Turn off MathJax
Article Contents
Article Navigation >  Journal of Radars  > 2026  > Proofreading [1st]
WANG Hongzhen, WANG Ding, NIE Fuquan, et al. A multi-target direct localization method based on fast completion of the covariance matrix of the mobile virtual interpolation array[J]. Journal of Radars, in press. doi: 10.12000/JR26006
Citation: WANG Hongzhen, WANG Ding, NIE Fuquan, et al. A multi-target direct localization method based on fast completion of the covariance matrix of the mobile virtual interpolation array[J]. Journal of Radars, in press. doi: 10.12000/JR26006
shu

A Multi-Target Direct Localization Method Based on Fast Completion of the Covariance Matrix of the Mobile Virtual Interpolation Array

DOI: 10.12000/JR26006 CSTR: 32380.14.JR26006
  • 1.

    School of Information System Engineering, Information Engineering University, Zhengzhou 450001, China

  • 2.

    National Digital Switching System Engineering and Technological Research Center, Zhengzhou 450002, China

  • 3.

    Henan Institute of Science and Technology, Xinxiang 453000, China

  • 4.

    Unit 93575 of the People's Liberation Army, Chengde 067000, China

Funds:  The National Natural Science Foundation of China (62171469, 62071029)
More Information
    Abstract
  • This paper addresses the multitarget direct localization problem for moving single stations using the coprime difference co-array. Existing methods based on matrix norm minimization often suffer from underutilization of redundant data from virtual array elements and high computational complexity. To overcome these limitations, we propose a multitarget direct localization approach that combines redundant data averaging for virtual array elements with fast completion of missing covariance matrix entries. First, redundant data averaging is applied to construct the difference co-array. Missing elements are then filled through zeroinitialization followed by Toeplitz matrix reconstruction, which restores the rank structure of the covariance matrix. An alternating projection iterative algorithm is subsequently developed to minimize the ratio of the nuclear norm to the Frobenius norm. By incorporating an adaptive threshold strategy and Toeplitz constraints, the algorithm efficiently completes the missing elements in the virtual array covariance matrix. Finally, a data fusion scheme is employed to obtain the localization results. Numerical simulations demonstrate that the proposed method reduces computational complexity while improving localization accuracy, particularly under low signal-to-noise ratios and limited observation data. The results indicate that the method effectively balances localization accuracy with real-time performance requirements.

     

    • FullText(HTML)
  • loading
    • References(49)
  • [1]
    ZHANG Min, PEI Yuhao, LI Xi, et al. Passive localization by a single moving observer using TOA only with unknown SRI: Observability analysis and algorithm[J]. Chinese Journal of Aeronautics, 2023, 36(6): 318–331. doi: 10.1016/j.cja.2023.04.021.
    [2]
    郭立民, 张逸飞, 马思达. 基于蛇优化的单站机载无源定位算法[J/OL]. 系统工程与电子技术, 1–9[2025-12-08]. https://link.cnki.net/urlid/11.2422.TN.20251028.1511.012.

    GUO Limin, ZHANG Yifei, and MA Sida. Single station airborne passive positioning algorithm based on snake optimizer[J/OL]. Systems Engineering and Electronics, 1–9[2025-12-08]. https://link.cnki.net/urlid/11.2422.TN.20251028.1511.012.
    [3]
    马晓萌, 邓东明, 沈永健, 等. 基于单站无源运动定位的多目标跟踪方法[J]. 系统工程与电子技术, 2025, 47(8): 2549–2557. doi: 10.12305/j.issn.1001-506X.2025.08.13.

