基于相位追踪的SAR运动目标高阶距离徙动校正方法

杜华贵 宋勇平 孙晓颖 姜南 范崇祎 陈乐平 黄晓涛

杜华贵, 宋勇平, 孙晓颖, 等. 基于相位追踪的SAR运动目标高阶距离徙动校正方法[J]. 雷达学报(中英文), 2024, 13(5): 955–973. doi: 10.12000/JR24122
引用本文: 杜华贵, 宋勇平, 孙晓颖, 等. 基于相位追踪的SAR运动目标高阶距离徙动校正方法[J]. 雷达学报(中英文), 2024, 13(5): 955–973. doi: 10.12000/JR24122
DU Huagui, SONG Yongping, SUN Xiaoying, et al. A new approach to high-order range cell migration correction for SAR ground moving targets based on phase tracking[J]. Journal of Radars, 2024, 13(5): 955–973. doi: 10.12000/JR24122
Citation: DU Huagui, SONG Yongping, SUN Xiaoying, et al. A new approach to high-order range cell migration correction for SAR ground moving targets based on phase tracking[J]. Journal of Radars, 2024, 13(5): 955–973. doi: 10.12000/JR24122

基于相位追踪的SAR运动目标高阶距离徙动校正方法

DOI: 10.12000/JR24122 CSTR: 32380.14.JR24122
基金项目: 国家自然科学基金(62101566)
详细信息
    作者简介:

    杜华贵,博士生,主要研究方向为雷达多径信号处理与SAR信号处理

    宋勇平,博士,讲师,主要研究方向为穿墙探测、MIMO雷达成像和微弱目标检测等

    孙晓颖,硕士,主要研究方向为雷达信号处理与SAR信号处理

    姜 南,博士,讲师,主要研究方向为合成孔径雷达成像、新体制雷达信号处理等

    范崇祎,博士,副教授,主要研究方向为阵列信号处理、SAR成像

    陈乐平,博士,副教授,主要研究方向为高分辨率合成孔径雷达成像

    黄晓涛,教授,主要研究方向为阵列信号处理、新体制雷达系统与技术、目标检测和SAR高分辨成像等

    通讯作者:

    宋勇平 sypopqjkl@163.com

  • 责任主编:孙光才 Corresponding Editor: SUN Guangcai
  • 11) BFGS-WOA方法:BFGS与鲸鱼优化算法(Whale Optimization Algorithm, WOA)的结合,其中,由布罗依丹(Broyden)、弗莱彻(Fletcher)、戈德福布(Goldfarb)和香诺(Shanno)共同提出的,因此得名BFGS,英文全称为Broyden-Fletcher-Goldfarb-Shanno algorithm。
  • 中图分类号: TN957.51

A New Approach to High-order Range Cell Migration Correction for SAR Ground Moving Targets Based on Phase Tracking

Funds: The National Natural Science Foundation of China (62101566)
More Information
  • 摘要: 距离徙动校正(RCMC)是合成孔径雷达(SAR)实现运动目标参数估计和聚焦成像的关键环节。当目标或平台运动复杂时,传统低阶RCMC方法将不再适用,而现有基于参数化的高阶RCMC方法易存在模型失配和计算复杂度高的问题、现有非参数化方法在低信噪比下性能也将大幅下降。对此,该文借助扩展卡尔曼滤波(EKF)对造成RCM的相位进行追踪,进而构建RCM补偿函数实现RCMC。所提方法不依赖于RCM的具体模型,追踪得到的相位包含高阶分量,因此可以实现SAR运动目标的高阶RCMC。此外,EKF在进行相位追踪的同时能对信号进行滤波处理,可有效降低所提方法的信噪比(SNR)门限。与传统方法相比,该方法适用性广,计算量适中,且能校正不可忽略的高阶残余距离徙动。该文详细阐释了所提方法的原理及数学模型,并通过多组仿真和实测数据处理验证了所提方法的有效性和优越性。

     

  • 图  1  机载SAR几何关系

    Figure  1.  Airborne SAR geometry

    图  2  数据预处理结果

    Figure  2.  Preprocessing results of SAR data

    图  3  多普勒相位历程追踪结果

    Figure  3.  Doppler phase tracking result

    图  4  全频段数据的RCMC结果

    Figure  4.  RCMC results for full-frequency band data

    图  5  不同方法的RCMC结果

    Figure  5.  RCMC results for different methods

    图  6  各方法RCMC后的二维聚焦结果

    Figure  6.  2D focusing results of each RCMC method

    图  7  所提方法的二维聚焦结果

    Figure  7.  2D focusing results of proposed method

    图  8  多散射点下的二维聚焦结果

    Figure  8.  2D focusing results for multi-scatters

    图  9  多频余弦耦合波动下的追踪结果

    Figure  9.  Phase tracking result under multifrequency cosine-coupled fluctuations

