Localization in modified polar representation: hybrid measurements and closed-form solution

doi:10.23919/JSEE.2023.000146

Journal of Systems Engineering and Electronics ›› 2024, Vol. 35 ›› Issue (3): 575-588.doi: 10.23919/JSEE.2023.000146

• HIGH-DIMENSIONAL SIGNAL PROCESSING • Previous Articles

Localization in modified polar representation: hybrid measurements and closed-form solution

Xunchao CONG¹(), Yimao SUN²^,*(), Yanbing YANG²(), Lei ZHANG²(), Liangyin CHEN²()

¹ The 10th Research Institute of China Electronics Technology Group Corporation, Chengdu 610036, China
² College of Computer Science and Institute for Industrial Internet Research, Sichuan University, Chengdu 610065, China

Received:2022-08-25 Accepted:2023-07-13 Online:2024-06-18 Published:2024-06-19
Contact: Yimao SUN E-mail:congxunchao@foxmail.com;yimaosun@scu.edu.cn;yangyanbing@scu.edu.cn;zhanglei@scu.edu.cn;chenliangyin@scu.edu.cn
About author:
CONG Xunchao was born in 1988. He received his Ph.D. degree from the School of Electronic Engineering, University of Electronic Science and Technology of China, Chengdu, China, in 2017. He is currently with the 10th Research Institute of China Electronics Technology Group Corporation. His research interests include radar signal processing, radio localization, and information fusion. E-mail: congxunchao@foxmail.com

SUN Yimao was born in 1990. He received his B.S. degree in the School of Electronic Engineering from University of Electronic Science and Technology of China (UESTC), Chengdu, China, in 2013, and Ph.D. degree in the School of Information and Communication Engineering from UESTC in 2019. From 2017 to 2018, he was awarded a scholarship under the State Scholarship Fund of China Scholarship Council to pursue his study in the Electrical Engineering and Computer Science (EECS) Department, University of Missouri (MU), MO, USA as a joint Ph.D. student. Since 2021, he has been with Sichuan University, Chengdu, China, where he is currently a research associate professor with the College of Computer Science and the Institute for Industrial Internet Research. He is a research scholar of courtesy appointment with the EECS, MU since 2019. His research interests include passive localization, unified near-far-field model, array signal processing, and time delay estimation. E-mail: yimaosun@scu.edu.cn

YANG Yanbing was born in 1987. He received his B.E. and M.E. degrees from the University of Electronic Science and Technology of China, China, and Ph.D. degree in computer science and engineering from Nanyang Technological University, Singapore. He is currently an associate research professor with the College of Computer Science, Sichuan University, China. His research interests include internet of things, visible light communication, visible light sensing, as well as their applications. E-mail: yangyanbing@scu.edu.cn

ZHANG Lei was born in 1978. He received his B.S., M.S., and Ph.D. degrees from the College of Computer Science, Sichuan University, in 2000, 2003, and 2011, respectively. He was a visiting researcher with the School of Computer Science, University of Maryland, Maryland, USA. He is currently in the Dean of Admissions Office and an associate professor with the College of Computer Science, Sichuan University. His current research interests include blockchains, data mining, and sentiment analysis. E-mail: zhanglei@scu.edu.cn

CHEN Liangyin was born in 1968. He received his Ph.D. degree from the School of Computer Science, Sichuan University, in 2008, where he is a professor. From 2009 to 2010, he was a visiting researcher with the University of Minnesota. He has authored and coauthored more than 40 papers, many of which were published in premier network journals and conferences. His research interests include wireless sensor networks, blockchains, embedded systems, computer networks, distributed systems, big data analytics, natural language processing, internet of things, and industrial internet. E-mail: chenliangyin@scu.edu.cn
Supported by:
This work was supported by the National Natural Science Foundation of China (62101359), Sichuan University and Yibin Municipal People’s Government University and City Strategic Cooperation Special Fund Project (2020CDYB-29), the Science and Technology Plan Transfer Payment Project of Sichuan Province (2021ZYSF007), and the Key Research and Development Program of Science and Technology Department of Sichuan Province (2020YFS0575;2021KJT0012-2021YFS-0067).

Abstract

Abstract:

Classical localization methods use Cartesian or Polar coordinates, which require a priori range information to determine whether to estimate position or to only find bearings. The modified polar representation (MPR) unifies near-field and far-field models, alleviating the thresholding effect. Current localization methods in MPR based on the angle of arrival (AOA) and time difference of arrival (TDOA) measurements resort to semidefinite relaxation (SDR) and Gauss-Newton iteration, which are computationally complex and face the possible diverge problem. This paper formulates a pseudo linear equation between the measurements and the unknown MPR position, which leads to a closed-form solution for the hybrid TDOA-AOA localization problem, namely hybrid constrained optimization (HCO). HCO attains Cramér-Rao bound (CRB)-level accuracy for mild Gaussian noise. Compared with the existing closed-form solutions for the hybrid TDOA-AOA case, HCO provides comparable performance to the hybrid generalized trust region subproblem (HGTRS) solution and is better than the hybrid successive unconstrained minimization (HSUM) solution in large noise region. Its computational complexity is lower than that of HGTRS. Simulations validate the performance of HCO achieves the CRB that the maximum likelihood estimator (MLE) attains if the noise is small, but the MLE deviates from CRB earlier.

Key words: localization, modified polar representation, time difference of arrival (TDOA), angle of arrival (AOA), closed-form solution

Xunchao CONG, Yimao SUN, Yanbing YANG, Lei ZHANG, Liangyin CHEN. Localization in modified polar representation: hybrid measurements and closed-form solution[J]. Journal of Systems Engineering and Electronics, 2024, 35(3): 575-588.

Figures/Tables 17

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Algorithm	HSUM	HGTRS	HCO	SDR	MLE-SDR	Yin-Cart	MLE-Cart
CPU time	1.12	2.16	1.85	932.43	8.10	1.66	5.68
Real processing time	1	1.77	1.52	765.45	6.64	1.36	4.65

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Localization in modified polar representation: hybrid measurements and closed-form solution

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