基于稀疏重构的全极化SAR联合多维重建

孙豆; 路东伟; 邢世其; 杨潇; 李永祯; 王雪松

doi:10.12000/JR20092

基于稀疏重构的全极化SAR联合多维重建

DOI: 10.12000/JR20092

孙豆^1,,
路东伟^1,,
邢世其^1, ,,
杨潇^2,,
李永祯^1,,
王雪松^1,

1.
国防科技大学电子信息系统复杂电磁环境效应国家重点实验室长沙 410073
2.
国防科技大学电子科学系长沙 410073

基金项目: 国家自然科学基金(61971429, 61901499)

详细信息

作者简介:
孙　豆(1992–)，女，博士研究生，主要研究方向为极化雷达成像和雷达信号处理。E-mail: sundou14@nudt.edu.cn

路东伟(1992–)，男，博士研究生，主要研究方向为合成孔径雷达对抗和雷达目标识别。E-mail: bookwormldw@qq.com

邢世其(1984–)，男，副研究员，主要研究方向为极化雷达成像、雷达信号处理以及合成孔径雷达对抗。E-mail: xingshiqi_paper@163.com

杨　潇(1983–)，男，助教，主要研究方向为雷达信号处理和雷达目标识别。E-mail: 297414430@qq.com

李永祯(1977–)，男，研究员，博士生导师，主要研究方向为极化雷达与电子对抗。E-mail: e0061@sina.com

王雪松(1972–)，男，教授，博士生导师，主要研究方向为极化雷达、目标识别与电子对抗。E-mail: wxs1019@vip.sina.com

通讯作者:
邢世其 xingshiqi_paper@163.com

责任主编：仇晓兰 Corresponding Editor: QIU Xiaolan
中图分类号: TN95
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出版历程
- 收稿日期: 2020-07-06
- 修回日期: 2020-09-24
- 网络出版日期: 2020-10-28

Full-polarization SAR Joint Multidimensional Reconstruction Based on Sparse Reconstruction

SUN Dou^1
,,
LU Dongwei^1
,,
XING Shiqi^{1
, ,},
YANG Xiao^2
,,
LI Yongzhen^1
,,
WANG Xuesong^1
,

1.
State Key Laboratory of Complex Electromagnetic Environment Effects on Electronics and Information System, National University of Defense Technology, Changsha 410073, China
2.
Department of Electronic Science, National University of Defense Technology, Changsha 410073, China

Funds: The National Natural Science Foundation of China (61971429, 61901499)

More Information

Corresponding author: XING Shiqi, xingshiqi_paper@163.com

摘要

摘要: 各极化通道独立处理和三维分步成像会忽视数据之间的关联性，造成散射中心的失配以及极化散射矩阵获取的不准确。鉴于此，该文提出一种基于稀疏重构的全极化联合多维重建方法。该方法通过设置联合稀疏约束对所有极化通道及所有维度进行联合，将全极化多维重建建模为多通道联合稀疏重构问题。通过数据插值对模型简化后，结合三维快速傅里叶变换、共轭梯度法和牛顿迭代法给出一种高效的模型求解方法，可以同时得到极化散射矩阵和目标三维信息。该文方法保证了不同极化通道、不同维度的稀疏支撑集一致，且充分利用了数据之间的关联性带来的额外信息。基于仿真数据和电磁计算数据的实验结果表明，该方法的性能不受目标类型影响，具有一定的抗噪性，能有效地获取目标的多维重建结果，得到的三维成像结果分辨率高且极化散射矩阵估计精度高。
- 合成孔径雷达 /
- 全极化 /
- 稀疏重构 /
- 三维成像 /
- 联合重建
Abstract: Independent processing of each polarization channel and three-dimensional multistage imaging ignore the correlation between data, resulting in the mismatch between scattering centers and the inaccurate acquisition of polarization scattering matrices. To address these issues, a full-polarization Synthetic Aperture Radar (SAR) joint multidimensional reconstruction method based on sparse reconstruction is proposed in this study. In this method, all polarization channels and dimensions are integrated by setting the joint sparse constraints, and the full-polarization SAR joint multidimensional reconstruction is modeled as a multichannel joint sparse reconstruction problem. After the model is simplified by data interpolation, an efficient model-solving method is proposed by combining the three-dimensional fast Fourier transform, conjugate gradient method, and Newton iteration method, where the polarization scattering matrix and three-dimensional information of the target can be obtained at the same time. The proposed method ensures that the sparse support sets of different polarization channels and dimensions are consistent and utilizes the additional information generated by the correlation between data. On the basis of the simulation and electromagnetic calculation data, the experimental results indicate that the proposed method is tolerant of noise and immune to the types of targets. Moreover, the proposed method can effectively obtain the multidimensional reconstruction results of the target, where both the resolution of the imaging results and the estimation accuracy of the polarization scattering matrix are high.
- Synthetic Aperture Radar (SAR) /
- Full-polarimetric /
- Sparse reconstruction /
- Three-dimensional imaging /
- Joint reconstruction