    图  10  多频余弦耦合波动下点目标的处理结果

    Figure  10.  Processing results of point target under multifrequency cosine-coupled fluctuations

    图  11  多频余弦耦合波动下多散射点目标的处理结果

    Figure  11.  Processing results of multi-point target under multifrequency cosine-coupled fluctuations

    图  12  MMW雷达实测数据脉压结果

    Figure  12.  Pulse compression result of MMW radar data

    图  13  所提方法处理结果

    Figure  13.  Processing results of the proposed method

    图  14  所提方法处理结果(人为加入噪声)

    Figure  14.  Processing results of the proposed method (artifical noise)

    图  15  实测场景

    Figure  15.  Observation scene

    图  16  Ka波段实测数据处理结果

    Figure  16.  Processing results of Ka-band measured data

    图  17  现有方法RCMC结果

    Figure  17.  RCMC results of existing methods

    图  18  不同方法的成像结果

    Figure  18.  Imaging results under different methods

    1  二元状态空间方程的迭代求解过程

    1.   Iterative solution of binary state-space equation

     输入:目标所在距离单元的方位向采样信号$ s_{{\mathrm{T}}}(k) $
     输出:相位历程$ \phi(k) $的估计值$\tilde \phi(k) $:$\left\{ \begin{aligned} &\tilde \phi(k)=\hat{\boldsymbol{\varphi}}_k(1);\;k \ne N_{\mathrm{a}}-1\\ & \left[ \tilde \phi(N_{\mathrm{a}}-2) \;\;\hat{\boldsymbol{\phi}}(N_{\mathrm{a}}-1)\;\;\hat{\boldsymbol{\phi}}(N_{\mathrm{a}})\right]^{\rm{T}}= \hat{\boldsymbol{\varphi}}_{N_{\mathrm{a}}-1};\;k=N_{\mathrm{a}}-1 \end{aligned}\right. $。  $ O(1) $
     1. 初始化参数:相位状态向量$ {\boldsymbol{\varphi}}_{2} $,对应的协方差矩阵$ \boldsymbol{\varPhi}_{2} $,相位状态方程噪声协方差矩阵$ \boldsymbol{W}_{2} $;幅度状态向量$ {\boldsymbol{p}}_{2} $,对应的协方差矩阵
     $ {\boldsymbol{P}}_{2} $,幅度状态方程噪声协方差矩阵$ {\boldsymbol{V}}_{2} $;观测方程噪声协方差矩阵$ \boldsymbol{R}_{2} $。
     2. EKF循环迭代开始,令 $ k={3} $
     3. 提取观测数据采样值:$ {\boldsymbol{s}}_{k}=\left[s_{{\mathrm{T}}}(k-1) \;\;s_{{\mathrm{T}}}(k) \;\;s_{{\mathrm{T}}}(k+1)\right]^{\mathrm{T}} $,并通过式(18)计算得$ {\boldsymbol{y}}_{k} $;  $ O(1) $
     4. 状态向量预测值更新:$ \hat{{\boldsymbol{\varphi}}}_{k|k-1}={\boldsymbol{B}} \hat{{\boldsymbol{\varphi}}}_{k-1} ;\,\hat{{\boldsymbol{p}}}_{k| k-1}=\boldsymbol{B} {\hat{\boldsymbol{p}}_{k-1}} $;  $ O\left(M^{2}\right) $
     5. 状态向量协方差矩阵计算:$ {\boldsymbol{\varPhi}}_{k|k-1}={\boldsymbol{B \varPhi}}_{k-1} {\boldsymbol{B}}^{{\mathrm{T}}}+{\boldsymbol{W}}_{k-1} ; {\boldsymbol{P}}_{k|k-1}={\boldsymbol{B P}}_{k|k-1} {\boldsymbol{B}}^{{\mathrm{T}}}+{\boldsymbol{V}}_{k-1} $;  $ O\left(M^{3}+M^{2}\right) $
     6. 雅可比矩阵计算:$ {\boldsymbol{H}}_{1 k}=\partial f\left({\boldsymbol{p}}_{k}, {\boldsymbol{\varphi}}_{k}\right) / \partial {\boldsymbol{\varphi}}_{k };\, \boldsymbol{H}_{2k}=\partial f\left({\boldsymbol{p}}_{k}, {\boldsymbol{\varphi}}_{k}\right) / \partial {\boldsymbol{p}}_{k} $;  $ O\left(M^{2}\right) $
