基于最小二乘谐波拟合的置信水平计算方法  

A Method for the Confidence Level Calculation Based on the Least Square Harmonic Fitting

作　　者：马民[1] 汪春峰[1] 

机构地区：[1]河南师范大学数学与信息科学学院,河南新乡453007

出　　处：《河南师范大学学报（自然科学版）》2016年第4期21-26,共6页Journal of Henan Normal University(Natural Science Edition)

基　　金：国家自然科学基金(41374158;41574143);河南省高等学校青年骨干教师资助计划项目(2014GGJS-047)

摘　　要：结合Lomb最小二乘谐波拟合的方法和Scargle归一化功率谱的置信水平的解析公式,给出了一种计算谐波拟合置信水平的方法.该方法的优势在于:直接计算拟合量的振幅,并给出拟合振幅的置信水平,物理意义明确;能够对多个频率进行扫描和拟合并给出各频率对应振幅的置信水平;通过对置信水平最大的频率进行拟合,获得时间序列的周期性变化规律.最后,通过数值试验说明了本方法的优势和实用性.The least square harmonic fitting （LSHF） method proposed by Lomb has obvious physical meaning, the method of confidence level calculation proposed by Scarglc has an explicit expression on the confidence of the normalized power spectrum. Based on the above two advantages, we propose a method for the confidence level calculations based on the LSHF. The advantages of our method are： the amplitude and its confidence level are calculated directly. And thus preserve the physical meaning the observation data; multiple frequencies can be scanned and fitted, their confidence levels can also be given simulta- neously; the periodic nature of the time series can be explored by fitting the frequency with maximum confidence. Finally, nu- merical experiments are performed to illustrate the advantages and applications of our method.

关 键 词：最小二乘法 谐波拟合 置信水平 

分 类 号：O241.6[理学—计算数学]