机载雷达深度展开空时自适应处理方法

朱晗归 冯为可 冯存前 邹帛 路复宇

朱晗归, 冯为可, 冯存前, 等. 机载雷达深度展开空时自适应处理方法[J]. 雷达学报, 2022, 11(4): 676–691. doi: 10.12000/JR22051
引用本文: 朱晗归, 冯为可, 冯存前, 等. 机载雷达深度展开空时自适应处理方法[J]. 雷达学报, 2022, 11(4): 676–691. doi: 10.12000/JR22051
ZHU Hangui, FENG Weike, FENG Cunqian, et al. Deep unfolding based space-time adaptive processing method for airborne radar[J]. Journal of Radars, 2022, 11(4): 676–691. doi: 10.12000/JR22051
Citation: ZHU Hangui, FENG Weike, FENG Cunqian, et al. Deep unfolding based space-time adaptive processing method for airborne radar[J]. Journal of Radars, 2022, 11(4): 676–691. doi: 10.12000/JR22051

机载雷达深度展开空时自适应处理方法

doi: 10.12000/JR22051
基金项目: 国家自然科学基金(62001507),陕西省高校科协青年人才托举计划(20210106)
详细信息
    作者简介:

    朱晗归(1997-),男,陕西渭南人,空军工程大学硕士研究生,主要研究方向为稀疏优化算法及其深度展开、深度学习在空时自适应处理、DOA估计的应用

    冯为可(1992-),男,河南平顶山人,空军工程大学防空反导学院讲师,博士,主要研究方向为机载雷达信号处理

    冯存前(1975-),男,陕西富平人,空军工程大学防空反导学院教授、博士生导师,博士,主要研究方向为雷达信号处理及雷达电子战系统

    邹 帛(1999-),男,安徽池州人,硕士研究生,主要研究方向为空时自适应处理、深度展开等

    路复宇(1998-),男,河南焦作人,空军工程大学在读硕士研究生,主要研究方向为DOA估计、目标检测与识别

    通讯作者:

    冯为可 fengweike007@163.com

  • 责任主编:谢文冲 Corresponding Editor: XIE Wenchong
  • 中图分类号: V221+.3; TN951

Deep Unfolding Based Space-Time Adaptive Processing Method for Airborne Radar

Funds: The National Natural Science Foundation of China (62001507), The Young Talent fund of University Association for Science and Technology in Shaanxi, China (20210106)
More Information
  • 摘要: 稀疏恢复空时自适应处理(SR-STAP)方法能够利用少量训练距离单元实现对机载雷达杂波的有效抑制。然而,现有SR-STAP方法均基于模型驱动实现,存在着参数设置困难、运算复杂度高等问题。针对这些问题,该文将基于模型驱动的SR方法和基于数据驱动的深度学习方法相结合,首次将深度展开(DU)引入到机载雷达杂波抑制和目标检测之中。首先,建立了阵列误差(AE)条件下的杂波空时谱和阵列误差参数联合估计模型,并利用交替方向乘子法(ADMM)进行求解;接着,将ADMM算法展开为深度神经网络AE-ADMM-Net,利用充足完备的数据集对其迭代参数进行优化;最后,利用训练后的AE-ADMM-Net对训练距离单元数据进行处理,快速获得杂波空时谱和阵列误差参数的准确估计。仿真结果表明:与典型SR-STAP方法相比,该文所提出的DU-STAP方法能够在保持较低运算复杂度的同时提高杂波抑制性能。

     

  • 图  1  机载雷达几何模型

    Figure  1.  Geometry model of airborne radar

    图  2  ADMM算法的数据流图

    Figure  2.  The data flow graph of ADMM algorithm

    图  3  AE-ADMM-Net的网络结构

    Figure  3.  The network structure of AE-ADMM-Net

    图  4  AE-ADMM-Net的4个子层

    Figure  4.  Four sub-layers of AE-ADMM-Net

    图  5  固定参数ADMM算法杂波空时谱和阵列误差参数估计结果(a1—a4:不同阵列误差参数下的空时谱估计结果,b1—b4:不同阵列误差参数下的幅度误差估计结果,c1—c4:不同阵列误差参数下的相位误差估计结果)

