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Open AccessArticle

A Semidefinite Relaxation Method for Elliptical Location

by Xin Wang 1,*, Ying Ding 1 and Le Yang 2
1
Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education), Department of Electronic Engineering, Jiangnan University, Wuxi 214122, China
2
Department of Electrical and Computer Engineering, College of Engineering, University of Canterbury, Christchurch 8020, New Zealand
*
Author to whom correspondence should be addressed.
Electronics 2020, 9(1), 128; https://doi.org/10.3390/electronics9010128
Received: 28 November 2019 / Accepted: 7 January 2020 / Published: 9 January 2020
(This article belongs to the Section Microwave and Wireless Communications)
Wireless location is a supporting technology in many application scenarios of wireless communication systems. Recently, an increasing number of studies have been conducted on range-based elliptical location in a variety of backgrounds. Specifically, the design and implementation of position estimators are of great significance. The difficulties arising from implementing a maximum likelihood estimator for elliptical location come from the nonconvexity of the negative log-likelihood functions. The need for computational efficiency further enhances the difficulties. Traditional algorithms suffer from the problems of high computational cost and low initialization justifiability. On the other hand, existing closed-form solutions are sensitive to the measurement noise levels. We recognize that the root of these drawbacks lies in an oversimplified linear approximation of the nonconvex model, and accordingly design a maximum likelihood estimator through semidefinite relaxation for elliptical location. We relax the elliptical location problems to semidefinite programs, which can be solved efficiently with interior-point methods. Additionally, we theoretically analyze the complexity of the proposed algorithm. Finally, we design and carry out a series of simulation experiments, showing that the proposed algorithm outperforms several widely used closed-form solutions at a wide range of noise levels. Extensive results under extreme noise conditions verify the deployability of the algorithm. View Full-Text
Keywords: elliptical location; maximum likelihood estimation; weighted least-squares; quadratic optimization; semidefinite relaxation; interior-point method elliptical location; maximum likelihood estimation; weighted least-squares; quadratic optimization; semidefinite relaxation; interior-point method
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Wang, X.; Ding, Y.; Yang, L. A Semidefinite Relaxation Method for Elliptical Location. Electronics 2020, 9, 128.

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