     7. 卡尔曼增益计算:
     ${\boldsymbol{K}}_{1k}={\boldsymbol{\varPhi}}_{k|k-1} {\boldsymbol{H}}^{\mathrm{T}}_{1k}({\boldsymbol{H}}_{1k}{\boldsymbol{\varPhi}}_{k|k-1}{\boldsymbol{H}}^{\mathrm{T}}_{1k}+{\boldsymbol{R}}_{k-1})^{-1};\;{\boldsymbol{K}}_{2k}={\boldsymbol{P}}_{k|k-1}{\boldsymbol{H}}^{\mathrm{T}}_{2k}({\boldsymbol{H}}_{2k}{\boldsymbol{P}}_{k|k-1}{\boldsymbol{H}}^{\mathrm{T}}_{2k}+{\boldsymbol{R}}_{k-1})^{-1} $;
     $ O\left(M^{3}+M^{2}\right) $
     8. 根据ADMM策略,令幅度状态值为$ \hat{{\boldsymbol{p}}}_{k} \approx \hat{{\boldsymbol{p}}}_{k|k-1} $;  $ O(1) $
     9. 状态向量更新:$ \hat{\boldsymbol{\varphi}}_k=\hat{\boldsymbol{\varphi}}_{k|k-1}+{\boldsymbol{K}}_{1k}\left[ {{{\boldsymbol{y}}_{{k}}} - \hat {\boldsymbol{A}}'_k \odot {{\boldsymbol{h}}_2}({{\hat {\boldsymbol{\varphi}} }_{k|k - 1}})} \right] ;{\hat {\boldsymbol{p}}_k} = {\hat {\boldsymbol{p}}_{k|{{k - 1}}}} + {\boldsymbol{K}}_{2k}\left[ {{{\boldsymbol{y}}_{{k}}} - \hat {\boldsymbol{A}}'_k \odot {{\boldsymbol{h}}_2}({{\hat {\boldsymbol{\varphi}} }_{k|k - 1}})} \right] $
     其中,$ \hat{{\boldsymbol{A}}}_{k}^{\prime}=\left[{\boldsymbol{p}}_{k}\; {\boldsymbol{p}}_{k}\right]^{{\mathrm{T}}} $。
     $ O\left(M^{2}+M\right) $
     10. 状态向量协方差矩阵更新:${\boldsymbol{\varPhi}}_k=({\boldsymbol{I}}_{3 \times 3}-{\boldsymbol{K}}_{1k}{\boldsymbol{H}}_{1k}){\boldsymbol{\varPhi}}_{k|k-1};\;{\boldsymbol{P}}_k=({\boldsymbol{I}}_{3 \times 3 }-{\boldsymbol{K}}_{2k}{\boldsymbol{H}}_{2k}){\boldsymbol{P}}_{k|k-1} $;  $ O\left(M^{3}+M^{2}\right) $
     11. 根据文献[36,37],对噪声协方差矩阵进行自适应更新:
     $ {\boldsymbol{W}}_{k}=\left(1-d_{k}\right) {\boldsymbol{W}}_{k-1}+d_{k} {\boldsymbol{K}}_{1 k}\left({\boldsymbol{\varepsilon}}_{k} {\boldsymbol{\varepsilon}}_{k}^{{\mathrm{T}}}\right) {\boldsymbol{K}}_{1k}^{{\mathrm{T}}};\; {\boldsymbol{V}}_{k}=\left(1-d_{k}\right) {\boldsymbol{V}}_{k-1}+d_{k} {\boldsymbol{K}}_{2k}\left({\boldsymbol{\varepsilon}}_{k} {\boldsymbol{\varepsilon}}_{k}^{{\mathrm{T}}}\right) {\boldsymbol{K}}_{2k}^{{\mathrm{T}}} $,
     $ \boldsymbol{R}_{k}=\left(1-d_{k}\right) {\boldsymbol{R}}_{k-1}+d_{k}\left({\boldsymbol{\varepsilon}}_{k} {\boldsymbol{\varepsilon}}_{k}^{\mathrm{T}}-\boldsymbol{H}_{1k} {\boldsymbol{\varPhi}}_{k|k-1} \boldsymbol{H}_{1 k}^{\mathrm{T}}\right) $
     其中,$ {\boldsymbol{\varepsilon}}_{k}={\boldsymbol{y}}_{k}-\hat{{\boldsymbol{A}}}'_{k} \odot {\boldsymbol{h}}_{2}\left(\hat{{\boldsymbol{\varphi}}}_{k|k-1}\right) $,且$ d_{k}=(1-b)/\left(1-b^{k}\right),(0<b<1) $,$ b $表示遗忘因子。
     $ O\left(M^{3}+M^{2}\right) $
     12. 更新EKF循环索引值:$ k=k+1 $;  $ O(1) $
     13. 重复上述步骤3—步骤12,直至$ k=N_{\rm a}-1 $,结束循环迭代。
    下载: 导出CSV