    MA Xiaomeng, DENG Dongming, SHEN Yongjian, et al. Multi-target tracking method based on single observer passive motion location[J]. Systems Engineering and Electronics, 2025, 47(8): 2549–2557. doi: 10.12305/j.issn.1001-506X.2025.08.13.
    [4]
    LIAO Yanping, XING Chanjuan, and GUO Qiang. An enhanced secretary bird optimization algorithm for target localization based on TDOA[J]. Physical Communication, 2025, 73: 102853. doi: 10.1016/j.phycom.2025.102853.
    [5]
    ZHANG Wenjun, LI Xi, LIU Yi, et al. Bayesian FDOA positioning with correlated measurement noise[J]. Remote Sensing, 2025, 17(7): 1266. doi: 10.3390/rs17071266.
    [6]
    LUAN Fenghu and DENG Chen. Passive sensor network localization using TDOA with sensor position errors[J]. Journal of Physics: Conference Series, 2025, 2999(1): 012037. doi: 10.1088/1742-6596/2999/1/012037.
    [7]
    YANG Yuxiao, LI Junjie, CAI Qirui, et al. Research on high-precision DOA estimation method for UAV platform in strong multipath environment[J]. Electronics, 2026, 15(1): 134. doi: 10.3390/electronics15010134.
    [8]
    MOHANTA K and AL-RUBAYE S. Integrated sensing and communication for UAV beamforming: Antenna design for tracking applications[J]. Vehicles, 2025, 7(4): 166. doi: 10.3390/vehicles7040166.
    [9]
    ZHU Rongxin, WANG Chao, ZHANG Qi, et al. A high-robustness algorithm for synthetic array using a single moving vector hydrophone[J]. The Journal of the Acoustical Society of America, 2025, 158(5): 3656–3671. doi: 10.1121/10.0039808.
    [10]
    ZHANG Chenhao, HONG Xi, WANG Wenjie, et al. A fourth-order cumulant based multi-source DOA estimation for distributed UAV cooperative systems with limited communication range[J]. Signal Processing, 2026, 239: 110233. doi: 10.1016/j.sigpro.2025.110233.
    [11]
    YE Chengzhi, ZHANG Ruoyu, HU Changcheng, et al. DOA estimation for movable antenna array systems under gain and phase errors[J]. Physical Communication, 2025, 72: 102808. doi: 10.1016/j.phycom.2025.102808.
    [12]
    ZHANG Yule, SHI Junpeng, ZHOU Hao, et al. Improved moving scheme for coprime arrays in direction of arrival estimation[J]. Digital Signal Processing, 2024, 149: 104514. doi: 10.1016/j.dsp.2024.104514.
    [13]
    ZHANG Shidong, ZHOU Zhengchun, ZHANG Sheng, et al. Improved coprime-like arrays on limited platform[J]. Signal Processing, 2024, 220: 109474. doi: 10.1016/j.sigpro.2024.109474.
    [14]
    YE Kun, ZHOU Lang, CHEN Zhendong, et al. DOA estimation based on a novel shifted coprime array structure[J]. AEUE-International Journal of Electronics and Communications, 2024, 179: 155308. doi: 10.1016/j.aeue.2024.155308.
    [15]
    YANG Youzhen, WANG Jianhui, CUI Weijia, et al. Coherent direction of arrival estimation based on low-rank matrix recovery utilising L2-norm with moving coprime arrays[J]. IET Radar, Sonar & Navigation, 2023, 17(11): 1646–1653. doi: 10.1049/rsn2.12454.
    [16]
    PATRA R K and DHAR A S. A novel translated coprime array configuration for moving platform in direction-of-arrival estimation[J]. Circuits, Systems, and Signal Processing, 2023, 42(4): 2494–2505. doi: 10.1007/S00034-022-02231-z.
    [17]
    JIANG Hang, LI Jianfeng, ZHU Kehui, et al. Sparse direct position determination based on TDOA information in correlation-domain[J]. Remote Sensing, 2023, 15(15): 3705. doi: 10.3390/rs15153705.
    [18]
    HE Shuming, JIANG Yuan, ZHAO Lei, et al. Direct position determination of moving targets based on DOA[J]. Electronics Letters, 2024, 60(15): e13297. doi: 10.1049/ell2.13297.
    [19]
    LI Jiaqi, LI Jianfeng, YOU Mingyi, et al. Direct position determination of coherently distributed sources based on canonical polyadic decomposition[J]. Digital Signal Processing, 2025, 166: 105353. doi: 10.1016/j.dsp.2025.105353.
    [20]
    ZHAO Ziheng, GUO Rui, LIU Qi, et al. Direct positioning of multiple targets based on electromagnetic vector sensors array[J]. Signal Processing, 2026, 239: 110292. doi: 10.1016/j.sigpro.2025.110292.
    [21]
    WU Guizhou, ZHANG Min, and GUO Fucheng. High-resolution direct position determination based on eigenspace using a single moving ULA[J]. Signal, Image and Video Processing, 2019, 13(5): 887–894. doi: 10.1007/s11760-019-01425-4.
    [22]
    OISPUU M and NICKEL U. Direct detection and position determination of multiple sources with intermittent emission[J]. Signal Processing, 2010, 90(12): 3056–3064. doi: 10.1016/j.sigpro.2010.05.010.
    [23]
    WU Guizhou, ZHANG Min, and GUO Fucheng. Self-calibration direct position determination using a single moving array with sensor gain and phase errors[J]. Signal Processing, 2020, 173: 107587. doi: 10.1016/j.sigpro.2020.107587.
    [24]
    WU Guizhou, ZHANG Min, and GUO Fucheng. On the use of a calibration emitter for direct position determination with single moving array in the presence of sensor gain and phase errors[J]. Digital Signal Processing, 2020, 102: 102734. doi: 10.1016/j.dsp.2020.102734.
    [25]
    YIN Jiexin, WU Ying, and WANG Ding. Direct position determination of multiple noncircular sources with a moving array[J]. Circuits, Systems, and Signal Processing, 2017, 36(10): 4050–4076. doi: 10.1007/s00034-017-0499-4.
    [26]
    WANG Ding, YIN Jiexin, CHEN Xin, et al. Direct position determination of multiple constant modulus sources based on direction of arrival and Doppler frequency shift[J]. Circuits, Systems, and Signal Processing, 2020, 39(1): 268–306. doi: 10.1007/s00034-019-01170-6.
    [27]
    邓杰, 尹洁昕, 杨宾. 面向非圆信号的四阶累积量直接定位方法[J]. 系统工程与电子技术, 2023, 45(9): 2690–2697. doi: 10.12305/j.issn.1001-506X.2023.09.06.

