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

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  • Ting Pong

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

Suggested Citation

  • Ting Pong, 2012. "Edge-based semidefinite programming relaxation of sensor network localization with lower bound constraints," Computational Optimization and Applications, Springer, vol. 53(1), pages 23-44, September.
    • Handle: RePEc:spr:coopap:v:53:y:2012:i:1:p:23-44
    DOI: 10.1007/s10589-011-9447-6
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    References listed on IDEAS

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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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    Cited by:

    1. Chao Ding & Hou-Duo Qi, 2017. "Convex Euclidean distance embedding for collaborative position localization with NLOS mitigation," Computational Optimization and Applications, Springer, vol. 66(1), pages 187-218, January.

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