    Figure  5.  Clutter space-time spectra and array error parameters estimated via ADMM algorithm with fixed parameters (a1—a4: Clutter space-time spectra estimation results in different array error parameters, b1—b4: Amplitude error estimation results in different array error parameters, c1—c4: Phase error estimation results in different array error parameters)

    图  6  AE-ADMM-Net的收敛性及其与ADMM算法的对比

    Figure  6.  Convergence performance of AE-ADMM-Net and its comparison with ADMM algorithm

    图  7  不同条件下不同算法的杂波空时谱估计结果(a1—a4:ADMM算法在不同阵列误差参数下的迭代25次的估计结果,b1—b4:ADMM算法在不同阵列误差参数下的迭代45次的估计结果,c1—c4:FOCUSS算法在不同阵列误差参数下的迭代200次的估计结果,d1—d4:SBL算法在不同阵列误差参数下的迭代400次的估计结果,e1—e4:25层的AE-ADMM-Net 在不同阵列误差参数下的的估计结果,f1—f4:45层的AE-ADMM-Net 在不同阵列误差参数下的估计结果)

    Figure  7.  Clutter space-time spectra estimated via different algorithms under different conditions (a1—a4: estimation results of ADMM algorithm with 25 iterations in different array error parameters, b1—b4: estimation results of ADMM algorithm with 45 iterations in different array error parameters, c1—c4: estimation results of FOCUSS algorithm with 200 iterations in different array error parameters, d1—d4: estimation results of SBL algorithm with 400 iterations in different array error parameters, e1—e4: estimation results of AE-ADMM-Net with 25 layers in different array error parameters, f1—f4: estimation results of AE-ADMM-Net with 45 layers in different array error parameters)

    图  8  不同条件下AE-ADMM-Net的阵列误差参数估计结果(a1—a4:不同阵列误差参数下的幅度误差估计结果,b1—b4:不同阵列误差参数下的相位误差估计结果)

    Figure  8.  Array error parameters estimated by AE-ADMM-Net under different conditions (a1—a4: Amplitude error estimation results in different array error parameters, b1—b4: Phase error estimation results in different array error parameters)

    图  9  不同条件下不同方法对应的SCNR损失曲线(a1—a4:不同阵列误差参数下的SCNR曲线结果,b1—b4:不同阵列误差参数下的SCNR曲线局部放大结果)

    Figure  9.  SCNR loss curves corresponding to different methods under different conditions (a1—a4: SCNR loss curves results in different array error parameters, b1—b4: SCNR loss curves results with enlarged scale in different array error parameters)

