization
ACM Transactions on Sensor Networks (TOSN)
A Theory of Network Localization
IEEE Transactions on Mobile Computing
Some theoretical aspects of position-location problems
SFCS '79 Proceedings of the 20th Annual Symposium on Foundations of Computer Science
Localization and routing in sensor networks by local angle information
ACM Transactions on Sensor Networks (TOSN)
A linear-space algorithm for distance preserving graph embedding
Computational Geometry: Theory and Applications
Graphical properties of easily localizable sensor networks
Wireless Networks
Global Rigidity: The Effect of Coning
Discrete & Computational Geometry
An as-rigid-as-possible approach to sensor network localization
ACM Transactions on Sensor Networks (TOSN)
Universal rigidity: towards accurate and efficient localization of wireless networks
INFOCOM'10 Proceedings of the 29th conference on Information communications
SIAM Journal on Imaging Sciences
Viewing Angle Classification of Cryo-Electron Microscopy Images Using Eigenvectors
SIAM Journal on Imaging Sciences
Distributed graph layout for sensor networks
GD'04 Proceedings of the 12th international conference on Graph Drawing
Ranking and sparsifying a connection graph
WAW'12 Proceedings of the 9th international conference on Algorithms and Models for the Web Graph
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We present a new approach to localization of sensors from noisy measurements of a subset of their Euclidean distances. Our algorithm starts by finding, embedding, and aligning uniquely realizable subsets of neighboring sensors called patches. In the noise-free case, each patch agrees with its global positioning up to an unknown rigid motion of translation, rotation, and possibly reflection. The reflections and rotations are estimated using the recently developed eigenvector synchronization algorithm, while the translations are estimated by solving an overdetermined linear system. The algorithm is scalable as the number of nodes increases and can be implemented in a distributed fashion. Extensive numerical experiments show that it compares favorably to other existing algorithms in terms of robustness to noise, sparse connectivity, and running time. While our approach is applicable to higher dimensions, in the current article, we focus on the two-dimensional case.