基于数值仿真的X波段极化SAR海杂波统计建模与特性分析

doi:10.12305/j.issn.1001-506X.2021.10.06

摘要/Abstract

摘要：

针对3~5级海况下X波段极化合成孔径雷达(synthetic aperture radar, SAR)海杂波的仿真和统计建模, 首先利用Apel海浪谱模型和Monte Carlo方法仿真不同风速下的大尺寸二维粗糙海面, 进而分别利用物理光学模型和弹跳射线法两种高频电磁散射模型考虑海面的单次散射和多次散射, 实现大尺寸海面的极化SAR海杂波仿真, 并利用X波段地球物理模式函数和岸基实测海杂波对仿真海杂波的精度和统计分布进行验证。基于仿真海杂波数据, 利用典型的乘积模型和Mellin类统计量开展海杂波统计建模和特性分析。仿真结果表明, 在2 m×2 m的高分辨率条件下, X波段同极化海杂波并不服从适用于中低分辨率海杂波的K分布, 且在不同风速风向下呈现出不同的纹理特征; X波段交叉极化海杂波表现出较弱的纹理特征, 服从Wishart分布; 随着入射角和雷达视数的增大, 海杂波的纹理特征逐渐减弱。

关键词: 海杂波, 极化合成孔经雷达, 电磁散射仿真, Mellin类统计量

Abstract:

This paper focuses on the numerical simulation and statistical modeling of X-band polarimetric synthetic aperture radar (SAR) sea clutter under level 3~5 sea states. Firstly, by using Apel spectrum and Monte Carlo method, we generate large-scale two-dimensional rough ocean surfaces at various wind speeds. Then, the high-frequency electromagnetic scattering methods are employed simulate polarimetric SAR sea clutter. In particular, the physical optics method and the shooting and bouncing ray method are used to separately consider the single scattering and multiple scattering on sea surfaces. The accuracy and statistical distribution of simulated sea clutter are validated using X-band geophysical mode function and the shore-based measurement. Finally, based on the simulated sea clutter data, the statistical modeling and characteristic analyses of sea clutter are conducted using typical product models and Mellin-kind statistics. The simulation results indicate that, at the high resolution of 2 m×2 m, the X-band co-pol sea clutter does not obey the classic K distribution which performs well for low-to-moderate resolution sea clutter, and presents different texture properties at various wind speeds and wind directions. X-band cross-pol sea clutter shows weak texture characteristics and basically obeys the Wishart distribution. With the increase of incident angle and radar look number, the texture characteristics of sea clutter gradually weaken.

Key words: sea clutter, polarimetric synthetic aperture radar (SAR), electromagnetic scattering simulations, Mellin-kind statistics

中图分类号:

TN95

杜延磊, 高帆, 刘涛, 杨健. 基于数值仿真的X波段极化SAR海杂波统计建模与特性分析[J]. 系统工程与电子技术, 2021, 43(10): 2742-2755.

Yanlei DU, Fan GAO, Tao LIU, Jian YANG. Statistical modeling and characteristic analysis of polarimetric SAR sea clutter at X-band based on numerical simulations[J]. Systems Engineering and Electronics, 2021, 43(10): 2742-2755.

图/表 14

图1

图2

表1

海面棱边散射几何示意图及参数定义"

