基于假设检验理论的统计分辨研究综述  

Research Review of Statistical Resolution Based on the Hypothesis Testing Theory

作　　者：张云雷[1] 李轲[1] 卢建斌[1] ZHANG Yun-lei;LI Ke;LU Jian-bin(Institute of Electronic Engineering,Navy University of Engineering,Wuhan 430033,China)

机构地区：[1]海军工程大学电子工程学院,武汉430033

出　　处：《科学技术与工程》2021年第12期4752-4759,共8页Science Technology and Engineering

基　　金：国家自然科学基金(61501486)。

摘　　要：对近邻目标的分辨一直以来是不同信号处理领域的关注热点。传统上基于相关分析或波束响应的瑞利限,难以反映实际系统中随机噪声等因素的影响,因此有学者提出了统计分辨(statistical resolution limit,SRL)的概念。当前关于统计分辨限的定义主要有两种:一是利用估计性能,即CRB(Cramér-Rao bound)界定义;二是采用二元假设检验(binary hypothesis test,BHT)理论定义。论文对后者的研究现状进行了梳理,得到一般的研究思路:构造二元假设检验分辨模型,进行泰勒近似得到关于待分辨参数的线性模型,或利用大快拍数条件的渐近分布理论,求解统计量的分布,进而得到统计分辨限与波形、信噪比等的关系。最后,指出该领域未来的一些研究建议。The resolvability of close targets has always been a hot research spot in the various signal processing fields.The Rayleigh limit,which is based on the correlation analysis or the beamform width,is difficult to reflect the stochastic influence of the noise in the actual system.Therefore,the concept of statistical resolution limit(SRL)has been proposed.There are mainly two kinds of definitions of SRL.One is based on the bound of estimation,defined as Cramér-Rao bound,and the other is based on the binary hypothesis test theory.The research of the latter was concluded and a general solution was obtained,which could be described as follows.First,the binary hypothesis test(BHT)theory was applied to model the resolution problem.Then,two ways were presented to resolve it—one is to utilize the Taylor expansion and approximation to obtain a linear model,the other is to utilize the asymptotic distribution with the condition of a large number snaps.Finally,the relationship between SRL and other variables,such as waveform,SNR etc.,was obtained.In the last section,some future research suggestions were presented.

关 键 词：瑞利限 统计分辨 统计分辨限(SRL) 二元假设检验(BHT) 广义似然比(GLRT) 

分 类 号：TN957.524[电子电信—信号与信息处理]