    DENG Jie, YIN Jiexin, and YANG Bin. Direct position determination method of fourth-order cumulant for noncircular signals[J]. Systems Engineering and Electronics, 2023, 45(9): 2690–2697. doi: 10.12305/j.issn.1001-506X.2023.09.06.
    [28]
    郭立民, 马思达, 王丽昂. 一种基于蛇优化的单站直接定位算法[J]. 舰船电子对抗, 2024, 47(6): 84–91. doi: 10.16426/j.cnki.jcdzdk.2024.06.017.

    GUO Limin, MA Sida, and WANG Li'ang. A single-station direct positioning algorithm based on snake optimization[J]. Shipboard Electronic Countermeasure, 2024, 47(6): 84–91. doi: 10.16426/j.cnki.jcdzdk.2024.06.017.
    [29]
    LIU Lutao, FAN Xueye, GUO Muran, et al. Joint estimation of location and polarization in direct position determination using a moving single station[J]. Circuits, Systems, and Signal Processing, 2025, 44(3): 1793–1816. doi: 10.1007/S00034-024-02884-y.
    [30]
    FAN Xueye, LIU Lutao, GUO Muran, et al. A sparse representation direct position determination method based on iterative local search[J]. Circuits, Systems, and Signal Processing, 2025, 44(5): 3161–3181. doi: 10.1007/s00034-024-02937-2.
    [31]
    KUMAR G, PONNUSAMY P, and AMIRI I S. Direct localization of multiple noncircular sources with a moving nested array[J]. IEEE Access, 2019, 7: 101106–101116. doi: 10.1109/ACCESS.2019.2929805.
    [32]
    YAN Hangqi, WANG Yuexian, OBAIDAT M S, et al. Direct position determination with a moving extended nested array by spatial sparsity[J]. IEEE Internet of Things Journal, 2024, 11(4): 6301–6313. doi: 10.1109/JIOT.2023.3312013.
    [33]
    ZHANG Yankui, XU Haiyun, BA Bin, et al. Direct position determination of non-circular sources based on a Doppler-extended aperture with a moving coprime array[J]. IEEE Access, 2018, 6: 61014–61021. doi: 10.1109/ACCESS.2018.2875822.
    [34]
    ZHANG Yankui, BA Bin, WANG Daming, et al. Direct position determination of multiple non-circular sources with a moving coprime array[J]. Sensors, 2018, 18(5): 1479. doi: 10.3390/s18051479.
    [35]
    吴癸周, 张源, 张文俊, 等. 基于互质阵列的运动单站信号直接定位方法[J]. 雷达学报, 2022, 11(4): 692–704. doi: 10.12000/JR22056.

    WU Guizhou, ZHANG Yuan, ZHANG Wenjun, et al. Coprime array based direct position determination of signals with single moving observation[J]. Journal of Radars, 2022, 11(4): 692–704. doi: 10.12000/JR22056.
    [36]
    WANG Zhaobo, GUO Hui, MIAO Yingjie, et al. Direct position determination of multiple sources using a moving virtual interpolation array[J]. Digital Signal Processing, 2025, 159: 104973. doi: 10.1016/j.dsp.2024.104973.
    [37]
    WANG Zhaobo, ZHANG Jun, GUO Hui, et al. An enhanced direct position determination of mixed circular and non-circular sources using moving virtual interpolation array[J]. Sensors, 2024, 24(20): 6718. doi: 10.3390/s24206718.
    [38]
    周善石, 胡小工, 刘利, 等. 导航卫星精密定轨与时间同步技术进展[J]. 天文学报, 2019, 60(4): 32. doi: 10.15940/j.cnki.0001-5245.2019.04.005.

    ZHOU Shanshi, HU Xiaogong, LIU Li, et al. Status of satellite orbit determination and time synchronization technology for global navigation satellites system[J]. Acta Astronomica Sinica, 2019, 60(4): 32. doi: 10.15940/j.cnki.0001-5245.2019.04.005.
    [39]
    刘瑞, 郭沐然, 孙昭乾. 移动平台正交偶极子阵列下的解相干DOA估计算法[J]. 信号处理, 2025, 41(7): 1219–1228. doi: 10.12466/xhcl.2025.07.007.

