一种α稳定分布参数估计方法及其在冰源噪声统计建模中的应用

A parameter estimation method of α stable distribution and its application in the statistical modeling of ice-generated noise

为研究冰源噪声的统计特性,扩展了一种用于合成孔径雷达图像信号参数估计的α稳定分布参数估计方法的适用范围,解决了该方法在特征指数α接近2时,偏斜参数β的估计精度严重下降的问题,并将其应用于北极冰源噪声的统计建模中。该方法利用两个特征函数点进行参数估计,第二个特征函数点ω_(0)的取值范围受尺度参数γ值影响。数值仿真表明:当γ∈[0.00006,0.4]时,ω_(0)>1时的参数估计性能更好;当γ∈(0.4,2]时,0<ω_(0)<0.5时的参数估计性能更好。北极噪声数据的验证结果表明,ω_(0)>1时的α稳定分布对冰源噪声表现出良好的建模效果。最后给出了不同海冰状态下α值的统计规律。

In order to study the statistical characteristics of ice-generated noise,the applicability of a parameter estimation method ofαstable distribution which is used to estimate the parameters of SAR image signals is extended.The problem of serious decline in the estimation accuracy of skew parameterβ,when the characteristic exponentαis close to 2,is solved effectively.The method is applied to statistical modeling of ice-generated noise.In this method,two characteristic function points are used for parameter estimation,and the value range of the second characteristic function pointω_(0)is affected by the scale parameterγ.The results of numerical simulations show that forγ∈[0.00006,0.4],the estimated parameters exhibit better performance whenω_(0)>1;forγ∈(0.4,2],the estimated parameters exhibit better performance when 0<ω_(0)<0.5.The results of the Arctic noise data show that theαstable distribution shows a good modeling effect on the ice-generated noise whenω_(0)>1.Finally,the statistical laws of the value ofαunder different sea ice conditions are given.