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

Published: 19 September 2008 Publication History

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.

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    cover image ACM Conferences
    MELT '08: Proceedings of the first ACM international workshop on Mobile entity localization and tracking in GPS-less environments
    September 2008
    142 pages
    ISBN:9781605581897
    DOI:10.1145/1410012
    Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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    Published: 19 September 2008

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    Author Tags

    1. anchors
    2. euclidean distance matrix completions
    3. graph realization
    4. semidefinite programming
    5. sensor network localization

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    • (2018)Distributed Localization: A Linear TheoryProceedings of the IEEE10.1109/JPROC.2018.2823638106:7(1204-1223)Online publication date: Jul-2018
    • (2014)On the structural nature of cooperation in distributed network localization2014 48th Asilomar Conference on Signals, Systems and Computers10.1109/ACSSC.2014.7094647(1194-1198)Online publication date: Nov-2014
    • (2012)Theory and algorithms for hop-count-based localization with random geometric graph models of dense sensor networksACM Transactions on Sensor Networks10.1145/2240116.22401248:4(1-38)Online publication date: 25-Sep-2012
    • (2012)Edge-based semidefinite programming relaxation of sensor network localization with lower bound constraintsComputational Optimization and Applications10.1007/s10589-011-9447-653:1(23-44)Online publication date: 1-Sep-2012
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    • (2011)A Diffusion Approach to Network LocalizationIEEE Transactions on Signal Processing10.1109/TSP.2011.212226159:6(2642-2654)Online publication date: 1-Jun-2011
    • (2011)(Robust) Edge-based semidefinite programming relaxation of sensor network localizationMathematical Programming: Series A and B10.1007/s10107-009-0338-x130:2(321-358)Online publication date: 1-Dec-2011
    • (2011)Euclidean Distance Matrices and ApplicationsHandbook on Semidefinite, Conic and Polynomial Optimization10.1007/978-1-4614-0769-0_30(879-914)Online publication date: 26-Sep-2011
    • (2010)Approximation accuracy, gradient methods, and error bound for structured convex optimizationMathematical Programming10.1007/s10107-010-0394-2125:2(263-295)Online publication date: 17-Aug-2010
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