    表  1  计算复杂度

    Table  1.   Computation complexity

    方法 计算复杂度
    GRFT $ O\left(N_{\rm r} N_{\rm a} N_{0}^{L}\right) $
    FAR $ O\left(N_{\rm a} N_{\rm r} \log N_{\rm r}\right) $
    ACCF $ O\left(N_{\rm a} N_{\rm r} \log N_{\rm r}\right) $
    ACCM $ O\left(N_{\rm a} N_{\rm r}\right) $
    BFGS-WOA $ O\left(N_{I} N_{{\mathrm{r}}} N_{\rm a}\right)+O\left(N_{I} N_{\rm a}^{3}\right) $
    所提方法 $ O\left(N_{\rm r} N_{\rm a}^{2}\right)+O\left(M^{3} N_{\rm a}\right) $
    下载: 导出CSV

    表  2  雷达仿真参数

    Table  2.   Radar simulation parameters

    参数 数值
    中心频率(GHz) 10
    信号带宽(MHz) 300
    距离向采样率(MHz) 360
    信号脉宽(μs) 10
    脉冲重复频率(Hz) 2000
    中心斜距(km) 10
    距离向采样点数 4096
    方位向采样点数 8192
    下载: 导出CSV

    表  3  平台与目标运动参数

    Table  3.   Platform and target motion parameters

    参数 数值
    平台速度$ V $(m/s) 100
    目标距离向速度$ v_{\rm r} $(m/s) –10
    目标距离向加速度$ a_{\rm r} $(m/s2) –2
    目标方位向速度$ v_{\rm a} $(m/s) 10
    目标方位向加速度$ a_{\rm a} $(m/s2) 2
    下载: 导出CSV

    表  4  不同SNR下各方法的图像对比度

    Table  4.   Image contrast of each method under different SNR

    方法 SNR (dB)
    5 2 0 –2 –4 –5 –6
    5阶GRFT 210.76 136.79 115.13 86.72 30.70 28.74 1.08
    FAR 10.05 8.32 7.56 7.43 5.31 3.48 1.36
    ACCF 12.31 7.24 6.37 4.86 4.52 1.38 1.04
    ACCM 10.61 6.15 2.61 1.22 1.08 1.05 1.04
    BFGS-WOA 206.30 134.21 106.30 76.33 24.49 10.16 1.01
    所提方法 491.58 243.74 157.03 112.70 110.76 100.62 100.22
    下载: 导出CSV

    表  5  各方法的计算时间

    Table  5.   Calculation time under different methods

    方法 平均耗时(s)
    5阶GRFT 8870.32
    FAR 13.48
    ACCF 12.86
    ACCM 10.04
    BFGS-WOA 36.25
    所提方法 19.64
    下载: 导出CSV

    表  6  MMW雷达参数

    Table  6.   MMW radar parameters

    参数 数值
    中心频率(GHz) 77
    信号带宽(GHz) 2.56
    距离向采样率(MHz) 10
    脉冲重复频率(Hz) 100
    中心斜距(m) 10
    雷达速度(cm/s) 2.13
    下载: 导出CSV

    表  7  Ka波段雷达参数

    Table  7.   Ka-band radar parameters

    参数 数值
    中心频率(GHz) Ka波段
    距离分辨率(m) 0.15
    观测时间(s) 70
    飞行半径(m) 6000
    飞行高度(km) 3
    雷达速度(m/s) 80
    下载: 导出CSV
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出版历程
  • 收稿日期:  2024-06-13
  • 修回日期:  2024-07-25
  • 网络出版日期:  2024-08-23
  • 刊出日期:  2024-10-28

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