基于 Fisher 分布的极化合成孔径雷达统计建模及其参数估计方法

摘要

为更准确地描述高分辨极化合成孔径雷达(Synthetic Aperture Radar,SAR)图像的尖峰和长拖尾等统计分布特性,提出了基于 Fisher 分布的极化图像多变量乘积模型,并研究了其参数估计方法。首先给出了柯西分布相干斑噪声等效纹理分量的概率密度函数及其低阶矩特征；然后利用散射因子服从 F 分布的等效纹理变量与高斯散斑变量相乘形成的多变量乘积统计模型,得到了 Fisher 分布模型的概率密度函数,并推导了其多视协方差矩阵的概率密度函数和矩阵行列式值的低阶矩特征；最后提出了基于矩阵行列式值的矩估计和基于 Mellin 变换的对数累积量估计等两种参数估计方法,并进行了对比,同时通过仿真数据和实测数据验证了理论模型和新参数估计方法的有效性。这为高分辨极化 SAR 图像建模、目标检测和识别等领域的理论研究和工程实现提供了新途径。%Based on the Fisher multiple variable product model,the Fisher statistical model of polari-metric synthetic aperture radar(SAR)images is put forward to describe the properties of heavy tail and peak,and the statistics and the estimation methods are obtained.Firstly,the probability density function (PDF)of developed t distribution is given based on Cauchy distribution,so are the fractal moments.Sec-ondly,the Fisher distribution model is obtained through the multiple variable product model mixed with the Fisher variable,and the PDF and the fractal moments of the covariance matrix moments are derived. At last,two estimation methods via Mellin transform and Matrix moments are presented.The perform-ances of the novel data model and novel parameter estimation methods are verified by the simulated data and real data.The research provides a simple analytical method to describe different distributed clutter, which is useful to target detection and recognition.