最大时间间隔误差与Allan方差关系研究  

A study of relationship between the maximum time interval error and Allan variance

作　　者：胡珍源[1,2,3] 杨西光 张攀 张首刚[1,3] HU Zhen-yuan;YANG Xi-guang;ZHANG pan;ZHANG Shou-gang(National Time Service Center,Chinese Academy of Sciences,Xi’an 710600,China;University of Chinese Academy of Sciences,Beijing 100049,China;Key Laboratory of Time Reference and Applications,Chinese Academy of Sciences,Xi’an 710600,China)

机构地区：[1]中国科学院国家授时中心,西安710600 [2]中国科学院大学,北京100049 [3]时间基准及应用重点实验室(中国科学院),西安710600

出　　处：《时间频率学报》2024年第3期229-234,共6页Journal of Time and Frequency

基　　金：国家重点研发计划(2020YFA0309801);中国科学院战略性先导B类(XDB35030101)。

摘　　要：最大时间间隔误差和Allan方差都是常用于对时间频率信号生成与传递系统进行分析或评价的统计量。在有些应用中,测量最大时间间隔误差较测量Allan方差更为方便。为了确定一个信号的最大时间间隔误差和Allan方差之间是否存在一定的统计关系以及是否可以通过最大时间间隔误差对Allan方差做出估计,介绍了最大时间间隔误差和Allan方差的数学定义,通过数学分析推导,得到了最大时间间隔误差与Allan方差之间不能直接换算,而最大时间间隔误差一定时Allan方差存在上限。该关系对不同取样时间都成立。对幂律谱模型中常见的5种噪声类型,使用计算机程序生成每种噪声条件下的数值数据,对这一关系做了验证。数学推导计算和数值数据验证都表明:根据数据的最大时间间隔误差可以确定其Allan方差的上限。The maximum time interval error(MTIE)and the Allan variance are commonly used to analyze or evaluate time-frequency signal generation and transmission systems.In some applications,measuring the maximum time interval error is more convenient than measuring Allan variance.To find whether there is a definite statistical relationship between them or whether it is possible to estimate the Allan variance via the maximum time interval error,we performed mathematical analysis and derivation.The results show that while direct conversion between them is impossible,an upper limit of the Allan variance exists for a fixed maximum time interval error,which holds for different sampling times.This relation is verified with the specific data generated by the computer program under five noise patterns in the Power Law Noise Model.Both derivation and data verification show that the upper limit of the Allan variance can be determined according to the maximum time interval error of the sampled data.

关 键 词：ALLAN方差 最大时间间隔误差 噪声 

分 类 号：TB939[一般工业技术—计量学]