分布模型	纹理参数τ		散射向量k的PDF	极化协方差矩阵C的PDF	公式编号
分布模型	模型	PDF	散射向量k的PDF	极化协方差矩阵C的PDF	公式编号
K分布	γ分布	$ p(\tau ; \alpha)=\frac{\alpha^{\alpha}}{\Gamma(\alpha)} \tau^{\alpha-1} \exp (-\alpha \tau) $	$ \begin{array}{c}p_{k}(k ; \alpha, L, \boldsymbol{\Sigma})=\frac{2 L^{L d}\left(\boldsymbol{k}^{\mathrm{H}} \boldsymbol{k}\right)^{L-\frac{d}{2}}}{\Gamma_{d}(L)\|\boldsymbol{\Sigma}\|^{L}} \frac{2 \alpha{\frac{\alpha+Ld}{2} }}{\Gamma(\alpha)}\left(L \boldsymbol{k}^{\mathrm{H}} \boldsymbol{\Sigma}^{-1} \boldsymbol{k}\right) \frac{\alpha-L d}{2} \times \\K_{\alpha-L d}\left(2 \sqrt{L_{\alpha} \boldsymbol{k}^{\mathrm{H}} \boldsymbol{\Sigma}^{-1} \boldsymbol{k}}\right)\end{array} $	$ \begin{array}{c}p_{C}(\boldsymbol{C} ; \alpha, L, \boldsymbol{\Sigma})= \\\frac{L^{L d}}{\Gamma_{d}(L)} \frac{\|\boldsymbol{C}\|^{L-d}}{\|\boldsymbol{\Sigma}\|^{L}} \frac{2 \alpha{\frac{\alpha+L d}{2}}}{\Gamma(\alpha)}\left(L \operatorname{tr}\left(\boldsymbol{\Sigma}^{-1} \boldsymbol{C}\right)\right){\frac{\alpha-L d}{2}} \times \\K_{\alpha-L d}\left[2 \sqrt{\alpha L\operatorname{tr}\left(\boldsymbol{\Sigma}^{-1} \boldsymbol{C}\right)}\right]\end{array} $	(32)
G⁰分布	逆γ分布	$ p(\tau ; \lambda)=\frac{(\lambda-1)^{\lambda}}{\Gamma(\lambda)} \tau^{-\lambda-1} \exp \left(-\frac{\lambda-1}{\tau}\right) $	$ \begin{aligned}p_{k}(k ; \lambda, L, \boldsymbol{\Sigma}) &=\frac{2 L^{L d}\left(\boldsymbol{k}^{\mathrm{H}} \boldsymbol{k}\right)^{L-\frac{d}{2}}}{\Gamma_{d}(L)\|\boldsymbol{\Sigma}\|^{L}} \frac{\Gamma(\lambda+L d)(\lambda-1)^{\lambda}}{\Gamma(\lambda)} \times \\&\left(\lambda-1+L \boldsymbol{k}^{\mathrm{H}} \boldsymbol{\Sigma}^{-1} \boldsymbol{k}\right)^{-\lambda-L d}\end{aligned} $	$ \begin{array}{c}p_{C}(\boldsymbol{C} ; \lambda, L, \boldsymbol{\Sigma})=\frac{L^{L d}\|\boldsymbol{C}\|^{L-d}}{\Gamma_{d}(L)\|\boldsymbol{\Sigma}\|^{L}} \frac{\Gamma(\lambda+L d)(\lambda-1)^{\lambda}}{\Gamma(\lambda)} \times \\{\left[\lambda-1+L \operatorname{tr}\left(\boldsymbol{\Sigma}^{-1} \boldsymbol{C}\right)\right]^{-\lambda-L d}}\end{array} $	(33)
Kummer-U分布	Fisher分布	$ \begin{array}{l}p(\tau ; \xi, \zeta)=\frac{\Gamma(\xi+\zeta)}{\Gamma(\xi) \Gamma(\zeta)} \frac{\xi}{\zeta-1} \times \\\left(\frac{\xi}{\zeta-1} \tau\right)^{\xi-1}\left(\frac{\xi}{\zeta-1} \tau+1\right)^{-\xi-\zeta}\end{array} $	$ \begin{array}{c}p_{k}(k ; \xi, \zeta, L, \boldsymbol{\Sigma})= \\\frac{2 L^{L d}\left(\boldsymbol{k}^{\mathrm{H}} \boldsymbol{k}\right)^{L-\frac{d}{2}}}{\Gamma_{d}(L)\|\boldsymbol{\Sigma}\|^ L} \frac{\Gamma(\xi+\zeta) \Gamma(\zeta+L d)}{\Gamma(\xi) \Gamma(\zeta)}\left(\frac{\xi}{\zeta-1}\right)^{L d} \times \\\boldsymbol{U}\left(L d+\zeta, L d-\xi+1, \frac{\xi}{\zeta-1} L \boldsymbol{k}^{\mathrm{H}} \boldsymbol{\Sigma}^{-1} \boldsymbol{k}\right)\end{array} $	$ \begin{array}{c}p_{C}(\boldsymbol{C} ; \xi, \zeta, L, \boldsymbol{\Sigma})= \\\frac{L^{L d}\|\boldsymbol{C}\|^{L-d}}{\Gamma_{d}(L)\|\boldsymbol{\Sigma}\|^{L}} \frac{\Gamma(\xi+\boldsymbol{\zeta}) \Gamma(\zeta+L d)}{\Gamma(\xi) \Gamma(\zeta)}\left(\frac{\xi}{\zeta-1}\right)^{L d} \times \\\boldsymbol{U}\left(L d+\zeta, L d-\xi+1, \frac{\xi}{\zeta-1} L \operatorname{tr}\left(\boldsymbol{\Sigma}^{-1} \boldsymbol{C}\right)\right)\end{array} $	(34)