    图  10  不同条件下不同算法的运行时间

    Figure  10.  Running time of different algorithms under different conditions

    图  11  Mountain Top实测数据处理结果

    Figure  11.  Processing results of Mountain Top actual measured data

    表  1  ADMM算法

    Table  1.   ADMM algorithm

     输入:A, y,迭代次数K,正则化因子$ \rho $,二次惩罚因子$ \gamma $,迭代步长$ \tau $,比例因子$ \delta $和w
     步骤1 初始化:${ {\boldsymbol{\alpha} } ^{(0)} } = { {\bf{0} }_{ {N_{{\rm{d}}} }{N_{{\rm{s}}} } } }$(${N_{{\rm{d}}} }{N_{{\rm{s}}} } \times 1$的全0列向量),${{\boldsymbol{\lambda}} ^{(0)} } = {{\bf{0}}_{NM} }$($NM \times 1$的全0列向量),${{\boldsymbol{t}}^{(0)} } = {{\bf{1}}_M}$($M \times 1$的全1列向量),
         ${{\boldsymbol{T}}^{(0)} } = {{\boldsymbol{I}}_N} \otimes {\rm{diag}}({{\boldsymbol{t}}^{(0)} })$,$k = 0$;
     步骤2 ${ {\boldsymbol{\eta} } ^{(k + 1)} } = \rho \gamma /(1 + \rho \gamma )({ {\boldsymbol{\lambda} } ^{(k)} }/\gamma - {\boldsymbol{A} }{ {\boldsymbol{\alpha} } ^{(k)} } + { {\boldsymbol T}^{(k)} }{\boldsymbol{y} })$;
     步骤3 ${{\boldsymbol{\alpha}} ^{(k + 1)} } = {\text{soft} }({{\boldsymbol{\alpha}} ^{(k)} } + \tau {{\boldsymbol{A}}^{{\rm{H}}} }{{\boldsymbol{\eta}} ^{(k + 1)} }/(\rho \gamma ),\tau /\gamma )$;
     步骤4-1 
         ${ {\boldsymbol{z} }^{(k)} } = {\boldsymbol{A} }{ {\boldsymbol{\alpha} } ^{(k + 1)} } + { {\boldsymbol{\eta} } ^{(k + 1)} } - {{\boldsymbol{\lambda}} ^{(k)} }/\gamma$, ${b_m} = \displaystyle\sum\nolimits_{n = 1}^N {y_{(n - 1)M + m}^ * z_{(n - 1)M + m}^{(k)} }$, ${a_m} = \displaystyle\sum\nolimits_{n = 1}^N {|{y_{(n - 1)M + m} }{|^2} }$,
         $\beta = \left[\delta + {\rm{j}}w - \sum\nolimits_{m = 1}^M {({b_m}/{a_m}} )\right]/\sum\nolimits_{m = 1}^M {(1/{a_m})}$。
     步骤4-2 ${ {\boldsymbol{t} }^{(k + 1)} } = {\left[ {({b_1} + \beta )/{a_1},({b_2} + \beta )/{a_2}, \cdots ,({b_M} + \beta )/{a_M} } \right]^{\rm{T}}}$;
     步骤5 ${ {\boldsymbol{\lambda} } ^{(k + 1)} } = { {\boldsymbol{\lambda} } ^{(k)} } - \gamma ({\boldsymbol{A} }{ {\boldsymbol{\alpha} } ^{(k + 1)} } + {{\boldsymbol{\eta}} ^{(k + 1)} } - { {\boldsymbol T}^{(k + 1)} }{\boldsymbol{y} })$;
     步骤6 令$ k \leftarrow k + 1 $,若$k \le K - 1$,则返回步骤2,否则结束。
     输出: ${\boldsymbol{\alpha}} = {{\boldsymbol{\alpha}} ^K}$, $ {e_m} = 1/t_m^K $, ${\boldsymbol{e} } = {[{e_1},{e_2}, \cdots ,{e_M}]^{\rm{T} } }$。
    下载: 导出CSV

    表  2  仿真参数

    Table  2.   Simulation parameters

    参数数值参数数值
    载机高度H3000 m载机速度v100 ms–1
    阵元数M10 个脉冲数N10 个
    阵元间距d0.1 m工作波长λ0.2 m
    脉冲重复频率fr2000 Hz距离范围[Rmin, Rmax][21,31] km
    距离单元数L100 个杂波块数Nc361 个
    阵元误差数P100 个杂噪比CNR60 dB
    训练数据集大小O7500测试数据集大小S2500
    频率范围f sf d[–0.5,0.5]网格数NsNd50 个
    下载: 导出CSV

    表  3  不同算法的运算复杂度

    Table  3.   Computational complexities of different algorithms

    算法运算复杂度
    FOCUSS$O\left( {3NM{N_{{\rm{s}}} }{N_{{\rm{d}}} } + { {(NM)}^3} + 2{ {(NM)}^2}{N_{{\rm{s}}} }{N_{{\rm{d}}} } } \right)$
    SBL$O\left( {5NM{N_{{\rm{s}}} }{N_{{\rm{d}}} } + { {(NM)}^3} + 2{ {(NM)}^2}{N_{{\rm{s}}} }{N_{{\rm{d}}} } + NM + {N_{{\rm{s}}} }{N_{{\rm{d}}} } } \right)$
    AE-ADMM-Net$O\left( {2NM{N_{{\rm{s}}} }{N_{{\rm{d}}} } + { {(NM)}^2} + 2NM + {N_{{\rm{s}}} }{N_{{\rm{d}}} } } \right)$
    下载: 导出CSV
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  • 收稿日期:  2022-03-25
  • 修回日期:  2022-05-19
  • 网络出版日期:  2022-06-10
  • 刊出日期:  2022-08-28

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