基于修正牛顿法的双基ISAR空变补偿快速成像与几何校正图像定标方法

符吉祥 张超 邢文洁 陈洪猛 闫群 李军 刘丹

符吉祥, 张超, 邢文洁, 等. 基于修正牛顿法的双基ISAR空变补偿快速成像与几何校正图像定标方法[J]. 雷达学报(中英文), 待出版. doi: 10.12000/JR25052
引用本文: 符吉祥, 张超, 邢文洁, 等. 基于修正牛顿法的双基ISAR空变补偿快速成像与几何校正图像定标方法[J]. 雷达学报(中英文), 待出版. doi: 10.12000/JR25052
FU Jixiang, ZHANG Chao, XING Wenjie, et al. Fast space-variant phase error compensation and geometric correction for bistatic ISAR imaging using a modified newton’s method[J]. Journal of Radars, in press. doi: 10.12000/JR25052
Citation: FU Jixiang, ZHANG Chao, XING Wenjie, et al. Fast space-variant phase error compensation and geometric correction for bistatic ISAR imaging using a modified newton’s method[J]. Journal of Radars, in press. doi: 10.12000/JR25052

基于修正牛顿法的双基ISAR空变补偿快速成像与几何校正图像定标方法

DOI: 10.12000/JR25052 CSTR: 32380.14.JR25052
基金项目: 国家自然科学青年基金(62301389),国家自然科学重点基金项目(62331020),国家自然科学基金联合基金项目(U22B2015),国家重点研发计划(2022YFB3901604),陕西省科学技术创新团队(2025RS-CXTD-002)
详细信息
    作者简介:

    符吉祥,博士,副教授,主要研究方向为双基ISAR运动补偿和成像处理、大转角ISAR成像、目标识别

    张 超,硕士生,主要研究方向为双基ISAR运动补偿和成像处理

    邢文洁,博士生,主要研究方向为双基ISAR成像处理、多站雷达协同处理

    陈洪猛,博士,高级工程师,主要研究方向为雷达总体设计

    闫 群,博士生,主要研究方向为舰船目标成像、运动补偿处理

    李 军,博士,研究员,主要研究方向为雷达总体设计

    刘 丹,博士,研究员,主要研究方向为雷达总体设计

    通讯作者:

    符吉祥 jxfu@xidian.edu.cn

  • 责任主编:李中余 Corresponding Editor: LI Zhongyu
  • 中图分类号: TN957

Fast Space-variant Phase Error Compensation and Geometric Correction for Bistatic ISAR Imaging Using a Modified Newton’s Method

Funds: The Young Scientist Fund of the National Natural Science Foundation of China (62301389), The Key Program of National Natural Science Foundation of China (62331020), The National Nature Science Foundation of China (U22B2015), The National Key R&D Program of China (2022YFB3901604), Shaanxi Province Science and Technology Innovation Team (2025RS-CXTD-002)
More Information
  • 摘要: 双基逆合成孔径雷达(Bi-ISAR)因其卓越的反隐身与抗干扰性能,受到广泛关注。然而,Bi-ISAR成像过程中双基角的变化会导致图像出现空变散焦和几何畸变,严重影响后续信息提取与目标识别的精度。为解决上述问题,该文提出了一种基于修正牛顿法的Bi-ISAR空变补偿快速成像与几何校正图像定标方法。该方法以Bi-ISAR成像结果的图像熵为代价函数,以空变系数和转动参数为优化变量,构建优化方程。通过对传统牛顿法进行修正,确保海森矩阵的正定性,从而保证代价函数在每次迭代中沿下降方向优化。通过求解该优化方程最小化图像熵,同时估计得到转动参数,进而构建几何校正函数并计算分辨率因子,实现对最终成像结果的几何校正与定标。所提方法可同步校正空变散焦误差与几何畸变,且为数据驱动模式(无需先验参数),对初始图像质量要求较低。此外,受益于牛顿法的二次收敛特性,相较于其他方法,该方法具有更高的计算效率。最后,通过对点目标仿真、电磁计算以及地面等效实验数据的处理与对比分析,验证了所提方法的有效性。

