稀疏轨迹毫米波雷达三维高分辨成像算法

马宇欣 海宇 李中余 黄鹏 王朝栋 武俊杰 杨建宇

马宇欣, 海宇, 李中余, 等. 稀疏轨迹毫米波雷达三维高分辨成像算法[J]. 雷达学报, 2023, 12(5): 1000–1013. doi: 10.12000/JR23001
引用本文: 马宇欣, 海宇, 李中余, 等. 稀疏轨迹毫米波雷达三维高分辨成像算法[J]. 雷达学报, 2023, 12(5): 1000–1013. doi: 10.12000/JR23001
MA Yuxin, HAI Yu, LI Zhongyu, et al. 3D high-resolution imaging algorithm with sparse trajectory for millimeter-wave radar[J]. Journal of Radars, 2023, 12(5): 1000–1013. doi: 10.12000/JR23001
Citation: MA Yuxin, HAI Yu, LI Zhongyu, et al. 3D high-resolution imaging algorithm with sparse trajectory for millimeter-wave radar[J]. Journal of Radars, 2023, 12(5): 1000–1013. doi: 10.12000/JR23001

稀疏轨迹毫米波雷达三维高分辨成像算法

doi: 10.12000/JR23001
基金项目: 国家自然科学基金(62171084, 61922023, 62101096),电子信息控制重点实验室开放基金
详细信息
    作者简介:

    马宇欣,硕士生,研究方向为合成孔径雷达三维成像、稀疏信号恢复等

    海 宇,博士生,研究方向为超高分辨率雷达成像、微波光子雷达成像、稀疏信号恢复等

    李中余,研究员,研究方向为双/多基合成孔径雷达成像技术等

    黄 鹏,硕士生,研究方向为ISAR超分辨成像、结构化成像等

    王朝栋,博士生,研究方向为合成孔径雷达三维成像等

    武俊杰,教授,博士生导师,研究方向为合成孔径雷达成像、双/多基合成孔径雷达、雷达信号处理等

    杨建宇,教授,博士生导师,研究方向为雷达信号处理、合成孔径雷达成像等

    通讯作者:

    海宇 hyuestcarticle@163.com

    李中余 zhongyu_li@uestc.edu.cn

  • 责任主编: 金添 Corresponding Editor: JIN Tian
  • 中图分类号: TN957

3D High-resolution Imaging Algorithm with Sparse Trajectory for Millimeter-wave Radar

Funds: The National Natural Science Foundation of China (62171084, 61922023, 62101096), Science and Technology on Electronic Information Control Laboratory Foundation
More Information
  • 摘要: 近年来,由于毫米波雷达具有穿透能力强、体积小巧、探测精度高等特性,因此被广泛应用于安全检测、零件无损探测和医学诊断等领域。然而,由于硬件发射带宽的限制,如何实现超高二维分辨率成为毫米波雷达应用中的挑战之一。采用雷达平台扫描形成二维孔径的方式可以实现高度向和方位向的二维高分辨。然而,在扫描过程中,毫米波雷达在高度维会产生稀疏的轨迹,使得高度向回波采样稀疏,进而降低成像质量。为了解决这一问题,该文提出了一种基于Hankel变换矩阵填充的毫米波雷达高分辨三维成像算法。该方法采用了矩阵填充算法对稀疏采样回波进行了恢复,保证了毫米波雷达在扫描平面的成像精度。该文首先分析了毫米波雷达高度-距离切面的低秩先验特性,为了解决稀疏轨迹采样时,数据整行整列缺失的问题,对回波数据矩阵采用Hankel变换进行重新构造,使得待恢复数据矩阵满足矩阵填充算法应用条件。然后,提出了一种融合低秩与稀疏先验的基于截断的Schatten-p范数的矩阵填充算法,对采样数据矩阵进行恢复,以保证稀疏轨迹毫米波雷达的三维分辨率。最后,通过仿真和多组实测数据,证明了采用该文方法可以在仅使用20%~30%的高度向回波时仍实现目标高分辨三维成像。