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图 1 各个极化通道的仿真目标成像结果

Figure 1. Each polarization channel’s imaging results of simulated targets

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图 2 仿真目标全极化联合多维重建结果

Figure 2. Full polarization joint multi-dimensional reconstruction results of simulated targets

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图 3 Slicy的CAD模型

Figure 3. CAD model of Slicy

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图 4 各个极化通道的Slicy成像结果

Figure 4. Each polarization channel’s imaging results of Slicy

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图 5 Slicy全极化联合多维重建结果

Figure 5. Full polarization joint multi-dimensional reconstruction results of Slicy

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图 6 卫星的CAD模型

Figure 6. CAD model of satellite

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图 7 各个极化通道的卫星成像结果

Figure 7. Each polarization channel’s imaging results of satellite

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图 8 卫星全极化联合多维重建结果

Figure 8. Full polarization joint multi-dimensional reconstruction results of satellite

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表 1 全极化联合多维重建方法的步骤

Table 1. Steps of full polarization joint multi-dimensional reconstruction method

　(1) 设定初值：

${{\tilde{ \beta }}^n} = {{0}}$ ；

　(2) 对每个极化通道，

　　　(a) 使用3-D NUFFT对

${G_l}(k_x^{},k_y^{},k_z^{})$ 进行插值，得到
　　　　

${\hat G_l}(\hat k_x^{},\hat k_y^{},\hat k_z^{})$ ，

　　　(b) 对

${\hat G_l}(\hat k_x^{},\hat k_y^{},\hat k_z^{})$ 进行3-D IFFT，并向量化结果得到
　　　　

${{\hat{ A}}^{\rm{H}}}{{\hat{ b}}_l}$ ；

　(3) 根据所有极化通道的

${{\hat{ A}}^{\rm{H}}}{{\hat{ b}}_l}$ ，得到

${{\hat{ A}}^{\rm{H}}}{\hat{ b}}$ ；

　(4) 结合3-D FFT，3-D IFFT和共轭梯度法计算
　　

${(2{{\hat{ A}}^{\rm{H}}}{\hat{ A}} + \mu p{{D}}({{\tilde{ \beta }}^n}))^{ - 1}}$ ；

　(5) 根据

${{\hat{ A}}^{\rm{H}}}{\hat{ b}}$ ，计算

${(2{{\hat{ A}}^{\rm{H}}}{\hat{ A}} + \mu p{{D}}({{\tilde{ \beta }}^n}))^{ - 1}}2{{\hat{ A}}^{\rm{H}}}{\hat{ b}}$ ；

　(6) 按式(17)迭代计算

${{\tilde{ \beta }}^{n + 1}}$ ，当

${ {\left\| { { { {\tilde{ \beta } } }^{n + 1} } - { { {\tilde{ \beta } } }^n} } \right\|_2^2} \Bigr/ {\left\| { { { {\tilde{ \beta } } }^n} } \right\|_2^2} } < \tau$ 时
　　得到解

