Evaluation approaches for spatial targets localization precision based on observation matrix condition number

doi:10.23919/JSEE.2025.000049

Journal of Systems Engineering and Electronics ›› 2026, Vol. 37 ›› Issue (2): 445-454.doi: 10.23919/JSEE.2025.000049

• DEFENCE ELECTRONICS TECHNOLOGY • Previous Articles

Evaluation approaches for spatial targets localization precision based on observation matrix condition number

Xinyong ZHANG(), Zhangming HE(), Xuanying ZHOU(), Huiyu CHEN(), Jiongqi WANG(), Haiyin ZHOU()

College of Science, National University of Defense Technology, Changsha 410073, China

Received:2024-08-28 Accepted:2025-04-07 Online:2026-04-18 Published:2026-04-30
Contact: Zhangming HE E-mail:867428705@qq.com;hzmnudt@163.com;julia_chow07@163.com;1633110563@qq.com;wjq_gfkd@163.com;gfkd_zhy@sina.com
About author:
ZHANG Xinyong was born in 1997. He received his B.S, degree in computer science and technology from the National University of Defense Technology, Changsha, China, in 2020. He is working towards his M.S. degree with the National University of Defense Technology, Changsha, China. His research interests include power system dynamics and controls, and data information fusion and its application. E-mail: 867428705@qq.com

HE Zhangming was born in 1985. He received his B.S. and M.S. degrees in applied mathematics from the National University of Defense Technology, Changsha, China, in 2008 and 2010, respectively. He received his Ph.D. degree in system science from the National University of Defense Technology in 2015. Since 2019, he has been an associate professor in the College of Sciences at the National University of Defense Technology, Changsha, China. His research interests include fault diagnosis and prognosis, signal processing, and system identification. E-mail: hzmnudt@163.com

ZHOU Xuanying was born in 1991. She received her B.S. degree in 2013, M.S. and Ph.D. degrees in applied mathematics from the National University of Defense Technology (NUDT), Hunan, in 2016 and 2019, respectively. She is a lecturer in NUDT. Her research interests include data processing, data fusion, missiles and signal process. E-mail: julia_chow07@163.com

CHEN Huiyu was born in 2001. He received his B.S, degree in applied statistics from the National University of Defense Technology, Changsha, China, in 2023. He is working towards his M.S. degree with the National University of Defense Technology, Changsha, China. His research interests include power system dynamics and controls, advanced signal processing, and data information fusion and its application. E-mail: 1633110563@qq.com

WANG Jiongqi was born in 1979. He received his B.S. degree in applied mathematics from Zhejiang University, Hangzhou, China in 2002 and his M.S. and Ph.D. degrees in system science from the National University of Defense Technology, in 2004 and 2008, respectively. He is currently a professor, College of Sciences at the National University of Defense Technology, Changsha, China. His research interests include measurement data analysis, parameter estimation, system identification, and space target state filtering and its applications. E-mail: wjq_gfkd@163.com

ZHOU Haiyin was born in 1965. He received his B.S. degree in applied mathematics from Wuhan University, Wuhan, China, in 1986, M.S. degree from Hunan University, Changsha, China in 1989, and Ph.D. degree in systems engineering from National University of Defense Technology, Changsha, China, in 2003. Since 2009, he has been a professor in the College of Science, National University of Defense Technology. His main research interests include data driven diagnosis approaches, power system dynamics and controls, advanced signal processing, and data information fusion and its application. E-mail: gfkd_zhy@sina.com
Supported by:
This work was supported by the National Natural Science Foundation of China (62203458), and the Postgraduate Scientific Research Innovation Project of Hunan Province (CX20220024, CX20230014).

Abstract

Abstract:

In this paper, we propose evaluation approaches for the spatial target localization precision based on the observation matrix conditional number. Three evaluation approaches for the spatial target localization precision are derived including relative condition numbers, absolute condition numbers, and volume condition numbers by properties of vectors and matrix norms. The theoretical analysis shows that the proposed methods are the upper certainty bound of the magnification of measurement error. Meanwhile, the proposed methods are able to account for variations of localization accuracy by exploiting geometric variations in the composition between the target and measurement stations. Finally, the proposed methods perform better, compared with the traditional evaluation methods. This is of great significance for the accuracy evaluation of high-precision measuring equipment, optimization of workstation layout and geometric configuration. Simulation experiments corroborate the effectiveness of the proposed methods.

Key words: target positioning, error amplification factor, condition number, geometric accuracy factor, upper bound

Xinyong ZHANG, Zhangming HE, Xuanying ZHOU, Huiyu CHEN, Jiongqi WANG, Haiyin ZHOU. Evaluation approaches for spatial targets localization precision based on observation matrix condition number[J]. Journal of Systems Engineering and Electronics, 2026, 37(2): 445-454.

Figures/Tables 7

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Evaluation approaches for spatial targets localization precision based on observation matrix condition number

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