基于矩阵填充的随机步进频雷达高分辨距离-多普勒谱稀疏恢复方法

胡雪瑶 梁灿 卢珊珊 王在洋 郑乐 李阳

胡雪瑶, 梁灿, 卢珊珊, 等. 基于矩阵填充的随机步进频雷达高分辨距离-多普勒谱稀疏恢复方法[J]. 雷达学报(中英文), 2024, 13(1): 200–214. doi: 10.12000/JR23176
引用本文: 胡雪瑶, 梁灿, 卢珊珊, 等. 基于矩阵填充的随机步进频雷达高分辨距离-多普勒谱稀疏恢复方法[J]. 雷达学报(中英文), 2024, 13(1): 200–214. doi: 10.12000/JR23176
HU Xueyao, LIANG Can, LU Shanshan, et al. Matrix completion-based range-Doppler spectrum estimation for random stepped-frequency radars[J]. Journal of Radars, 2024, 13(1): 200–214. doi: 10.12000/JR23176
Citation: HU Xueyao, LIANG Can, LU Shanshan, et al. Matrix completion-based range-Doppler spectrum estimation for random stepped-frequency radars[J]. Journal of Radars, 2024, 13(1): 200–214. doi: 10.12000/JR23176

基于矩阵填充的随机步进频雷达高分辨距离-多普勒谱稀疏恢复方法

doi: 10.12000/JR23176
基金项目: 国家自然科学基金(62388102),国家重点研发计划(2018YFE0202101, 2018YFE0202103)
详细信息
    作者简介:

    胡雪瑶,博士,副研究员,硕士生导师,主要研究方向为毫米波雷达系统设计与雷达信号处理技术等

    梁 灿,博士生,主要研究方向为毫米波雷达系统设计与雷达信号处理技术等

    卢珊珊,硕士,工程师,主要研究方向为雷达信息研究等

    王在洋,硕士生,主要研究方向为毫米波雷达信号处理技术等

    郑 乐,博士,教授,博士生导师,主要研究方向为毫米波雷达信号处理与数据处理技术等

    李 阳,博士,研究员,博士生导师,主要研究方向为宽带雷达系统、雷达信号处理与雷达系统设计等

    通讯作者:

    郑乐 le.zheng@bit.edu.cn

  • 责任主编:兰岚 Corresponding Editor: LAN Lan
  • 中图分类号: TN958.6

Matrix Completion-based Range-Doppler Spectrum Estimation for Random Stepped-frequency Radars

Funds: The National Natural Science Foundation of China (62388102), The National Key R&D Program of China (2018YFE0202101, 2018YFE0202103)
More Information
  • 摘要: 随机步进频雷达通过合成大带宽,能在较低硬件复杂度下获得距离高分辨效果,同时由于其每个脉冲的载频随机捷变,因而具有强的抗干扰、电磁兼容能力,在复杂电磁环境高精度探测领域具有重要的应用价值。然而,由于其波形在时频域稀疏的感知形式,造成回波相参信息有所缺失,因而传统匹配滤波方法在估计高分辨距离-多普勒时会演化为欠定估计,导致估计谱中产生起伏高旁瓣,严重影响探测性能。为此,该文提出一种基于Hankel重构矩阵填充的随机步进频雷达高分辨距离-多普勒谱低旁瓣稀疏恢复方法。该方法采用低秩矩阵填充思想补全波形在时频域稀疏感知时造成的缺失采样,恢复目标连续相参信息,可以有效解决欠定估计问题。文章首先构建了随机步进频雷达的慢时间-载频(时-频)回波欠采样数据矩阵;然后,重构待恢复数据矩阵为双重Hankel型,并分析证明了矩阵满足低秩先验特性;最后,利用ADMM算法补全未采样时频数据,恢复相参信息,保证了高分辨距离-多普勒谱低旁瓣稀疏恢复。仿真和实测试验证明了该文所提方法的有效性和优越性。

     

  • 图  1  调频RSF信号预处理流程图

    Figure  1.  Diagram of the RSF chirp signal pre-processing flow

    图  2  回波信号矩阵填充处理流程图

    Figure  2.  Matrix completion flow

    图  3  单点目标高分辨距离-速度谱估计结果

    Figure  3.  Range-velocity spectrum for single point target

    图  4  点目标响应函数

    Figure  4.  Point spread functions response

    图  5  PSLR随输入信噪比变化关系

    Figure  5.  PSLR versus input SNR

    图  6  ISLR随输入信噪比变化关系

    Figure  6.  ISLR versus input SNR

    图  7  多目标高分辨距离-速度谱估计结果

    Figure  7.  Range-velocity spectrum for multi-target

    图  8  多目标响应函数

    Figure  8.  Point spread functions response for multi-target

    图  9  多目标场景PSLR随目标数量变化关系

    Figure  9.  PSLR versus the number of targets

    图  10  多目标场景ISLR随目标数量变化关系

    Figure  10.  ISLR versus the number of targets

    图  11  高分辨距离-速度谱估计结果

    Figure  11.  Range-velocity spectrum for multi-target

    图  12  距离-速度对角线点目标响应函数

    Figure  12.  Point spread function response in diagonal line

    图  13  厢货卡车实测数据采集场景

    Figure  13.  Radar prototype and test scenario

    图  14  距离-速度谱估计结果(红框内为目标强散射点)