W分布	β分布	$ \begin{array}{c}p(\tau ; \xi, \zeta)=\frac{\Gamma(\zeta)}{\Gamma(\xi) \Gamma(\zeta-\xi)} \frac{\xi}{\zeta} \times \\\left(\frac{\xi}{\zeta} \tau\right)^{\xi-1}\left(1-\frac{\xi}{\zeta} \tau\right)^{\zeta-\xi-1} \\, \tau \in[0, \zeta / \xi]\end{array} $	$ \begin{array}{c}p_{k}(k ; \xi, \zeta, L, \boldsymbol{\Sigma})=\\\frac{2 L^{L d}\left(\boldsymbol{k}^{\mathrm{H}} \boldsymbol{k}\right)^{L-\frac{d}{2}}}{\Gamma_{d}(L)\|\boldsymbol{\Sigma}\|^{L}} \frac{\Gamma(\zeta)}{\Gamma(\xi)}\left(\frac{\xi}{\zeta}\right)^{\frac{\xi+L d-1}{2}}\left(L \boldsymbol{k}^{\mathrm{H}} \boldsymbol{\Sigma}^{-1} \boldsymbol{k}\right) \frac{{\xi}-L d-1}{2} \times\\\exp \left(-\frac{\xi}{2 \zeta} L \boldsymbol{k}^{\mathrm{H}} \boldsymbol{\Sigma}^{-1} \boldsymbol{k}\right) W \frac{L d+1+\xi-2 \xi}{2}, \frac{\xi-L d}{2}\left(\frac{\xi}{\zeta} L \boldsymbol{k}^{\mathrm{H}} \boldsymbol{\Sigma}^{-1} \boldsymbol{k}\right)\end{array} $	$ \begin{array}{c}p_{C}(\boldsymbol{C} ; \xi, \zeta, L, \boldsymbol{\Sigma})= \\\frac{L^{L d}\|\boldsymbol{C}\|^{L-d}}{\Gamma_{d}(L)\|\boldsymbol{\Sigma}\|^{L}} \frac{\Gamma(\zeta)}{\Gamma(\xi)}\left(\frac{\xi}{\zeta}\right)^{\frac{\xi+l d-1}{2}}\left[L\operatorname{tr}\left(\boldsymbol{\Sigma}^{-1} \boldsymbol{C}\right)\right]^{\frac{{\xi}{-} L d-1}{2}} \times \\\exp \left(-\frac{\xi}{2 \zeta} L \operatorname{tr}\left(\boldsymbol{\Sigma}^{-1} \boldsymbol{C}\right)\right) W \frac{L d+1+\xi-2 \zeta}{2}, \frac{\hat{s}-L d}{2}\left(\frac{\xi}{\zeta} L \operatorname{tr}\left(\boldsymbol{\Sigma}^{-1} \boldsymbol{C}\right)\right)\end{array} $	(35)
M分布	逆β分布	$ \begin{array}{c}p(\tau ; \xi, \zeta)=\frac{\Gamma(\zeta)}{\Gamma(\xi) \Gamma(\zeta-\xi)} \frac{\zeta-1}{\xi-1} \times \\\left(\frac{\zeta-1}{\xi-1} \tau\right)^{-\zeta}\left(\frac{\zeta-1}{\xi-1} \tau-1\right)^{\zeta-\xi-1} ,\\ \tau>\xi-1 / \zeta-1\end{array} $	$ \begin{array}{c}p_{k}(k ; \xi, \zeta, L, \boldsymbol{\Sigma})= \\\frac{2 L^{L d}\left(\boldsymbol{k}^{\mathrm{H}} \boldsymbol{k}\right)^{L-\frac{d}{2}}}{\Gamma_{d}(L)\|\boldsymbol{\Sigma}\|^{L}} \frac{\Gamma(\zeta) \Gamma(\xi+L d)}{\Gamma(\xi) \Gamma(\zeta+L d)}\left(\frac{\zeta-1}{\xi-1}\right)^{L d} \times \\M\left(\xi+L d, \zeta+L d,-\frac{\zeta-1}{\xi-1} L \boldsymbol{k}^{\mathrm{H}} \boldsymbol{\Sigma}^{-1} \boldsymbol{k}\right)\end{array} $	$ \begin{array}{c}p_{C}(\boldsymbol{C} ; \xi, \zeta, L, \boldsymbol{\Sigma})= \\\frac{L^{L d}\|\boldsymbol{C}\|^{L-d}}{\Gamma_{d}(L)\|\boldsymbol{\Sigma}\|^{L}} \frac{\Gamma(\zeta) \Gamma(\xi+L d)}{\Gamma(\xi) \Gamma(\zeta+L d)}\left(\frac{\zeta-1}{\xi-1}\right)^{L d} \times \\M\left(\xi+L d, \zeta+L d,-\frac{\zeta-1}{\xi-1} L \operatorname{tr}\left(\boldsymbol{\Sigma}^{-1} \boldsymbol{C}\right)\right)\end{array} $	(36)

