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Convex Euclidean distance embedding for collaborative position localization with NLOS mitigation

Author

Listed:
  • Chao Ding

    (Chinese Academy of Sciences)

  • Hou-Duo Qi

    (The University of Southampton)

Abstract

One of the challenging problems in collaborative position localization arises when the distance measurements contain non-line-of-sight (NLOS) biases. Convex optimization has played a major role in modelling such problems and numerical algorithm developments. One of the successful examples is the semi-definite programming (SDP), which translates Euclidean distances into the constraints of positive semidefinite matrices, leading to a large number of constraints in the case of NLOS biases. In this paper, we propose a new convex optimization model that is built upon the concept of Euclidean distance matrix (EDM). The resulting EDM optimization has an advantage that its Lagrangian dual problem is well structured and hence is conducive to algorithm developments. We apply a recently proposed 3-block alternating direction method of multipliers to the dual problem and tested the algorithm on some real as well as simulated data of large scale. In particular, the EDM model significantly outperforms the existing SDP model and several others.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:coopap:v:66:y:2017:i:1:d:10.1007_s10589-016-9858-5
    DOI: 10.1007/s10589-016-9858-5
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    References listed on IDEAS

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    1. João Gouveia & Ting Pong, 2012. "Comparing SOS and SDP relaxations of sensor network localization," Computational Optimization and Applications, Springer, vol. 52(3), pages 609-627, July.
    2. Jiawang Nie, 2009. "Sum of squares method for sensor network localization," Computational Optimization and Applications, Springer, vol. 43(2), pages 151-179, June.
    3. 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.
    4. Gale Young & A. Householder, 1938. "Discussion of a set of points in terms of their mutual distances," Psychometrika, Springer;The Psychometric Society, vol. 3(1), pages 19-22, March.
    5. Norbert Gaffke & Rudolf Mathar, 1989. "A cyclic projection algorithm via duality," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 36(1), pages 29-54, December.
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    Cited by:

    1. Fengzhen Zhai & Qingna Li, 2020. "A Euclidean distance matrix model for protein molecular conformation," Journal of Global Optimization, Springer, vol. 76(4), pages 709-728, April.
    2. Panpan Yu & Qingna Li, 2018. "Ordinal Distance Metric Learning with MDS for Image Ranking," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 35(01), pages 1-19, February.
    3. Si-Tong Lu & Miao Zhang & Qing-Na Li, 2020. "Feasibility and a fast algorithm for Euclidean distance matrix optimization with ordinal constraints," Computational Optimization and Applications, Springer, vol. 76(2), pages 535-569, June.
    4. Qian Zhang & Xinyuan Zhao & Chao Ding, 2021. "Matrix optimization based Euclidean embedding with outliers," Computational Optimization and Applications, Springer, vol. 79(2), pages 235-271, June.

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