     

  • 图  1  双基ISAR工作几何模型

    Figure  1.  Geometry model of Bistatic ISAR

    图  2  点目标位置示意图

    Figure  2.  Point target location diagram

    图  3  点目标相位曲线示意图

    Figure  3.  Point target phase curve diagram

    图  4  单基ISAR成像示意图

    Figure  4.  Single base ISAR imaging diagram

    图  5  双基ISAR成像示意图

    Figure  5.  Bistatic ISAR imaging diagram

    图  6  基于修正牛顿法的双基ISAR空变补偿流程图

    Figure  6.  Flowchart of two-dimensional spatial variation correction for Bi-ISAR based on modified Newton’s method

    图  7  基于修正牛顿法的双基ISAR空变补偿快速成像与几何校正图像定标流程图

    Figure  7.  Flow chart of space-variant phase error compensation and geometric correction image scaling for Bi-ISAR imaging based on modified Newton’s method

    图  8  仿真目标模型

    Figure  8.  The model of simulated target

    图  9  双基角变化趋势

    Figure  9.  The changing trend of bistatic angle

    图  10  Keystone变换后的RD成像结果

    Figure  10.  Imaging result after Keystone transform

    图  11  参数初始值补偿后成像结果

    Figure  11.  Imaging results after initial parameter value compensation

    图  12  二维空变校正后的RD成像结果

    Figure  12.  Imaging result after 2D space-variant phase error compensation

    图  13  二维空变校正后定标结果

    Figure  13.  Imaging result after optimization

    图  14  几何畸变校正后定标结果

    Figure  14.  Imaging result after geometric correction

    图  15  补偿后8倍插值点P1等高线图

    Figure  15.  Contour map of 8 times interpolated point P1 after compensation

    图  16  补偿后8倍插值点P2等高线图

    Figure  16.  Contour map of 8 times interpolated point P2 after compensation

    图  17  P1, P2点方位向切片图和距离向切片图

    Figure  17.  Azimuth and Range slice diagram of points P1 and P2

    图  18  对比方法(BFGS方法)成像结果

    Figure  18.  Imaging result of the contrast method (BFGS)

    图  19  所提方法与对比方法(BFGS方法)图像熵变化曲线

    Figure  19.  Image entropy change curves of the proposed method and the contrast method

    图  20  所提方法图像熵变化曲线放大图

    Figure  20.  Enlarged image of the entropy change curve of the proposed method

    图  21  不同SNR下两种方法成像结果

    Figure  21.  Imaging results of two methods under different SNR

    图  22  CST软件仿真卫星图(视角1)

    Figure  22.  CST software simulation satellite image (view 1)

    图  23  交叉极化电磁仿真信号包络和RD成像结果

    Figure  23.  Cross-polarized electromagnetic simulation signal’s envelope and RD imaging results

    图  24  交叉极化所提方法校正结果

    Figure  24.  Correction results of the proposed method under cross-polarization

    图  25  对比方法(BFGS)的成像结果图

    Figure  25.  Imaging result of the contrast method (BFGS)

    图  26  所提方法与对比方法图像熵变化曲线(视角1)

    Figure  26.  Image entropy change curves of the proposed method and the contrast method (view 1)

    图  27  所提方法图像熵变化曲线放大图(视角1)

    Figure  27.  Enlarged image of the entropy change curve of the proposed method (view 1)

    图  28  CST软件仿真卫星图(视角2)

    Figure  28.  CST software simulation satellite image (view 2)

    图  29  水平极化和交叉极化电磁仿真信号包络和RD成像结果

    Figure  29.  Horizontally polarized and cross-polarized electromagnetic simulation signal’s envelope and RD imaging results

    图  30  所提方法二维空变校正前后结果对比

    Figure  30.  Comparison of the results before and after two-dimensional space-variant correction for the proposed method

    图  31  水平极化下对比方法的成像结果图

    Figure  31.  Imaging results of the contrast method under horizontal polarization