表1

表2

图3

图4

图5

图6

图7

图8

图9

图10

图11

图12

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纹理模型	对数累积量υ_v{τ}
γ分布	$ \left\{\begin{array}{l}v_{1}=\psi^{(0)}(\alpha)-\ln (\alpha) \\v_{v}=\psi(v-1)(\alpha), v>1\end{array}\right. $
逆γ分布	$ \left\{\begin{array}{l}v_{1}=-\psi^{(0)}(\lambda)+\ln (\lambda-1) \\v_{v}=(-1)^{v} \psi(v-1)(\lambda), v>1\end{array}\right. $
Fisher分布	$ \left\{\begin{array}{l}v_{1}=\psi(0)(\xi)-\psi(0)(\zeta)+\ln \left(\frac{\zeta-1}{\xi}\right) \\v_{v}=\psi(v-1)(\xi)+(-1)^{v} \psi(v-1)(\zeta), v>1\end{array}\right. $
β分布	$ \left\{\begin{array}{l}v_{1}=\psi(0)(\xi)-\psi(0)(\xi+\zeta)+\ln \left(\frac{\xi+\zeta}{\xi}\right) \\v_{v}=\psi(v-1)(\xi)-\psi(v-1)(\xi+\zeta), v>1\end{array}\right. $
逆β分布	$ \left\{\begin{array}{l}v_{1}=-\psi(0)(\xi)+\psi(0)(\xi+\zeta)+\ln \left(\frac{\zeta-1}{\xi+\zeta-1}\right) \\v_{v}=(-1)^{v}[\psi(v-1)(\xi)-\psi(v-1)(\xi+\zeta)], v>1\end{array}\right. $

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