${\tilde{ \beta }} = {{\tilde{ \beta }}^{n + 1}}$ ；

　(7) 对

${\tilde{ \beta }}$ 进行Cameron分解，得到全极化联合多维重建结果。

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表 2 仿真目标信息

Table 2. Information of simulated targets

类型	散射矩阵	幅度	位置
三面角	$\left[ {\begin{array}{*{20}{c}} 1&0 \\ 0&1 \end{array}} \right]$	1	$x = 1.0\,{\rm{m} },y = - 0.5\,{\rm{m} },z = 0.7\,{\rm{m} }$
偶极子	$\left[ {\begin{array}{*{20}{c}} 1&0 \\ 0&0 \end{array}} \right]$	1	$x = - 1.0\,{\rm{m} },y = 0.5\,{\rm{m} },z = - 0.7\,{\rm{m} }$
30°二面角	$\left[ {\begin{array}{*{20}{c}} {0.5}&{0.866} \\ {0.866}&{ - 0.5} \end{array}} \right]$	1	$x = - 0.5\,{\rm{m} },y = - 1.0\,{\rm{m} },z = 0.7\,{\rm{m} }$
45°二面角	$\left[ {\begin{array}{*{20}{c}} 0&1 \\ 1&0 \end{array}} \right]$	1	$x = 0.5\,{\rm{m} },y = 1.0\,{\rm{m} },z = - 0.7\,{\rm{m} }$

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表 3 目标的仿真参数

Table 3. Simulation parameters of simulated targets

雷达扫描参数	值
频率范围	[8 GHz, 12 GHz]
频率采样间隔	20 MHz
方位角范围	[–4°, 6°]
方位角采样间隔	1/14°
俯仰角范围	[18°, 42°]
俯仰角采样间隔	1/14°
极化方式	HH, HV, VH, VV

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表 4 仿真目标的极化散射矩阵估计结果

Table 4. Polarization scattering matrix estimation results of simulated targets

方法	目标类型	三面角	偶极子	30°二面角	45°二面角
联合多维重建	变型前	$\left[ {\begin{array}{*{20}{c}} {0.4\operatorname{j} }&0 \\ 0&{0.4{\rm{j}}} \end{array}} \right]$	$\left[ {\begin{array}{*{20}{c}} { - 0.38{\rm{j}}}&0 \\ 0&0 \end{array}} \right]$	$\left[ {\begin{array}{*{20}{c}} { - 0.21}&{ - 0.37} \\ { - 0.37}&{0.21} \end{array}} \right]$	$\left[ {\begin{array}{*{20}{c}} 0&{ - 0.42} \\ { - 0.42}&0 \end{array}} \right]$
联合多维重建	变型后	${\color{Blue}{0.4} }{ {\rm{e} }^{ {\rm{j} }{ {90}^ \circ } } }{\color{red}{\left[ {\begin{array}{*{20}{c} } 1&0 \\ 0&1 \end{array} } \right] } }$	${\color{Blue}{0.38} }{ {\rm{e} }^{ {\rm{j} }( - { {90}^ \circ })} }{\color{red}{\left[ {\begin{array}{*{20}{c} } 1&0 \\ 0&0 \end{array} } \right] } }$	${\color{Blue}{0.42} }{ {\rm{e} }^{ {\rm{j} }{ {180}^ \circ } } }{\color{red}{\left[ {\begin{array}{*{20}{c} } {0.5}&{0.88} \\ {0.88}&{ - 0.5} \end{array} } \right]} }$	${\color{Blue}{0.42} }{ {\rm{e} }^{ {\rm{j} }{ {180}^ \circ } } }{\color{red}{\left[ {\begin{array}{*{20}{c} } 0&1 \\ 1&0 \end{array} } \right]}}$
独立多维重建	变型前	$\left[ {\begin{array}{*{20}{c}} {0.38{\rm{j}}}&0 \\ 0&{0.38{\rm{j}}} \end{array}} \right]$	$\left[ {\begin{array}{*{20}{c}} { - 0.38{\rm{j}}}&0 \\ 0&0 \end{array}} \right]$	$\left[ {\begin{array}{*{20}{c}} { - 0.13 + 0.02{\rm{j}}}&{ - 0.34 + 0.06{\rm{j}}} \\ { - 0.34 + 0.06{\rm{j}}}&{0.13 - 0.02{\rm{j}}} \end{array}} \right]$	$\left[ {\begin{array}{*{20}{c}} 0&{ - 0.4 - 0.07{\rm{j}}} \\ { - 0.4 - 0.07{\rm{j}}}&0 \end{array}} \right]$
独立多维重建	变型后	${\color{Blue}{0.38} }{ {\rm{e} }^{ {\rm{j} }{ {89}^ \circ } } }{\color{red}{\left[ {\begin{array}{*{20}{c} } 1&0 \\ 0&1 \end{array} } \right]}}$	${\color{Blue}{0.38} }{ {\rm{e} }^{ {\rm{j} }( - { {89}^ \circ })} }{\color{red}{\left[ {\begin{array}{*{20}{c} } 1&0 \\ 0&0 \end{array} } \right]}}$	${\color{Blue}{0.26} }{ {\rm{e} }^{ {\rm{j} }{ {170}^ \circ } } }{\color{red}{\left[ {\begin{array}{*{20}{c} } {0.5}&{1.35} \\ {1.35}&{ - 0.5} \end{array} } \right]}}$	${\color{Blue}{0.41} }{ {\rm{e} }^{ {\rm{j} }( - { {170}^ \circ })} }{\color{red}{\left[ {\begin{array}{*{20}{c} } 0&1 \\ 1&0 \end{array} } \right]}}$