    图  32  所提方法与对比方法图像熵变化曲线(视角2)

    Figure  32.  Image entropy change curves of the proposed method and the contrast method (view 2)

    图  33  所提方法图像熵变化曲线放大图(视角2)

    Figure  33.  Enlarged image of the entropy change curve of the proposed method (view 2)

    图  34  试验场景图

    Figure  34.  The picture of the experiment

    图  35  实测数据双基角变化趋势

    Figure  35.  The trend of the measured data of the bistatic angle

    图  36  Keystone变换后的RD成像结果及其与光学照片的对应情况

    Figure  36.  Imaging result after Keystone transform and its corresponding part in the optical picture

    图  37  参数初始值补偿后实测数据成像结果

    Figure  37.  Imaging results of measured data after initial parameter value compensation

    图  38  二维空变校正后的实测数据RD成像结果

    Figure  38.  RD imaging results of measured data after two-dimensional space-variation correction

    图  39  二维空变校正后实测数据定标结果

    Figure  39.  Calibration results of measured data after two-dimensional space-variable correction

    图  40  几何畸变校正后实测数据定标结果

    Figure  40.  Calibration results of measured data after geometric distortion correction

    图  41  所提方法成像结果标记点选择位置

    Figure  41.  The location map for the selection of marking points in the imaging results of the proposed method

    图  42  对比方法二维空变校正后实测数据定标结果

    Figure  42.  Calibration results of measured data after two-dimensional space-variable correction by contrast method

    图  43  对比方法成像结果及标记点选择位置

    Figure  43.  Comparison method imaging results and marker point selection location map

    图  44  实测数据所提方法与对比方法图像熵变化曲线

    Figure  44.  Image entropy change curve of the proposed method and the comparison method for measured data

    图  45  实测数据所提方法图像熵变化曲线放大图

    Figure  45.  Enlarged image of the entropy change curve of the proposed method for measured data

    表  1  仿真雷达参数表

    Table  1.   Parameters of simulated radar

    参数 数值
    载频 35 GHz
    带宽 1 GHz
    脉冲重复频率 300 Hz
    脉宽 1 μs
    脉冲数 2048
    下载: 导出CSV

    表  2  各点补偿前后方位向峰值旁瓣比和积分旁瓣比

    Table  2.   Azimuth’s PSLR and ISLR before and after compensation for each point

    峰值旁瓣比(dB) 积分旁瓣比(dB)
    补偿前 补偿后 补偿前 补偿后
    P1 0.0981 11.7714 4.0537 10.2959
    P2 0.2306 12.9285 0.3414 10.6454
    下载: 导出CSV

    表  3  各点补偿前后距离向峰值旁瓣比和积分旁瓣比

    Table  3.   Range’s PSLR and ISLR before and after compensation for each point

    峰值旁瓣比(dB) 积分旁瓣比(dB)
    补偿前 补偿后 补偿前 补偿后
    P1 13.1455 13.4884 11.2785 11.2984
    P2 12.7365 13.2731 11.2785 11.4938
    下载: 导出CSV

    表  4  本文方法与对比方法(BFGS方法)指标对比

    Table  4.   The method of this paper is compared with the method of comparison (BFGS)

    指标 本文所提方法 对比方法
    图像熵值 7.0949 7.0952
    对比度 23.5014 23.4998
    $ O{P_1} $和$O{P_2}$夹角 88.9365° 88.7987°
    迭代次数 13 202
    运行时间 0.737570 s 5.835382 s
    下载: 导出CSV

    表  5  不同SNR下两种方法成像指标对比

    Table  5.   Comparison of imaging indicators of the two methods under different SNRs

