Convex Euclidean distance embedding for collaborative position localization with NLOS mitigation
Convex Euclidean distance embedding for collaborative position localization with NLOS mitigation
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.
187-218
Ding, Chao
67300df2-ae66-48d2-89a4-c488d148aa4a
Qi, Hou-Duo
e9789eb9-c2bc-4b63-9acb-c7e753cc9a85
January 2017
Ding, Chao
67300df2-ae66-48d2-89a4-c488d148aa4a
Qi, Hou-Duo
e9789eb9-c2bc-4b63-9acb-c7e753cc9a85
Ding, Chao and Qi, Hou-Duo
(2017)
Convex Euclidean distance embedding for collaborative position localization with NLOS mitigation.
Computational Optimization and Applications, 66 (1), .
(doi:10.1007/s10589-016-9858-5).
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.
Text
NLOS_Revised.pdf
- Accepted Manuscript
More information
Accepted/In Press date: 11 June 2016
e-pub ahead of print date: 22 June 2016
Published date: January 2017
Organisations:
Operational Research
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Local EPrints ID: 396745
URI: http://eprints.soton.ac.uk/id/eprint/396745
ISSN: 0926-6003
PURE UUID: e659fa5d-84ba-402e-89a0-20699b99d7ed
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Date deposited: 14 Jun 2016 08:11
Last modified: 15 Mar 2024 05:39
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Author:
Chao Ding
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