     

  • 图  1  稀疏轨迹毫米波雷达几何构型

    Figure  1.  Geometric configuration of sparse trajectory millimeter wave radar

    图  2  采样布局图

    Figure  2.  Diagram of sampling layout

    图  3  Hankel构造变换示意图

    Figure  3.  Diagram of Hankel structural transformation

    图  4  成像方法流程图

    Figure  4.  Flow diagram of imaging method

    图  6  不同方法的高度-距离切面矩阵恢复图

    Figure  6.  Different methods of height-distance section matrix restoration

    图  5  多点目标布局及成像图

    Figure  5.  Multi-point target layout and imaging diagram

    图  7  点目标不同稀疏度轨迹下成像结果

    Figure  7.  Imaging results of point targets with different sparsity trajectories

    图  8  20%稀疏轨迹下中心点高度剖面对比图

    Figure  8.  Height profile comparison of center points under 20% sparse trajectory

    图  9  系统及目标示意图[28]

    Figure  9.  System and target diagram[28]

    图  10  稀疏度为20%的稀疏轨迹位置示意图

    Figure  10.  Location diagram of sparse trajectory with a sparsity of 20%

    图  11  柠檬芯成像图

    Figure  11.  Images of lemon core

    图  12  不同稀疏度的稀疏轨迹位置示意图

    Figure  12.  Location diagram of sparse trajectory with different sparsity

    图  13  不同目标不同稀疏轨迹下成像结果图

    Figure  13.  Imaging results of different targets with different sparse trajectories

    1  联合Hankel变换的TSPN矩阵填充算法(Hankel-TSPN)

    1.   TSPN matrix completion algorithm combined with Hankel transformation (Hankel-TSPN)

     输入:获取第m个方位向的高度-距离切面${\boldsymbol{S} }' _{ {\text{H-R} } } \left( {t,{y_m},z} \right)$,
        距离向长度K
     输出:第m个方位向的恢复高度-距离切面信号${ {\boldsymbol{S} }_{ {\rm{full} } } }\left( {t,{y_m},z} \right)$
     1. for kk=1 to K do
     2. 对距离单元向量做Hankel变换:${ {\boldsymbol{H} }_{{1} } } = { {\bf{H} } }\left( { {\boldsymbol{S} }{'_{\bf{H} } }\left( { {t_{kk} },{y_m},z} \right)} \right)$
     3. TSPN矩阵填充
       (a) 初始化:${{\boldsymbol{S}}_0} = {{\boldsymbol{D}}_0} = {{\boldsymbol{H}}_1}$, ${{\boldsymbol{Y}}}_{0},{{\boldsymbol{W}}}_{0},{{\boldsymbol{Z}}}_{0}$为零矩阵;迭代
         次数MAX;惩罚参数${\beta _0}$;步长扩张算子$\rho $
       (b) for k=1 to ${\text{MAX}}$ do
         i. 更新S: ${{\boldsymbol{S}}^{k + 1}} = \arg \min \left\{ {L\left( {{\boldsymbol{S}},{{\boldsymbol{D}}^k},{{\boldsymbol{W}}^k},{{\boldsymbol{Y}}^k},{{\boldsymbol{Z}}^k}} \right)} \right\}$
         ii. 更新W
           ${{\boldsymbol{W}}^{k + 1}} = \arg \min \left\{ {L\left( {{{\boldsymbol{S}}^{k + 1}},{{\boldsymbol{D}}^k},{\boldsymbol{W}},{{\boldsymbol{Y}}^k},{{\boldsymbol{Z}}^k}} \right)} \right\}$
         iii. 更新D
          ${{\boldsymbol{D}}^{k + 1}} = \arg \min \left\{ {L\left( {{{\boldsymbol{S}}^{k + 1}},{\boldsymbol{D}},{{\boldsymbol{W}}^{k + 1}},{{\boldsymbol{Y}}^k},{{\boldsymbol{Z}}^k}} \right)} \right\}$
         iv. 更新Y:${{\boldsymbol{Y}}^{k + 1}} = {{\boldsymbol{Y}}^k} + {\beta ^k}\left( {{{\boldsymbol{D}}^{k + 1}} - {{\boldsymbol{S}}^{k + 1}}} \right)$
         v. 更新Z:${{\boldsymbol{Z}}^{k + 1}} = {{\boldsymbol{Z}}^k} + {\beta ^k} $$\left( {{{\boldsymbol{W}}^{k + 1}} - {\text{DCT}}\left( {{{\boldsymbol{S}}^{k + 1}}} \right)} \right)$
         vi. 更新$\beta $:${\beta ^{k + 1}} = \rho {\beta ^k}$
       (c) end
     4. Hankel逆变换:${ {\boldsymbol{S} }_{ {\rm{full} } } }\left( { {t_{kk} },{y_m},z} \right) = { {{\boldsymbol{H}}}^{ { - 1} } }\left( { { {\boldsymbol{X} }^{ {\bf{MAX} } } } } \right)$
     5. end
    下载: 导出CSV

