基于假设检验理论的统计分辨研究综述
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TN957

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国家自然科学基金资助项目(61501486);


Research review of statistical resolution based on the hypothesis testing theory
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    摘要:

    同一分辨单元内近邻目标的分辨一直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,难以反映实际系统随机噪声等因素的影响,因此提出了统计分辨的概念。当前关于统计分辨限的定义主要有两种方式:一是直接利用克拉美罗界定义,二是采用二元假设检验理论定义。论文对后者的研究现状进行了梳理,得到一般的研究思路——利用二元假设检验构造分辨模型,进行泰勒近似得到关于待分辨参数的线性模型进行求解,或利用大快拍数条件下的渐近分布求解,得到统计分辨限与波形、信噪比等的关系。最后,指出了该领域未来的一些研究建议。

    Abstract:

    The resolution of close targets in a tested unit has always been a hot research spot in various signal processing fields. The Rayleigh limit, which is based on the correlation analysis or beamforming, is hard to reflect the stochastic influence as the noise existing in the actual system. Therefore, the concept of statistical resolution has been proposed. There are two definitions of statistical resolution limit (SRL)—— one is based on the Cramér–Rao lower bound and the other is the binary hypothesis testing theory. In this paper, the current research of the latter has been concluded, and a general solution has been obtained. The binary hypothesis test is applied to model the resolution problem, which is solved by resorting to a linear model after the Taylor expansion and approximation, or with the conclusion of the asymptotic distribution under the condition of a large number snaps. Based on those tools, the relationship between SRL and other variables, such as waveform, SNR etc., has been obtained. Finally, some future research suggestions are also presented.

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张云雷,李轲,卢建斌. 基于假设检验理论的统计分辨研究综述[J]. 科学技术与工程, 2021, 21(12): 4752-4759.
Zhang Yunlei, Li Ke, Lu Jianbin. Research review of statistical resolution based on the hypothesis testing theory[J]. Science Technology and Engineering,2021,21(12):4752-4759.

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  • 收稿日期:2020-08-15
  • 最后修改日期:2021-04-25
  • 录用日期:2020-10-25
  • 在线发布日期: 2021-05-17
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