Three-dimensional interferometric direction-finding for non-planar antenna arrays

doi:10.23919/JSEE.2025.000117

Journal of Systems Engineering and Electronics ›› 2026, Vol. 37 ›› Issue (2): 377-392.doi: 10.23919/JSEE.2025.000117

• ELECTRONICS TECHNOLOGY • Previous Articles

Three-dimensional interferometric direction-finding for non-planar antenna arrays

Wangjie CHEN¹^,²(), Weiqiang ZHU²(), Zhenhong FAN¹^,*(), Li WU¹(), Yi HE²()

¹School of Electronic and Optical Engineering, Nanjing University of Science and Technology, Nanjing 210094, China
²Nanjing Electronic Equipment Institute, Nanjing 210007, China

Received:2025-02-22 Accepted:2025-06-06 Online:2026-04-18 Published:2026-04-30
Contact: Zhenhong FAN E-mail:njust_cwj36@126.com;zhuweq8511@sina.com;zhfan@mail.njust.edu.cn;li_wu@njust.edu.cn;1028256748@qq.com
About author:
CHEN Wangjie was born in 1986. He received his B.S. and M.S. degrees in electronic engineering from Nanjing University of Science and Technology, Nanjing, China, in 2009 and 2012, respectively. He is a senior engineer with Nanjing Electronic Equipment Institute. His research interests include signal and information processing, and passive localization technology. E-mail: njust_cwj36@126.com

ZHU Weiqiang was born in 1964. He received his Ph.D. degree in navigation, guidance, and control from the Defense Technology Academy of China Aerospace Science & Industry, Corporation Beijing, China, in 2011. He is a professor at Nanjing Electronic Equipment Institute. His research interests include space electronic countermeasure technology, signal and information processing, and passive localization technology. E-mail: zhuweq8511@sina.com

FAN Zhenhong was born in 1978. He received his M.S. and Ph.D. degrees in the electromagnetic field and microwave technique from Nanjing University of Science and Technology (NJUST), Nanjing, China, in 2003 and 2007, respectively. In 2006, he was with the Center of Wireless Communication, City University of Hong Kong, Hong Kong, as a research assistant. He is a professor at the School of Electronic and Optical Engineering, NJUST. His research interests include computational electromagnetics, electromagnetic scattering, and radiation. E-mail: zhfan@mail.njust.edu.cn

WU Li was born in 1981. He received his B.S., M.S. and Ph.D. degrees in electronic engineering from Nanjing University of Science and Technology, Nanjing, China, in 2003, 2005, and 2009, respectively. He is currently an associate professor with the School of Electronic and Optical Engineering, Nanjing University of Science and Technology. His research interests include millimeter wave antennas, microwave imaging, and millimeter wave systems. E-mail: li_wu@njust.edu.cn

HE Yi was born in 1996. She received her M.S. degree from Nanjing University of Aeronautics and Astronautics, Nanjing, China, in 2021. She is currently an engineer with Nanjing Electronic Equipment Institute. Her research interests include direction-finding, passive location, and signal processing. E-mail: 1028256748@qq.com

Abstract

Abstract:

This paper proposes a three-dimensional (3D) interferometer direction-finding (DF) method to address the reduced accuracy of conventional two-dimensional (2D) interferometer DF methods in non-planar antenna configurations. First, we enhance the multi-channel soft synchronization (MCSS) technique by dynamically compensating for sampling point offsets, achieving phase estimation accuracy better than 0.01 sampling points. Second, we construct a 3D baseline model based on the 3D distribution characteristics of the antennas and introduce a 3D error allocation model to improve the system error estimation method, allowing for dynamic correction of calibration deviations. This effectively addresses the phase ambiguity issues caused by 3D mechanical errors. Finally, we develop a 3D DF algorithm and an optimized multi-pulse fusion approach utilizing the maximum-ratio combining (MFA-MRC) method to reduce DF errors and enhance system stability. Simulation experiments and flight tests demonstrate that the proposed method has a computational load of only 0.31% of the multiple signal classification (MUSIC) algorithm. When the baseline offset exceeds 10 mm, the angular accuracy improves from 0.9° to 0.3°, and the positioning accuracy is enhanced from approximately 10 km to around 1 km. The study holds significant theoretical and practical value in engineering.

Key words: three-dimensional interferometric, direction finding, multi-channel soft synchronization, system error estimation, installation error correction

Wangjie CHEN, Weiqiang ZHU, Zhenhong FAN, Li WU, Yi HE. Three-dimensional interferometric direction-finding for non-planar antenna arrays[J]. Journal of Systems Engineering and Electronics, 2026, 37(2): 377-392.

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Specific step	Operation
Covariance matrix construction	8 192
Eigenvalue decomposition of covariance matrix	20 480
Total computational complexity for different angles	2 059 320
Overall computational complexity	2 087 992

Specific step	Operation
Covariance matrix construction	8 192
Eigenvalue decomposition of covariance matrix	20 480
Rotation matrix solution	176
Eigenvalue decomposition of rotation matrixs	40
Overall computational complexity	28 888

Frequency/ GHz	k_max	Iteration times	AJTNum	Proportion
Frequency/ GHz	k_max	Iteration times	AJTNum	MUSIC/%	ESPRIT/%
1	9	369	450	0.02	1.56
2	15	900	1125	0.05	3.89
3	21	900	1341	0.06	4.64
4	27	900	1629	0.08	5.64
5	33	900	1 989	0.10	6.89
6	39	900	2421	0.12	8.38
7	45	900	2925	0.14	10.13
8	51	900	3501	0.17	12.12
9	57	900	4149	0.20	14.36
10	63	900	4869	0.23	16.85
11	69	900	5661	0.27	19.60
12	75	900	6525	0.31	22.59

Antenna	X-axis		Y-axis		Z-axis
Antenna	Mean	Variance	Mean	Variance	Mean	Variance
1	−0.5	0.51	2.55	1.58	0.8	0.85
2	2.4	1.49	−4.8	1.19	21.4	7.92
3	2.45	1.28	0.55	0.49	−1.55	0.48
4	0.85	1.73	0.7	3.96	23.35	19.49

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Three-dimensional interferometric direction-finding for non-planar antenna arrays

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