    LIU Rui, GUO Muran, and SUN Zhaoqian. Decoherence direction of arrival estimation algorithm based on orthogonal dipole array for mobile platforms[J]. Journal of Signal Processing, 2025, 41(7): 1219–1228. doi: 10.12466/xhcl.2025.07.007.
    [40]
    郇浩, 陶选如, 陶然, 等. 多普勒频率变化率快速最大似然估计辅助的高动态载波跟踪环路[J]. 电子与信息学报, 2014, 36(3): 577–582. doi: 10.3724/SP.J.1146.2013.00638.

    HUAN Hao, TAO Xuanru, TAO Ran, et al. Carrier tracking loop in high dynamic environment aided by fast maximum likelihood estimation of Doppler frequency rate-of-change[J]. Journal of Electronics & Information Technology, 2014, 36(3): 577–582. doi: 10.3724/SP.J.1146.2013.00638.
    [41]
    金磊. 高动态环境下载波频率的精确估计算法[J]. 航天控制, 2018, 36(6): 47–52. doi: 10.16804/j.cnki.issn1006-3242.2018.06.009.

    JIN Lei. Accuracy estimation algorithm for carrier frequency under high dynamic condition[J]. Aerospace Control, 2018, 36(6): 47–52. doi: 10.16804/j.cnki.issn1006-3242.2018.06.009.
    [42]
    张苗, 高宏亮, 邓志安. 基于虚拟阵列孔洞插值的互质阵列直接定位方法[J]. 舰船电子工程, 2024, 44(2): 70–75. doi: 10.3969/j.issn.1672-9730.2024.02.015.

    ZHANG Miao, GAO Hongliang, and DENG Zhi'an. Direct position determination of coprime array based on hole interpolation of virtual array[J]. Ship Electronic Engineering, 2024, 44(2): 70–75. doi: 10.3969/j.issn.1672-9730.2024.02.015.
    [43]
    孙兵, 阮怀林, 吴晨曦, 等. 基于Toeplitz协方差矩阵重构的互质阵列DOA估计方法[J]. 电子与信息学报, 2019, 41(8): 1924–1930. doi: 10.11999/JEIT181041.

    SUN Bing, RUAN Huailin, WU Chenxi, et al. Direction of arrival estimation with coprime array based on Toeplitz covariance matrix reconstruction[J]. Journal of Electronics & Information Technology, 2019, 41(8): 1924–1930. doi: 10.11999/JEIT181041.
    [44]
    QI Bingbing, LIU Xiaogang, DOU Daowei, et al. An enhanced DOA Estimation method for coherent sources via Toeplitz matrix reconstruction and Khatri–Rao subspace[J]. Electronics, 2023, 12(20): 4268. doi: 10.3390/electronics12204268.
    [45]
    AOUNALLAH N. Robust min-norm algorithms for coherent sources DOA estimation based on Toeplitz matrix reconstruction methods[J]. International Journal of Wireless and Mobile Computing, 2023, 24(1): 9–16. doi: 10.1504/ijwmc.2023.129082.
    [46]
    GAO Kaixin, HUANG Zhenghai, and GUO Lulu. Low-rank matrix recovery problem minimizing a new ratio of two norms approximating the rank function then using an ADMM-type solver with applications[J]. Journal of Computational and Applied Mathematics, 2024, 438: 115564. doi: 10.1016/j.cam.2023.115564.
    [47]
    ZHOU Lang, YE Kun, and ZHANG Xuebo. Two-dimensional direction finding for L-shaped coprime array via minimization of the ratio of the nuclear norm and the Frobenius norm[J]. Remote Sensing, 2024, 16(18): 3543. doi: 10.3390/rs16183543.
    [48]
    RECHT B, FAZEL M, and PARRILO P A. Guaranteed minimum-rank solutions of linear matrix equations via nuclear norm minimization[J]. SIAM Review, 2010, 52(3): 471–501. doi: 10.1137/070697835.
    [49]
    BOYD S, PARIKH N, CHU E, et al. Distributed optimization and statistical learning via the alternating direction method of multipliers[J]. Foundations and Trends® in Machine Learning, 2011, 3(1): 1–122. doi: 10.1561/2200000016.
    • Relative Articles
    • Supplements(0)
    • Cited By
  • 加载中

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索
    Get Citation
    PDF
    XML
    Article views(34) PDF downloads(2) Cited by()
    Proportional views
    Related

    京ICP备20021838号-14   Supported by: Beijing Renhe Information Technology Co. Ltd     百度统计

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return