    SNR值 图像熵值 对比度 $O{P_1}$和$O{P_2}$夹角 迭代次数 运行时间
    本文所提方法 对比方法 本文所提方法 对比方法 本文所提方法 对比方法 本文所提方法 对比方法 本文所提方法 对比方法
    10 dB 7.5515 7.5518 22.0521 22.0509 88.9554° 88.3489° 17 127 0.969786 s 4.162207 s
    5 dB 8.5377 8.5378 18.4484 18.4475 88.9483° 88.6062° 10 128 0.568464 s 4.012253 s
    0 dB 10.0005 10.0006 12.1812 12.1809 88.8443° 88.3880° 23 137 1.310209 s 4.404005 s
    下载: 导出CSV

    表  6  交叉极化下本文方法与对比方法指标对比

    Table  6.   The index of this method is compared with the comparison method under cross polarization

    方法 图像熵值 对比度 迭代次数 运行时间
    本文所提方法 6.7704 27.9896 13 0.805566 s
    对比方法(BFGS) 6.7754 28.0345 260 9.678188 s
    下载: 导出CSV

    表  7  水平极化下本文方法与对比方法指标对比

    Table  7.   The index of this method is compared with the comparison method under horizontal polarization

    方法 图像熵值 对比度 迭代次数 运行时间
    本文所提方法 5.3443 96.2904 37 2.258587 s
    对比方法(BFGS) 5.3443 96.3270 122 5.285292 s
    下载: 导出CSV

    表  8  实测数据雷达参数表

    Table  8.   Radar parameter table of measured data

    参数数值
    载频33 GHz
    带宽300 MHz
    脉冲重复频率150 Hz
    采样率500 MHz
    脉冲数1024
    下载: 导出CSV

    表  9  本文方法与对比方法指标对比

    Table  9.   The method of this paper is compared with the method of comparison

    方法 图像熵值 对比度 OP1
    OP2夹角(°)
    迭代
    次数
    运行时间(s)
    本文所提方法 6.9455 111.7340 50.4275 61 11.896714
    对比方法(BFGS) 6.9457 111.8247 50.2595 269 29.319547
    下载: 导出CSV
  • [1] 李俊颜, 杨青, 李中余, 等. 基于空变多普勒参数聚类的微波光子ISAR高精度成像方法[J]. 电子学报, 2024, 52(12): 3941–3956. doi: 10.12263/DZXB.20240442.

    LI Junyan, YANG Qing, LI Zhongyu, et al. High-precision microwave photonic ISAR imaging method based on spatially variant Doppler parameter clustering[J]. Acta Electronica Sinica, 2024, 52(12): 3941–3956. doi: 10.12263/DZXB.20240442.
    [2] 邢孟道, 谢意远, 高悦欣, 等. 电磁散射特征提取与成像识别算法综述[J]. 雷达学报, 2022, 11(6): 921–942. doi: 10.12000/JR22232.

    XING Mengdao, XIE Yiyuan, GAO Yuexin, et al. Electromagnetic scattering characteristic extraction and imaging recognition algorithm: A review[J]. Journal of Radars, 2022, 11(6): 921–942. doi: 10.12000/JR22232.
    [3] 符吉祥, 邢孟道, 徐丹, 等. 一种基于微波光子超高分辨雷达机翼振动参数估计方法[J]. 雷达学报, 2019, 8(2): 232–242. doi: 10.12000/JR19001.

    FU Jixiang, XING Mengdao, XU Dan, et al. Vibration-parameters estimation method for airplane wings based on microwave-photonics ultrahigh-resolution radar[J]. Journal of Radars, 2019, 8(2): 232–242. doi: 10.12000/JR19001.
    [4] 田彪, 刘洋, 呼鹏江, 等. 宽带逆合成孔径雷达高分辨成像技术综述[J]. 雷达学报, 2020, 9(5): 765–802. doi: 10.12000/JR20060.