    表  1  仿真参数

    Table  1.   Simulation parameter

    参数名称数值
    载波频率${f_{\rm{c}}}$92.5 GHz
    信号带宽${B_r}$5 GHz
    方位孔径长度${L_{\rm{A} } }$0.16 m
    方位采样点数100
    高度孔径长度${L_{\rm{H}}}$0.16 m
    高度采样点数100
    等效面阵与目标距离${Z_0}$0.4 m
    下载: 导出CSV

    表  2  20%稀疏轨迹下高度剖面的峰值旁瓣比与积分旁瓣比(dB)

    Table  2.   Peak sidelobe ratio and integral sidelobe ratio of height profile at 20% sparse trajectory (dB)

    高度剖面指标PSLRISLR
    满采–11.0653–7.6698
    稀疏–10.6606–4.5651
    TSPN–10.0541–6.7948
    Hankel-TSPN–10.6915–6.9017
    下载: 导出CSV

    表  3  柠檬芯实测目标参数

    Table  3.   Lemon core measured target parameter

    参数名称参数值
    载波频率${f_{\rm{c}}}$136 GHz
    信号带宽${B_r}$8 GHz
    方位孔径长度${L_{\rm{A}}}$0.11 m
    方位采样点数101
    高度孔径长度${L_{\rm{H}}}$0.11 m
    高度采样点数101
    等效面阵与目标距离${Z_0}$0.315 m
    轨迹稀疏度I20%
    下载: 导出CSV

    表  4  三维方位-高度切面图图像质量比较

    Table  4.   Comparison of image quality of 3D azimuth-height slice

    成像指标对比度锐度图像熵图像相似度
    满采24.38841.63E+108.52211
    Hankel-TSPN20.27661.42E+108.39770.8855
    压缩感知15.40882.77E+087.96590.2723
    稀疏2.51195.42E+078.32590.1115
    下载: 导出CSV

    表  5  不同算法的计算复杂度

    Table  5.   Computational complexity of different algorithms

    算法名称计算复杂度
    本文算法(Hankel-TSPN)O(MNKDxDyDz + MKiterN 3),iter为TSPN循环次数
    压缩感知(CS-SRBIM)$O\left( {{{\left( {MNK} \right)}^2}{D_x}{D_y}{D_z}} \right)$
    后向投影(BP)$O\left( {MNK{D_x}{D_y}{D_z}} \right)$
    下载: 导出CSV
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  • 收稿日期:  2023-01-04
  • 修回日期:  2023-04-18
  • 网络出版日期:  2023-05-17
  • 刊出日期:  2023-10-28

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