Research on Spaceborne High Resolution Wide Swath Imaging Method Based on Relax Algorithm
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摘要:
现代星载合成孔径雷达(SAR)系统要求同时具备高分辨率和宽测绘带的能力，而传统单通道星载SAR系统在分辨率和测绘带两个重要指标之间存在固有矛盾，因此方位向多通道的方法被提出并用于解决上述问题。该文在分析方位向多通道回波模型的基础上，结合Relax算法的特点，提出了一种基于Relax算法的星载SAR高分宽幅(HRWS)成像方法，并给出了新方法的详细迭代流程。通过点目标回波仿真，并与传统的方位向多通道HRWS重建方法进行对比，验证了新方法的可靠性和有效性。
Abstract:The modern spaceborne SAR system requires both high resolution and wide swath, and the conventional single channel spaceborne SAR system has a contradiction between the two important indexes, the azimuth multichannel method is proposed and used to solve the above problem. Based on the analysis of the azimuth multichannel echo model and the characteristics of the Relax algorithm, a spaceborne SAR High Resolution Wide Swath (HRWS) imaging method is proposed, and the iterative process of the new method is described in detail. By the simulation of point target echo, and comparing with the traditional azimuth multichannel HRWS reconstruction methods, the reliability and effectiveness of the proposed method are verified.
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表 1 公式中用到的符号说明
符号 说明 $M$ 通道个数 $r$ 距离变量，$r = {\rm c}t/2$ c 光速 $t$ 距离向时间变量 ${f_{\rm d}}$ 多普勒频率 $\vartheta $ 目标参数向量，$\vartheta = {[{T_0}, {R_0}, {\sigma ^2}, \varTheta ]^{\rm{T}}}$ ${T_0}$ 最小斜距对应的时间 ${R_0}$ 最小斜距$\min \{ R(T\,)\} = R({T_0}) = {R_0}$ ${\sigma ^2}$ 目标功率 $\varTheta $ 目标相位 ${f\!_{p}}$ 各通道的脉冲重复频率 $\varOmega $ 2次相位项的变化率 $R(T\,)$ 雷达与目标之间的距离 $T\,$ 慢时间变量 ${{u}}[{f_{\rm d}}, \vartheta ]$ 天线与目标间的瞄准线向量 ${A_m}$ 第$m$个通道的双向天线方向图 ${d_m}$ 第$m$个通道的等效相位中心 
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表 2 基于Relax算法的模糊抑制
For $m = 1: \rm Na$ For $n = 1:{\rm Nr}$
%遍历所有距离-多普勒单元(其中，$\rm Na$表示多普勒单元的个数，
$\rm Nr$表示距离单元的个数)
${Z_{{\rm{rec_{-}1}}}}(r, {f_{\rm d}} + p{f\!_{p}}) = \frac{{{{a}}_p^{\rm{H}}\left( {{f_{\rm d}}} \right){{Z}}\left( {r, {f_{\rm d}}} \right)}}{M}$ %初始化操作
%第1次迭代
$\begin{align}{{{Z}}_{p_{-}1}}\left( {r, {f_{\rm d}}} \right) =& {{Z}}\left( {r, {f_{\rm d}}} \right) \\&- \sum\limits_{i = - \left( {M - 1} \right)/2, i \ne p}^{\left( {M - 1} \right)/2} {{{{a}}_i}\left( {{f_{\rm d}}} \right)} \cdot {Z_{{\rm{rec_{-}1}}}}\left( {r, {f_{\rm d}} + p{f\!_{p}}} \right)\end{align}$
${\hat Z_{{\rm{rec_{-}1}}}}\left( {r, {f_{\rm d}} + p{f\!_{p}}} \right) = \frac{{{{a}}_p^{\rm{H}}\left( {{f_{\rm d}}} \right){{{Z}}_{p_{-}1}}\left( {r, {f_{\rm d}}} \right)}}{M}$
如果未满足收敛条件或者未达到迭代次数
%第$k$次迭代($k \ge 2$)
$\begin{align}{{{Z}}_{p_{-}k}}\left( {r, {f_{\rm d}}} \right) =& {{Z}}\left( {r, {f_{\rm d}}} \right) \\& - \sum\limits_{i = - \left( {M - 1} \right)/2, i \ne p}^{\left( {M - 1} \right)/2} {{{{a}}_i}\left( {{f_{\rm d}}} \right)} \cdot {\hat Z_{{{{\rm rec}_{-}k - 1}}}}\left( {r, {f_{\rm d}} + p{f\!_{p}}} \right)\end{align}$
${\hat Z_{{{{\rm rec}_{-}k}}}}\left( {r, {f_{\rm d}} + p{f\!_{p}}} \right) = \frac{{{{a}}_p^{\rm{H}}\left( {{f_{\rm d}}} \right){{{Z}}_{p_{-}k}}\left( {r, {f_{\rm d}}} \right)}}{M}$
End
End
End
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表 3 不同重建方法的性能对比
算法类别 PSLR(dB) 方位向分辨率(m) SNR(dB) SANR(dB) 矩阵求逆法 13.99 1.66 39.46 27.08 最大信号法 13.99 1.66 40.33 12.97 Relax法 13.82 1.66 50.56 21.22
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