    TIAN Biao, LIU Yang, HU Pengjiang, et al. Review of high-resolution imaging techniques of wideband inverse synthetic aperture radar[J]. Journal of Radars, 2020, 9(5): 765–802. doi: 10.12000/JR20060.
    [5] CHEN Hongmeng, LI Jun, ZHOU Rui, et al. Optimal Bi-ISAR imaging arc selection method with bistatic angle derivative constraint[C]. 2024 IEEE International Conference on Signal, Information and Data Processing (ICSIDP), Zhuhai, China, 2024: 1–4. doi: 10.1109/ICSIDP62679.2024.10869106.
    [6] JIANG Yicheng, WEI Jin, and LIU Zitao. Bistatic ISAR imaging and scaling algorithm based on the estimation of bistatic factor and effective rotation velocity[J]. IEEE Transactions on Aerospace and Electronic Systems, 2024, 60(6): 8522–8538. doi: 10.1109/TAES.2024.3432109.
    [7] CHEN Hongmeng, LI Jun, ZHOU Rui, et al. Focused bistatic ISAR imaging demonstration with nonparametric autofocusing[C]. IET International Radar Conference, Chongqing, China, 2023: 3370–3374. doi: 10.1049/icp.2024.1643.
    [8] DING Jiabao, LI Yachao, WANG Jiadong, et al. Integration of high-order motion compensation and 2-D scaling for maneuvering target bistatic ISAR imaging[J]. IEEE Transactions on Geoscience and Remote Sensing, 2025, 63: 5205120. doi: 10.1109/TGRS.2025.3533881.
    [9] FU Jixiang, YANG Weichao, XUE Min, et al. A novel bistatic ISAR space-variant phase error compensation and geometric correction method based on entropy minimization[C]. IEEE International Geoscience and Remote Sensing Symposium, Athens, Greece, 2024: 3536–3539. doi: 10.1109/IGARSS53475.2024.10641057.
    [10] DING Jiabao, WANG Jiadong, LI Yachao, et al. A spatial variant phase compensation algorithm for bistatic ISAR imaging of maneuvering targets based on optimal parameter estimation[C]. 2021 CIE International Conference on Radar, Haikou, China, 2021: 2087–2090. doi: 10.1109/Radar53847.2021.10027972.
    [11] QIAN Guangzhao and WANG Yong. Satellite-missile bistatic forward-looking SAR imaging of ship target via hybrid SAR-ISAR algorithm[C]. IET International Radar Conference, Chongqing, China, 2023: 2669–2674. doi: 10.1049/icp.2024.1510.
    [12] QIAN Guangzhao and WANG Yong. Monostatic-equivalent algorithm via Taylor expansion for BiSAR ship target imaging[J]. IEEE Transactions on Geoscience and Remote Sensing, 2023, 61: 5200919. doi: 10.1109/TGRS.2022.3233384.
    [13] 朱瀚神, 胡文华, 郭宝锋, 等. 双基地ISAR稀疏孔径机动目标MTRC补偿成像算法[J]. 系统工程与电子技术, 2023, 45(7): 2022–2030. doi: 10.12305/j.issn.1001-506X.2023.07.12.

    ZHU Hanshen, HU Wenhua, GUO Baofeng, et al. Bistatic ISAR sparse aperture maneuvering target MTRC compensation imaging algorithm[J]. Systems Engineering and Electronics, 2023, 45(7): 2022–2030. doi: 10.12305/j.issn.1001-506X.2023.07.12.
    [14] LI Rui, LUO Ying, ZHANG Qun, et al. Time-varying bistatic radar coincidence imaging for rotating targets[C]. IEEE 2nd International Conference on Electronic Information and Communication Technology, Harbin, China, 2019: 495–498. doi: 10.1109/ICEICT.2019.8846253.
    [15] 李中余, 桂亮, 海宇, 等. 基于变分模态分解与优选的超高分辨ISAR成像微多普勒抑制方法[J]. 雷达学报(中英文), 2024, 13(4): 852–865. doi: 10.12000/JR24043.