    Figure  14.  Range-velocity spectrum of MF, CS and MC (the target strong scattering points are in the red box)

    图  15  目标高分辨距离像

    Figure  15.  High resolution range profiles of target

    1  基于ADMM的Hankel变换矩阵填充算法

    1.   Matrix completion algorithm combined with Hankel transformation based on ADMM

     输入:时频欠采样矩阵Y,载频编码${{U}_{n}}$
     输出:时频满采样恢复矩阵$ \hat{\boldsymbol{\varDelta}} $
     1. 对时频欠采样矩阵Hankel变换得到$ {{\boldsymbol{Y}}_{\rm H}} $
     2. ADMM矩阵填充:
      (a) 初始化:$ {\left( {{{\hat{\boldsymbol{\varDelta}} }_{\rm H}}} \right)_1} = {{\boldsymbol{W}}_1} = {{\boldsymbol{Y}}_{\rm H}} $, Z = 0,迭代次数K,惩罚
       因子$ \beta $,步长因子$ \rho $
      (b) for k = 1 to K do
        i. 更新$ {\hat{\boldsymbol{\varDelta}} _{\rm H}} $:$ {\left( {{{\hat{\boldsymbol{\varDelta}} }_{\rm H}}} \right)_{k + 1}} = {D_{\textstyle\frac{1}{\beta }}}\left({{\boldsymbol{W}}_k} - \dfrac{1}{\beta }{{\boldsymbol{Z}}_k}\right) $
        ii. 更新W:$ {{\boldsymbol{W}}_{k + 1}} = {\left( {{{\hat{\boldsymbol{\varDelta}} }_{\rm H}}} \right)_{k + 1}} + \dfrac{1}{\beta }({{\boldsymbol{A}}^{\rm H}}{\boldsymbol{B}} + {{\boldsymbol{Z}}_k}) $
       保持原有观测采样数据不变,即:
       $ {{\boldsymbol{W}}_{k + 1}} = {P_{\varOmega \notin {\varOmega _{\rm H}}}}\left( {{{\boldsymbol{W}}_{k + 1}}} \right) + {P_{\varOmega \in {\varOmega _{\rm H}}}}\left( {{{\boldsymbol{Y}}_{\rm H}}} \right) $
        iii. 更新Z:$ {{\boldsymbol{Z}}_{k + 1}} = {{\boldsymbol{Z}}_k} + \beta \left( {{{\left( {{{\hat{\boldsymbol{\varDelta}} }_{\rm H}}} \right)}_{k + 1}} - {{\boldsymbol{W}}_{k + 1}}} \right) $
        iv. 更新$ \beta $:$ {\beta _{k + 1}} = \rho {\beta _k} $
      (c) end
     3. 对$ {\left( {{{\hat{\boldsymbol{\varDelta}} }_{\rm H}}} \right)_K} $进行Hankel逆变换得到$ \hat{\boldsymbol{\varDelta}} $
    下载: 导出CSV

    表  1  仿真参数

    Table  1.   Simulation parameters

    参数 数值
    中心频率${{f}_0}$ 93 GHz
    最小步进带宽$\Delta $f 18.75 MHz
    脉冲重复时间T 25 μs
    脉冲个数N 64
    捷变频点数M 64
    载频编码$ {{U}}_{{n}} $ 随机均匀分布
    二维FFT处理时窗函数 Hamming窗
    下载: 导出CSV

    表  2  运行时间对比结果(s)

    Table  2.   Runtimes comparison (s)

    栅格点数 所提方法 压缩感知 栅格点数 所提方法 压缩感知
    64×64 5.6 23.6 256×256 5.7 412.6
    128×128 5.6 90.5 320×320 5.7 810.9
    192×192 5.7 187.1
    下载: 导出CSV

    表  3  雷达波形参数

    Table  3.   Waveform parameters of the test radar

    参数 数值
    中心频率${{f}_0}$ 93.31 GHz
    最小步进带宽$\Delta $f 18.75 MHz
    脉冲重复时间T 25.8 μs
    捷变频点数M 64
    脉冲个数N 64
    调频带宽B 25 MHz
    脉冲宽度Tp 2 μs
    载频编码$ {{U}}_{{n}} $ 随机均匀分布
    下载: 导出CSV
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出版历程
  • 收稿日期:  2023-10-03
  • 修回日期:  2023-12-28
  • 网络出版日期:  2024-01-09
  • 刊出日期:  2024-02-28

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