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

Abstract

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

CLC Number:

TN95

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.

Figures/Tables 14

Fig.1

Fig.2

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)

Table 2

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Fig.6

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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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Statistical modeling and characteristic analysis of polarimetric SAR sea clutter at X-band based on numerical simulations

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