High-resolution Inverse Synthetic Aperture Radar Imaging with Sparse Stepped-frequency Chirp Signals under Low Signal to Noise Ratio
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摘要: 针对稀疏步进调频信号对目标径向运动敏感且低信噪比(SNR)下难以聚焦成像的问题，该文提出基于遗传算法和稀疏贝叶斯学习的平动补偿与高分辨逆合成孔径雷达(ISAR)成像方法。首先，针对稀疏步进调频信号建立回波模型和稀疏观测模型，通过构造参数化字典，将ISAR成像问题转换为目标运动参数估计与高分辨距离像(HRRP)合成的联合问题。然后，对目标高分辨距离像引入Gamma-Gauss先验，并采用变分贝叶斯推断(VBI)对散射点进行估计。在此基础上，通过遗传算法迭代同步获得目标运动参数与高质量HRRP，最终实现高分辨聚焦成像和运动参数精确估计。不同场景下的仿真和实测数据处理结果验证了所提算法的有效性。
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关键词:
- 逆合成孔径雷达(ISAR) /
- 运动参数估计 /
- 稀疏贝叶斯学习 /
- 遗传算法
Abstract: To solve the sensitivity of sparse stepped-frequency chirp signals to target radial motion and to achieve high-resolution imaging with low Signal to Noise Ratio (SNR), a translation compensation and high-resolution Inverse Synthetic Aperture Radar (ISAR) imaging based on genetic algorithm and sparse Bayesian learning is proposed. Firstly, an echo model and a sparse observation model are established for the sparse stepped-frequency chirp signal. A parameterized dictionary is then constructed to turn ISAR imaging to the joint estimation of target motion parameter and High-Resolution Range Profile (HRRP) synthesis. Secondly, the Gamma-Gaussian prior is introduced to the high-resolution range profile of the target, and the scattering center is estimated by the Variational Bayesian Inference (VBI) algorithm. On this basis, target motion parameters and high-quality HRRP are obtained through the iteration of genetic algorithm. Hence, high-resolution imaging of the moving targets is achieved while the motion parameters are accurately estimated. The effectiveness of the proposed method is verified by simulation and real data processing result in various scenes. -
表 1 所提算法伪代码
算法：基于稀疏步进调频信号的低信噪比ISAR成像 (1) 初始化种群$\left( {\Delta {{\hat v}_{\rm{R}}},\Delta {{\hat a}_{\rm{R}}}} \right)$, ${v_1}$, ${v_2}$, ${v_3}$, ${v_4}$, ${\boldsymbol{\varLambda}} $, $\alpha $, ${{{G}}_{\rm{1}}}$, ${{{G}}_{\rm{2}}}$, ${\eta _1}$。 (2) For iter1=1:${{{G}}_{\rm{1}}}$ (a) For k=1:${{K}}$ 构造${\boldsymbol{D}}_k^{\left( {{\rm{iter1}}} \right)}\left( {\Delta {{\hat v}_{\rm{R}}},\Delta {{\hat a}_{\rm{R}}}} \right)$； For iter2=1:${{{G}}_{\rm{2}}}$ 利用式(22)更新$\alpha $； 利用式(24)更新${\boldsymbol{\varLambda}} $； 利用式(26)更新${\boldsymbol{\theta}} $； 若$\hat {\boldsymbol{\theta}} _k^{\left( {{\rm{iter1}}} \right)}$相对于前一次估计的变化量小于${\eta _1}$则停止循环； End End (b) 构建距离像矩阵${\boldsymbol{s} }_{\rm{r} }^{\left( { {\rm{iter1} } } \right)}\left( {\Delta { {\hat v}_{\rm{R} } },\Delta { {\hat a}_{\rm{R} } } } \right) = \left[ { {\boldsymbol{\theta} } _{\rm{1} }^{\left( { {\rm{iter1} } } \right)},{\boldsymbol{\theta} } _{\rm{2} }^{\left( { {\rm{iter1} } } \right)}, \cdots,{\boldsymbol{\theta} } _K^{\left( { {\rm{iter1} } } \right)} } \right]$，得${I^{\left( {{\rm{iter1}}} \right)}}\left( {\Delta {{\hat v}_{\rm{R}}},\Delta {{\hat a}_{\rm{R}}}} \right)$； (c) 根据式(18)计算图像熵； (d) 保留图像熵较小的个体并更新种群； (e) 判断是否达到循环次数${{{G}}_{\rm{1}}}$； End (3) 实现高分辨ISAR成像。 
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表 2 运算复杂度对比
重构算法 OMP GD VBI 运算复杂度 ${\cal{O}}\left( {{k_0}{L^2}} \right)$ ${\cal{O}}\left( {{L^{\rm{3}}}} \right)$ ${\cal{O}}\left( {{L^{\rm{3}}}} \right)$
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表 3 雷达系统参数
${f_{\rm{c}}}$ ${\rm{PRF}}$ ${T_{\rm{R}}}$ $B$ $\Delta f$ 10 GHz 6.4 kHz 20 μs 800 MHz 10 MHz
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