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表 5 不同SNR下仿真目标的极化散射矩阵估计结果

Table 5. Polarization scattering matrix estimation results of simulated targets under different SNR

目标类型		SNR=13 dB	SNR=18 dB	SNR=23 dB
三面角	变型前	$\left[\!\! {\begin{array}{*{20}{c}} {0.01 + 0.39{\rm{j}}} \!\!\!&\!\!\! {0.02} \\ {0.01 + 0.01{\rm{j}}} \!\!\!&\!\!\! { - 0.02 + 0.39{\rm{j}}} \end{array}} \!\!\right]$	$\left[\!\! {\begin{array}{*{20}{c}} { - 0.02 + 0.4{\rm{j}}} \!\!\!&\!\!\! {0.01 - 0.02{\rm{j}}} \\ {0.03{\rm{j}}} \!\!\!&\!\!\! {0.01 + 0.4{\rm{j}}} \end{array}} \!\!\right]$	$\left[\!\! {\begin{array}{*{20}{c}} {0.01 + 0.41{\rm{j}}} \!\!\!&\!\!\! {0.02{\rm{j}}} \\ { - 0.01} \!\!\!&\!\!\! {0.01 + 0.40{\rm{j}}} \end{array}} \!\!\right]$
三面角	变型后	${\color{blue}{0.39}}{ {\rm{e} }^{ {\rm{j8} }{ {8.7}^ \circ } } }{\color{red}{\left[\!\! {\begin{array}{*{20}{c} } 1 \!\!\!&\!\!\! {0.02 - 0.06{\rm{j} } } \\ {0.03 - 0.04{\rm{j} } } \!\!\!&\!\!\! {1.03 + 0.07{\rm{j} } } \end{array} } \!\!\right]}}$	${\color{blue}{0.4}}{ {\rm{e} }^{ {\rm{j92} }{\rm{.} }{ {\rm{2} }^{\rm{o} } } }}{\color{red}{\left[\!\! {\begin{array}{*{20}{c} } 1 \!\!\!&\!\!\! { - 0.04 - 0.03{\rm{j} } } \\ {0.09 - 0.01{\rm{j} } } \!\!\!&\!\!\! {1.01 - 0.06{\rm{j} } } \end{array} } \!\!\right] }}$	${\color{blue}{0.41} }{ {\rm{e} }^{ {\rm{j} }{ {88.6}^ \circ } } }{\color{red}{\left[\!\! {\begin{array}{*{20}{c} } 1 \!\!\!&\!\!\! {0.04} \\ {0.02 + 0.03{\rm{j} } } \!\!\!&\!\!\! {0.97 - 0.01{\rm{j} } } \end{array} } \!\!\right]} }$
偶极子	变型前	$\left[\!\! {\begin{array}{*{20}{c}} {0.02 - 0.38{\rm{j}}} \!\!\!&\!\!\! {0.01{\rm{j}}} \\ { - 0.02 + 0.02{\rm{j}}} \!\!\!&\!\!\! { - 0.03{\rm{j}}} \end{array}} \!\!\right]$	$\left[\!\! {\begin{array}{*{20}{c}} {0.02 - 0.41{\rm{j}}} \!\!\!&\!\!\! {0.02 + 0.01{\rm{j}}} \\ { - 0.01 + 0.01{\rm{j}}} \!\!\!&\!\!\! {0.01} \end{array}} \!\!\right]$	$\left[\!\! {\begin{array}{*{20}{c}} { - 0.4{\rm{j}}} \!\!\!&\!\!\! {0.02{\rm{j}}} \\ 0 \!\!\!&\!\!\! 0 \end{array}} \!\!\right]$
偶极子	变型后	${\color{blue}{0.3} }{\rm{8} }{ {\rm{e} }^{ {\rm{j( - 86} }{\rm{.} }{ {\rm{8} }^{\rm{o} } }{\rm{)} } } }\!{\color{red}{\left[\!\!\!\! {\begin{array}{*{20}{c} } 1 \!\!\!&\!\!\! { - 0.03} \\ { - 0.05 \!-\! 0.05{\rm{j} } } \!\!\!&\!\!\! {0.08 \!-\! 0.13{\rm{j} } } \end{array} } \!\!\!\right]} }$	$\;{\color{blue}{0.41} }{ {\rm{e} }^{ {\rm{j( - 87} }{\rm{.} }{ {\rm{3} }^{\rm{o} } }{\rm{)} } } }\!{\color{red}{\left[\!\!\!\! {\begin{array}{*{20}{c} } 1 \!\!\!&\!\!\! { - 0.02 \!+\! 0.06{\rm{j} } } \\ { - 0.02 \!-\! 0.01{\rm{j} } } \!\!\!&\!\!\! { - 0.01 \!+\! 0.01{\rm{j} } } \end{array} } \!\!\!\!\right]} }$	${\color{blue}{0.4} }{ {\rm{e} }^{ {\rm{j - 9} }{ {\rm{0} }^{\rm{o} } } } }{\color{red}{\left[\!\! {\begin{array}{*{20}{c} } 1 \!\!\!&\!\!\! { - 0.05} \\ 0 \!\!\!&\!\!\! 0 \end{array} } \!\!\right]} }$
