Conditions for unique graph realizations
SIAM Journal on Computing
SIAM Review
Solving spatial basic geometric constraint configurations with locus intersection
Proceedings of the seventh ACM symposium on Solid modeling and applications
Localization from mere connectivity
Proceedings of the 4th ACM international symposium on Mobile ad hoc networking & computing
Robust distributed network localization with noisy range measurements
SenSys '04 Proceedings of the 2nd international conference on Embedded networked sensor systems
Discrete & Computational Geometry
Connected rigidity matroids and unique realizations of graphs
Journal of Combinatorial Theory Series B
Image deformation using moving least squares
ACM SIGGRAPH 2006 Papers
Semidefinite programming based algorithms for sensor network localization
ACM Transactions on Sensor Networks (TOSN)
Theory of semidefinite programming for Sensor Network Localization
Mathematical Programming: Series A and B
SpaseLoc: An Adaptive Subproblem Algorithm for Scalable Wireless Sensor Network Localization
SIAM Journal on Optimization
IPSN '08 Proceedings of the 7th international conference on Information processing in sensor networks
Universal rigidity: towards accurate and efficient localization of wireless networks
INFOCOM'10 Proceedings of the 29th conference on Information communications
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Sensor network localization is an instance of the NP-Hard graph realization problem. Thus, methods used in practice are not guaranteed to find the correct localization, even if it is uniquely determined by the input distances. In this article, we show the following: if the sensors are allowed to wiggle, giving us perturbed distance data, we can apply a novel algorithm to realize arbitrary Generically Globally Rigid graphs (GGR), or certain vertex subsets in non-GGR graphs whose relative positions are fixed (which include vertex sets of GGR subgraphs). And this strategy works in any dimension. In the language of structural rigidity theory, our approach corresponds to calculating the approximate kernel of a generic stress matrix for the given graph and distance data. To make our algorithm suitable for real-world applications, we also present: (i) various techniques for improving the robustness of the algorithm in the presence of measurement noise; (ii) an algorithm for detecting certain subsets of graph vertices whose relative positions are fixed in any generic realization of the graph and robustly localizing these subsets of vertices, (iii) a strategy for reducing the number of measurements needed by the algorithm. We provide simulation results of our algorithm.