    LI Zhongyu, GUI Liang, HAI Yu, et al. Ultrahigh-resolution ISAR micro-Doppler suppression methodology based on variational mode decomposition and mode optimization[J]. Journal of Radars, 2024, 13(4): 852–865. doi: 10.12000/JR24043.
    [16] ZHANG Shuanghui, LIU Yongxiang, LI Xiang, et al. Fast ISAR cross-range scaling using modified newton method[J]. IEEE Transactions on Aerospace and Electronic Systems, 2018, 54(3): 1355–1367. doi: 10.1109/TAES.2017.2785560.
    [17] 柴守刚, 陈卫东, 陈畅. 联合几何畸变校正及定标的B-ISAR稀疏成像算法[J]. 现代雷达, 2015, 37(1): 32–37. doi: 10.3969/j.issn.1004-7859.2015.01.008.

    CHAI Shougang, CHEN Weidong, and CHEN Chang. B-ISAR sparse imaging algorithm with geometric distortion correction and calibration[J]. Modern Radar, 2015, 37(1): 32–37. doi: 10.3969/j.issn.1004-7859.2015.01.008.
    [18] 史林, 郭宝锋, 马俊涛, 等. 基于图像旋转相关的空间目标ISAR等效旋转中心估计算法[J]. 电子与信息学报, 2019, 41(6): 1280–1286. doi: 10.11999/JEIT181086.

    SHI Lin, GUO Baofeng, MA Juntao, et al. Rotation center estimation algorithm for ISAR image of the space target based on image rotation and correlation[J]. Journal of Electronics & Information Technology, 2019, 41(6): 1280–1286. doi: 10.11999/JEIT181086.
    [19] AI Xiaofeng, HUANG Yan, ZHAO Feng, et al. Imaging of spinning targets via narrow-band T/R-R bistatic radars[J]. IEEE Geoscience and Remote Sensing Letters, 2013, 10(2): 362–366. doi: 10.1109/LGRS.2012.2205893.
    [20] JIANG Yicheng, SUN Sibo, YEO T S, et al. Bistatic ISAR distortion and defocusing analysis[J]. IEEE Transactions on Aerospace and Electronic Systems, 2016, 52(3): 1168–1182. doi: 10.1109/TAES.2016.140028.
    [21] 夏靖远, 杨志雄, 周治兴, 等. 一种基于元学习的稀疏孔径ISAR成像算法[J]. 雷达学报, 2023, 12(4): 849–859. doi: 10.12000/JR23121.

    XIA Jingyuan, YANG Zhixiong, ZHOU Zhixing, et al. A metalearning-based sparse aperture ISAR imaging method[J]. Journal of Radars, 2023, 12(4): 849–859. doi: 10.12000/JR23121.
    [22] YUAN Zhengkun, WANG Junling, ZHAO Lizhi, et al. An MTRC-AHP compensation algorithm for Bi-ISAR imaging of space targets[J]. IEEE Sensors Journal, 2020, 20(5): 2356–2367. doi: 10.1109/JSEN.2019.2951735.
    [23] WANG Jiannan, MA Jingtao, HUANG Penghui, et al. Linear-geometry distortion correction for bistatic inverse synthetic aperture radar imaging based on deep learning model[C]. IEEE International Geoscience and Remote Sensing Symposium, Athens, Greece, 2024: 11414–11417. doi: 10.1109/IGARSS53475.2024.10640941.
    [24] DING Jiabao, LI Yachao, WANG Jiadong, et al. Joint motion compensation and distortion correction for maneuvering target bistatic ISAR imaging based on parametric minimum entropy optimization[J]. IEEE Transactions on Geoscience and Remote Sensing, 2022, 60: 5118919. doi: 10.1109/TGRS.2022.3213579.
    [25] FU Jixiang, XING Mengdao, and AMIN M G. ISAR imaging motion compensation in low SNR environments using phase gradient and filtering techniques[J]. IEEE Transactions on Aerospace and Electronic Systems, 2021, 57(6): 4296–4312. doi: 10.1109/TAES.2021.3098129.
    [26] KRAGH T J. Monotonic iterative algorithm for minimum-entropy autofocus[C]. Adaptive Sensor Array Processing Workshop, Lexington, USA, 2006: 1147–1159.
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  • 收稿日期:  2025-03-24
  • 修回日期:  2025-07-04
  • 网络出版日期:  2025-09-04

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