30° 二面角	变型前	$\left[\!\! {\begin{array}{*{20}{c}} { - 0.16 + 0.02{\rm{j}}} \!\!\!&\!\!\! { - 0.28 + 0.04{\rm{j}}} \\ { - 0.39 + 0.07{\rm{j}}} \!\!\!&\!\!\! {0.2 - 0.04{\rm{j}}} \end{array}} \!\!\right]$	$\left[\!\! {\begin{array}{*{20}{c}} { - 0.22 + 0.03{\rm{j}}} \!\!\!&\!\!\! { - 0.37 + 0.06{\rm{j}}} \\ { - 0.39 + 0.06{\rm{j}}} \!\!\!&\!\!\! {0.24 - 0.04{\rm{j}}} \end{array}} \!\!\right]$	$\left[\!\! {\begin{array}{*{20}{c}} { - 0.22 + 0.04{\rm{j}}} \!\!\!&\!\!\! { - 0.39 + 0.06{\rm{j}}} \\ { - 0.37 + 0.05{\rm{j}}} \!\!\!&\!\!\! {0.22 - 0.04{\rm{j}}} \end{array}} \!\!\right]$
30° 二面角	变型后	${\color{blue}{0.33} }{ {\rm{e} }^{ {\rm{j172} }{\rm{.} }{ {\rm{4} }^{\rm{o} } } } }{\color{red}{\left[\!\! {\begin{array}{*{20}{c} } {0.5} \!\!\!&\!\!\! {0.84} \\ {1.18 - 0.07{\rm{j} } } \!\!\!&\!\!\! { - 0.6 + 0.04{\rm{j} } } \end{array} } \!\!\right]} }$	${\color{blue}{0.45} }{ {\rm{e} }^{ {\rm{j172} }{\rm{.} }{ {\rm{3} }^{\rm{o} } } } }{\color{red}{\left[\!\! {\begin{array}{*{20}{c} } {0.5} \!\!\!&\!\!\! {0.85 - 0.03{\rm{j} } } \\ {0.89 - 0.02{\rm{j} } } \!\!\!&\!\!\! { - 0.53 + 0.03{\rm{j} } } \end{array} } \!\!\right]} }$	${\color{blue}{0.45} }{ {\rm{e} }^{ {\rm{j169} }{\rm{.} }{ {\rm{4} }^{\rm{o} } } } }{\color{red}{\left[\!\! {\begin{array}{*{20}{c} } {0.5} \!\!\!&\!\!\! {0.87 + 0.02{\rm{j} } } \\ {0.84 + 0.04{\rm{j} } } \!\!\!&\!\!\! { - 0.5} \end{array} } \!\!\right]} }$
45° 二面角	变型前	$\left[\!\! {\begin{array}{*{20}{c}} {0.02} \!\!\!&\!\!\! { - 0.41 - 0.06{\rm{j}}} \\ { - 0.45 - 0.06{\rm{j}}} \!\!\!&\!\!\! { - 0.02} \end{array}} \!\!\right]$	$\left[\!\! {\begin{array}{*{20}{c}} { - 0.01 + 0.01{\rm{j}}} \!\!\!&\!\!\! { - 0.46 - 0.06{\rm{j}}} \\ { - 0.44 - 0.08{\rm{j}}} \!\!\!&\!\!\! { - 0.01{\rm{j}}} \end{array}} \!\!\right]$	$\left[\!\! {\begin{array}{*{20}{c}} 0 \!\!\!&\!\!\! { - 0.43 - 0.01{\rm{j}}} \\ { - 0.42 - 0.08{\rm{j}}} \!\!\!&\!\!\! {0.02{\rm{j}}} \end{array}} \!\!\right]$
45° 二面角	变型后	${\color{blue}{0.42} }{ {\rm{e} }^{ {\rm{j( - 171} }{\rm{.} }{ {\rm{8} }^{\rm{o} } }{\rm{)} } } }{\color{red}{\left[\!\! {\begin{array}{*{20}{c} } { - 0.05} \!\!\!&\!\!\! 1 \\ {1.01} \!\!\!&\!\!\! {0.04} \end{array} } \!\!\right]} }$	${\color{blue}{0.46} }{ {\rm{e} }^{ {\rm{j( - 172} }{\rm{.} }{ {\rm{4} }^{\rm{o} } }{\rm{)} } } }{\color{red}{\left[\!\! {\begin{array}{*{20}{c} } {0.02 \!-\! 0.01{\rm{j} } } \!\! & \!\! 1 \\ {0.96 \!+\! 0.05{\rm{j} } } \!\! & \!\! {0.01 \!+\! 0.02{\rm{j} } } \end{array} } \!\!\right]} }$	${\color{blue}{0.44} }{ {\rm{e} }^{ {\rm{j( - 170} }{\rm{.} }{ {\rm{7} }^{\rm{o} } }{\rm{)} } } }{\color{red}{\left[\!\! {\begin{array}{*{20}{c} } 0 \!\!\!&\!\!\! 1 \\ {0.98 \!+\! 0.01{\rm{j} } } \!\!\!&\!\!\! { - 0.02 \!-\! 0.05{\rm{j} } } \end{array} } \!\!\right]} }$

