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Edge-based semidefinite programming relaxation of sensor network localization with lower bound constraints

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  • Ting Pong

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    Abstract

    In this paper, we strengthen the edge-based semidefinite programming relaxation (ESDP) recently proposed by Wang, Zheng, Boyd, and Ye (SIAM J. Optim. 19:655–673, 2008 ) by adding lower bound constraints. We show that, when distances are exact, zero individual trace is necessary and sufficient for a sensor to be correctly positioned by an interior solution. To extend this characterization of accurately positioned sensors to the noisy case, we propose a noise-aware version of ESDP lb (ρ-ESDP lb ) and show that, for small noise, a small individual trace is equivalent to the sensor being accurately positioned by a certain analytic center solution. We then propose a postprocessing heuristic based on ρ-ESDP lb and a distributed algorithm to solve it. Our computational results show that, when applied to a solution obtained by solving ρ-ESDP proposed of Pong and Tseng (Math. Program. doi: 10.1007/s10107-009-0338-x ), this heuristics usually improves the RMSD by at least 10%. Furthermore, it provides a certificate for identifying accurately positioned sensors in the refined solution, which is not common for existing refinement heuristics. Copyright Springer Science+Business Media, LLC 2012

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    File URL: http://hdl.handle.net/10.1007/s10589-011-9447-6
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    Bibliographic Info

    Article provided by Springer in its journal Computational Optimization and Applications.

    Volume (Year): 53 (2012)
    Issue (Month): 1 (September)
    Pages: 23-44

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    Handle: RePEc:spr:coopap:v:53:y:2012:i:1:p:23-44

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    Web page: http://www.springer.com/math/journal/10589

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    Related research

    Keywords: Sensor network localization; Semidefinite programming relaxation; Error bound; Log-barrier; Coordinate gradient descent;

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    1. Jiawang Nie, 2009. "Sum of squares method for sensor network localization," Computational Optimization and Applications, Springer, vol. 43(2), pages 151-179, June.
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