A Robust Multi-Channel Moving Target Detection Algorithm for Complex Scenes
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摘要: 针对鲁棒主成分分析(RPCA)算法在多通道慢速地面动目标指示(GMTI)中存在的高虚警以及对通道误差敏感问题，该文提出一种数据重构与速度合成孔径雷达(VSAR)-RPCA联合处理的方法。首先，通过样本挑选与联合像素法完成通道间数据精确重构；然后结合VSAR检测模式提出一种新的RPCA优化模型，通过采用交替投影乘子法对其进行求解得到空间频域的稀疏矩阵，进一步利用动目标与强杂波残余在空间频域通道的分布特性差异实现强杂波残余剔除与动目标检测；最后采用沿航迹干涉算法估计目标径向速度完成动目标重定位。相较于传统RPCA算法，所提算法在非理想强杂波背景下的虚警率显著降低。理论分析与实测实验验证了所提算法的有效性。Abstract: Aiming at the problems of high false alarm and sensitivity to channel error of Robust Principal Component Analysis (RPCA) algorithm in multi-channel Ground Moving Target Indication (GMTI), this paper proposes a data reconstruction and Velocity Synthetic Aperture Radar (VSAR)-RPCA joint processing method. Firstly, the sample selection and joint pixel method are used to complete the accurate reconstruction of inter-channel data; then a new RPCA optimization model is proposed by combining the VSAR detection mode, and the sparse matrix in the spatial frequency domain is obtained by solving the new RPCA optimization model with the alternating projection multiplier method, and then the differences in the distribution characteristics of the moving target and the strong clutter residuals in the spatial frequency domain channel are used to realize the strong clutter residuals rejection and the detection of the moving target; finally, the radial velocity of the target is estimated by the Along-Track Interferometry algorithm to complete the moving target relocation. Compared with the traditional RPCA algorithm, the proposed algorithm significantly reduces the false alarm rate under the background of non-ideal strong clutter. Theoretical analyses and experiments verify the effectiveness of the proposed algorithm.
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1 传统RPCA模型求解算法
输入：观测矩阵$ {\boldsymbol{D}} $，参数$ \kappa $； 输出：低秩矩阵$ {{\boldsymbol{A}}_{k + 1}} $，稀疏矩阵$ {{\boldsymbol{E}}_{k + 1}} $； 初始化：$ {{\boldsymbol{Y}}_0} $=0，$ {\mu _0} \gt 0 $, $k = 0$, $\delta = 1{\rm{e}} - 6$, ${\mathrm{iter}} = 1000$； While ${\left\| {{\boldsymbol{D}} - {{\boldsymbol{A}}_{k + 1}} - {{\boldsymbol{E}}_{k + 1}}} \right\|_{\rm F}} > \delta $ or $k < {\text{iter}}$ do $ \left( {{\boldsymbol{U,\varXi ,V}}} \right) = {\rm{svd}}\left( {{\boldsymbol{D}} - {{\boldsymbol{E}}_k} + {{{{\boldsymbol{Y}}_k}} \mathord{\left/ {\vphantom {{{{\boldsymbol{Y}}_k}} \mu }} \right. } \mu }} \right) $; $ {{\boldsymbol{A}}_{k + 1}} = {\boldsymbol{U}}{{S}_{{1 \mathord{\left/ {\vphantom {1 \mu }} \right. } \mu }}}\left[ {\boldsymbol{\varXi }} \right]{{\boldsymbol{V}}^{\mathrm{H}}} $; $ {{\boldsymbol{E}}_{k + 1}} = {{S}_{{\kappa \mathord{\left/ {\vphantom {\kappa \mu }} \right. } \mu }}}\left( {{\boldsymbol{D}} - {{\boldsymbol{A}}_{k + 1}} + {{{{\boldsymbol{Y}}_k}} \mathord{\left/ {\vphantom {{{{\boldsymbol{Y}}_k}} \mu }} \right. } \mu }} \right) $; $ {{\boldsymbol{Y}}_{k + 1}} = {{\boldsymbol{Y}}_k} + \mu \left( {{\boldsymbol{D - }}{{\boldsymbol{A}}_{k + 1}}{\boldsymbol{ - }}{{\boldsymbol{E}}_{k + 1}}} \right) $; $k = k + 1$; End while 
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2 所提RPCA优化模型求解流程
输入：观测矩阵$ {\boldsymbol{D}} $，参数$ \lambda $； 输出：低秩矩阵$ {{\boldsymbol{A}}_{k + 1}} $，稀疏矩阵$ {F}{\left( {\boldsymbol{E}} \right)_{k + 1}} $； 初始化：$ {{\boldsymbol{Y}}_0} $=0; $ {\mu _0} \gt 0 $, $k = 0$, $\delta = 1{\rm{e}} - 6$, ${\mathrm{iter}} = 1000$； While ${\left\| {{\boldsymbol{D}} - {{\boldsymbol{A}}_{k + 1}} - {{\boldsymbol{E}}_{k + 1}}} \right\|_{\rm F}} > \delta $ or $k < {\mathrm{iter}}$ do $ \left( {{\boldsymbol{U,\varSigma ,V}}} \right) = {\rm{svd}}\left( {{\boldsymbol{D}} - {{\boldsymbol{E}}_k} + {{{{\boldsymbol{Y}}_k}} \mathord{\left/ {\vphantom {{{{\boldsymbol{Y}}_k}} \mu }} \right. } \mu }} \right) $; $ {{\boldsymbol{A}}_{k + 1}} = {\boldsymbol{U}}{S_{{1 \mathord{\left/ {\vphantom {1 \mu }} \right. } \mu }}}\left[ {\boldsymbol{\varXi }} \right]{{\boldsymbol{V}}^{\mathrm{H}}} $; $ {F}{\left( {\boldsymbol{E}} \right)_{k + 1}} = {S_{{\kappa \mathord{\left/ {\vphantom {\kappa \mu }} \right. } \mu }}}\left( {{F}\left( {{\boldsymbol{D}} - {{\boldsymbol{A}}_{k + 1}} + {{{{\boldsymbol{Y}}_k}} \mathord{\left/ {\vphantom {{{{\boldsymbol{Y}}_k}} \mu }} \right. } \mu }} \right)} \right) $; ${{\boldsymbol{E}}_{k + 1}} = {{F}^{ - 1}}\left( {{F}{{\left( {\boldsymbol{E}} \right)}_{k + 1}}} \right)$; $ {{\boldsymbol{Y}}_{k + 1}} = {{\boldsymbol{Y}}_k} + \mu \left( {{\boldsymbol{D}} - {{\boldsymbol{A}}_{k + 1}} - {{\boldsymbol{E}}_{k + 1}}} \right) $; $k = k + 1$; End while
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表 1 多通道SAR系统参数
参数 值 载频(GHz) 8.85 带宽(MHz) 40 采样频率(MHz) 60 脉冲重复频率(Hz) 1000 通道间距(m) 0.559 平台速度(m/s) 115 通道数目(个) 3
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