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Probability Model-driven Airborne Bayesian Forward-looking Super-resolution Imaging for Multitarget Scenario
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摘要: 雷达前视成像技术在精确制导打击、自主下降着陆、汽车自动驾驶等军民领域具有广阔的应用前景。由于多普勒相位历程的限制，机载平台的前视成像分辨率较低。解卷积方法可以进行前视成像，但当前视成像场景复杂时，现有的前视成像方法的成像质量会下降。针对复杂前视成像构型下的场景稀疏度度量和表征问题，该文提出一种基于概率模型驱动的机载贝叶斯前视超分辨多目标成像方法。首先通过将前视成像场景的数据维度由单帧空间扩展到多帧空间提升场景的稀疏度，然后基于广义高斯概率模型对成像场景的稀疏特性进行统计建模和稀疏度求解，最后基于贝叶斯框架完成稀疏前视成像。由于选取的稀疏度表征参数嵌入到前视成像的整个过程中，在每次迭代期间都会进行前视成像参数的更新，从而保证了前视成像算法的稳健性。通过计算机结果和实测数据处理，验证了该文方法的有效性。Abstract: Forward-looking imaging is crucial in many civil and military fields, such as precision guidance, autonomous landing, and autonomous driving. The forward-looking imaging performance of airborne radar may deteriorate significantly due to the constraint of the Doppler history. The deconvolution method can be used to improve the quality of forward-looking imaging; however, it will not work well for complex imaging scenes. To solve the problem of scene sparsity measurement and characterization in complex forward-looking imaging configurations, an efficient probability model-driven airborne Bayesian forward-looking super-resolution imaging algorithm is proposed for multitarget scenarios to improve the azimuth resolution. First, the data dimension of the forward-looking imaging scene was expanded from single-frame to multiframe spaces to enhance the sparsity of the imaging scene. Then, the sparse characteristics of the imaging scene were statistically modeled using the generalized Gaussian probability model. Finally, the super-resolution imaging problem was solved using the Bayesian framework. Because the sparsity characterization parameters are embedded in the entire process of imaging, the forward-looking imaging parameters will be updated during each iteration. The effectiveness of the proposed algorithm was verified using simulation and real data.
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图 5 不同SNR下的仿真点目标RMSE变化曲线
Figure 5. RMSE curves of simulation point targets under different SNRs
图 7 不同方法的多目标前视成像结果对比
Figure 7. Angular super-resolution results of different methods for multitarget scenario
图 8 不同SNR下的仿真面目标RMSE变化曲线
Figure 8. RMSE curves of simulation surface targets under different SNRs
图 9 不同方法的实测数据前视成像结果对比
Figure 9. Angular super-resolution results of different methods for real data
表 1 点目标仿真实验雷达参数
Table 1. Radar parameters for simulation experiment with point targets
参数 数值 参数 数值 平台速度(m/s) 300 时宽(μs) 10 平台高度(m) 1000 方位波束(°) 3 带宽(MHz) 512 扫描范围(°) –15～15 
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1 前视超分辨成像方法求解流程
1. Solution flow of the proposed algorithm
输入：天线方向图矩阵H，扩展的多普勒卷积矩阵${\boldsymbol{\varPhi}}$，观测数
据Y初始化：迭代次数$m = 1$，${\hat {\boldsymbol{X} }^1} = {\boldsymbol{Y}}$ 更新迭代过程： (1) 更新p：
$p = {F^{ { { - } }1} }\left( {\frac{ { { {\left( {\dfrac{1}{M}\displaystyle\sum\limits_{i = 1}^M {\left| { {X_i} } \right|} } \right)}^2} } }{ {\dfrac{1}{M}{ {\displaystyle\sum\limits_{i = 1}^M {\left( { {X_i} - \dfrac{1}{M}\displaystyle\sum\limits_{i = 1}^M {\left| { {X_i} } \right|} } \right)} }^2} } } } \right)$,
$F\left( x \right) = \dfrac{ { {\Gamma ^2}\left( { {2 \mathord{\left/ {\vphantom {2 p} } \right. } p} } \right)} }{ {\Gamma \left( { {1 \mathord{\left/ {\vphantom {1 p} } \right. } p} } \right)\Gamma \left( { {3 \mathord{\left/ {\vphantom {3 p} } \right. } p} } \right)} }$(2) 更新${\boldsymbol{J}}\left( { { {\hat {\boldsymbol{X}}}^n} } \right)$： ${\boldsymbol{J} }\left( { { {\hat {\boldsymbol{X} } }^n} } \right) = \arg {\text{min} }\left\{ {\left\| { {\boldsymbol{Y} }{ { - } }{\boldsymbol{H} } \odot {\boldsymbol{\varPhi} } { {\boldsymbol{X} }^n} } \right\|_2^2 + \mu { {\displaystyle\sum\limits_{i = 1}^L {\left( {\left| { {x^n} } \right|_i^2 + \varepsilon } \right)} }^{\textstyle\frac{p}{2} } } } \right\}$ (3) 更新$\nabla {\boldsymbol{J}}\left( { { {\hat {\boldsymbol{X}}}^n} } \right)$： $\nabla {\boldsymbol{J} }\left( { { {\hat {\boldsymbol{X} } }^n} } \right) = \left[ {2{ {\left( { {\boldsymbol{H} } \odot {\boldsymbol{\varPhi} } } \right)}^{\text{H} } }{\boldsymbol{H} } \odot {\boldsymbol{\varPhi}} + \mu {\boldsymbol{\varLambda } }\left( { { {\hat {\boldsymbol{X} } }^n} } \right)} \right]{\boldsymbol{X} } - 2{\left( { {\boldsymbol{H} } \odot {\boldsymbol{\varPhi} } } \right)^{\text{H} } }{\boldsymbol{Y} }$ (4) 更新${A^n}$： ${A^n}{\text{ = } }2{\left( {{\boldsymbol{H}} \odot {\boldsymbol{\varPhi}} } \right)^{\text{H} } }{\boldsymbol{H}} \odot {\boldsymbol{\varPhi}} + \mu {\boldsymbol{\varLambda } }$ (5) 更新${\hat {\boldsymbol{X}}^n}$： ${\hat {\boldsymbol{X} }^{n + 1} } = {\hat {\boldsymbol{X} }^n} - {\left[ {A\left( { { {\hat {\boldsymbol{X} } }^n} } \right)} \right]^{ { { - } }1} } \cdot \nabla {\boldsymbol{J}}\left( { { {\hat {\boldsymbol{X} } }^n} } \right)$ 输出：图像矩阵${\hat {\boldsymbol{X}}^{n + 1} }$
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表 2 面目标仿真实验雷达参数
Table 2. Radar parameters for simulation experiment with surface targets
参数 数值 参数 数值 平台速度(m/s) 300 时宽(μs) 10 平台高度(m) 1000 方位波束(°) 3 带宽(MHz) 300 扫描范围(°) –15～15
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