Computational Optimization and Applications

, Volume 66, Issue 1, pp 187–218 | Cite as

Convex Euclidean distance embedding for collaborative position localization with NLOS mitigation

  • Chao DingEmail author
  • Hou-Duo Qi


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.


Euclidean distance matrix Collaborative localization Non-line of sight (NLOS) Augmented Lagrangian Alternating direction method of multipliers (ADMM) 



We would like to thank the two referees for their constructive comments that have helped to improve the quality of the paper. This work is supported in part by Engineering and Physical Science Research Council (UK) Project EP/K007645/1.


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Institute of Applied Mathematics, Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijingPeople’s Republic of China
  2. 2.School of MathematicsThe University of SouthamptonSouthamptonUK

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