Sensor network localization, euclidean distance matrix completions, and graph realization

Authors:
Yichuan Ding;Nathan Krislock;Jiawei Qian;Henry Wolkowicz
Affiliations:
Stanford University, Stanford, CA, USA;University of Waterloo, Waterloo, ON, Canada;Cornell University, Ithaca, NY, USA;University of Waterloo, Waterloo, ON, Canada
Venue:
Proceedings of the first ACM international workshop on Mobile entity localization and tracking in GPS-less environments
Year:
2008

Citing 6
Cited 2

The Euclidian Distance Matrix Completion Problem

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Scalable sensor localization algorithms for wireless sensor networks

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Theory of semidefinite programming for Sensor Network Localization

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Theory and algorithms for hop-count-based localization with random geometric graph models of dense sensor networks

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Abstract

We study Semidefinite Programming, SDP, relaxations for Sensor Network Localization, SNL, with anchors and with noisy distance information. The main point of the paper is to view SNL as a (nearest) Euclidean Distance Matrix, EDM, completion problem and to show the advantages for using this latter, well studied model. We first show that the current popular SDP relaxation is equivalent to known relaxations in the literature for EDM completions. The existence of anchors in the problem is not special. The set of anchors simply corresponds to a given fixed clique for the graph of the EDM problem. We next propose a method of projection when a large clique or a dense subgraph is identified in the underlying graph. This projection reduces the size, and improves the stability, of the relaxation. In addition, the projection/reduction procedure can be repeated for other given cliques of sensors or for sets of sensors, where many distances are known. Thus, further size reduction can be obtained.