下载: 导出CSV

表 6 Slicy的仿真参数

Table 6. Simulation parameters of Slicy

参数类型	参数	取值
雷达扫描参数	频率范围	[8 GHz, 12 GHz]
	频率采样间隔	20 MHz
	方位角范围	[–4°, 6°]
	方位角采样间隔	1/14°
	俯仰角范围	[18°, 42°]
	俯仰角采样间隔	1/14°
	极化方式	HH, HV, VH, VV
场景参数	方位角0°	沿x 轴正方向
	俯仰角0°	沿z 轴正方向
	x 轴方向场景范围	[–0.6 m, 0.6 m]
	y 轴方向场景范围	[–0.9 m, 0.9 m]
	z 轴方向场景范围	[0 m, 0.75 m]

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表 7 卫星的仿真参数

Table 7. Simulation parameters of satellite

参数类型	参数	取值
雷达扫描参数	频率范围	[9 GHz, 11 GHz]
	频率采样间隔	20 MHz
	方位角范围	[–20°, 20°]
	方位角采样间隔	0.1°
	俯仰角范围	[45°, 65°]
	俯仰角采样间隔	0.2°
	极化方式	HH, HV, VH, VV
场景参数	方位角0°	沿x 轴正方向
	俯仰角0°	沿z 轴正方向
	x 轴方向场景范围	[–0.5 m, 0.5 m]
	y 轴方向场景范围	[–4.105 m, 4.105 m]
	z 轴方向场景范围	[–1.775 m, 1.775 m]

下载: 导出CSV

参考文献(23)

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