GPS坐标时间序列时变振幅周期信号的Huber M估计  

Estimating time-varying amplitude seasonal signal in GPS position time series via Huber M-estimators

作　　者：伍浩琛 边家文[1] 陈保周 周侗 WU Haochen;BIAN Jiawen;CHEN Baozhou;ZHOU Tong(School of Mathematics and Physics,China University of Geosciences,Wuhan 430074,China)

机构地区：[1]中国地质大学数学与物理学院,武汉430074

出　　处：《测绘科学》2021年第2期62-70,共9页Science of Surveying and Mapping

基　　金：国家自然科学基金项目(61302138)。

摘　　要：GPS时间序列周期信号的精准提取对趋势的估计具有重要的影响。相较于传统的常数振幅周期信号模型,已有研究表明GPS时间序列周期信号的振幅是随时间变化的。实际的GPS时间序列存在异常值,且在提取周期信号过程中会产生新的异常值。针对以上两点,该文提出了一种基于Huber函数M估计(HM)的GPS坐标时间序列时变振幅周期信号估计方法:采用关于时间的多项式函数来建立时变振幅模型,由HM方法及交替方向乘子法求解。通过模拟数据及实际GPS站点数据将HM方法与小波分解方法、奇异谱分析方法和滑动最小二乘方法进行比较,结果表明HM方法在估计精度上要优于其他3种方法,弥补了已有方法在时变振幅情形下会吸收噪声以及噪声较强时对周期信号提取能力较弱的不足。Accurate extraction of the periods from the global positioning system(GPS)time series has an important influence on the estimation of the trend.The periods are routinely modeled with constant amplitude,however,many studies have shown that the amplitude of the seasonal signals vary over time.Moreover,there are outliers in GPS time series,and new outliers will be brought in extracting seasonal signals.In the view of the two points,a new method based on Huber M-estimators(HM)for estimating the time-varying seasonal signals in time series was proposed.Time-varying amplitude was modeled by polynomial function about time,and the model was solved by HM and alternating direction method of multiplier algorithm.Comparing HM with wavelet decomposition method(WD),singular spectral analysis method(SSA)and moving ordinary least squares(MOLS)by using simulated data and the real GPS site data,the results indicated that HM was better than the other three methods in estimating precision,which made up for the deficiency that the three methods might absorb noise and could not completely extract the seasonal signal when the noise was heavy.

关 键 词：GPS时间序列 时变振幅周期信号 Huber M估计方法 小波分解方法 奇异谱分析方法 滑动最小二乘方法 交替方向乘子法 

分 类 号：P228[天文地球—大地测量学与测量工程]