基于EEMD和Husrt指数的GNSS基准站的垂向速率估计
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摘要
连续的全球卫星导航系统(GNSS)基准站的坐标时间序列中包含了复杂的噪声信号、非构造形变及其它因素的影响,尤其在垂直方向,对GNSS基准站在国际地球参考框架(ITRF)下的运动速率估计产生了较大的干扰。为进一步提高速率精度,文中采用整体模态分解(EEMD)方法对GNSS基准站的垂向观测时间序列进行分解,并根据各种信号的Hurst值进行分类及重构为噪声信号、季节性信号和长期趋势信号,采用最小二乘方法拟合长期趋势信号得到垂向速率。通过对中国大陆构造环境监测网络(CMONOC)的GNSS台站从2001—2013年近13a的垂向坐标时间序列的实例分析,采用基于EEMD和Husrt指数的最小二乘法能够准确地估计GNSS基准站的垂向速率。
The daily coordinate time series of Global satellite navigation system(GNSS)reference stations contain the complex effects of noise signals,non-tectonic deformation and other factors,particularly in the vertical direction,of which the factors have a greater impact on the velocity estimation of GNSS reference station on the International Terrestrial Reference Frame(ITRF).In order to improve the accuracy of the velocity estimation,this paper uses the Ensemble Empirical Mode Decomposition(EEMD)method to decompose the vertical time series of GNSS reference station,and the noise signal,seasonal signal and longterm trend signal can be reconstructed respectively based on the Hurst value of signals.Then the vertical velocity can be estimated by using the least square method to fit the long-term trend signals.By analyzing the vertical time series of GNSS stations of Crustal Movement Observation Network of China(CMONOC)from January 2001 to December 2013,the EEMD method and Husrt exponent based on the least square method can accurately estimate the vertical velocity of GNSS reference station.
The daily coordinate time series of Global satellite navigation system(GNSS)reference stations contain the complex effects of noise signals,non-tectonic deformation and other factors,particularly in the vertical direction,of which the factors have a greater impact on the velocity estimation of GNSS reference station on the International Terrestrial Reference Frame(ITRF).In order to improve the accuracy of the velocity estimation,this paper uses the Ensemble Empirical Mode Decomposition(EEMD)method to decompose the vertical time series of GNSS reference station,and the noise signal,seasonal signal and longterm trend signal can be reconstructed respectively based on the Hurst value of signals.Then the vertical velocity can be estimated by using the least square method to fit the long-term trend signals.By analyzing the vertical time series of GNSS stations of Crustal Movement Observation Network of China(CMONOC)from January 2001 to December 2013,the EEMD method and Husrt exponent based on the least square method can accurately estimate the vertical velocity of GNSS reference station.
引文
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[14]田云锋,沈正康.GPS坐标时间序列中非构造噪声的剔除方法研究进展[J].地震学报,2009,31(1):68-81.
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[16]荣敏,孙付平,贾小林,等.利用GPS基准站数据浅析我国地壳垂直运动[J].测绘工程,2009,18(4):7-9.
[17]GRECH D,MAZUR Z.On the scaling ranges of detrended fluctuation analysis for long-term memory correlated short series of data[J].Physica A:Statistical Mechanics and its Applications,2013,392(10):2384-2397
[18]WILLIAMS S D P.CATS:GPS coordinate time series analysis software[J].GPS solutions,2008,12(2):147-153.
[2]ZHANG J,BOCK Y,JOHNSON H,et al.Southern California Permanent GPS Geodetic Array:Error analysis of daily position estimates and site velocities[J].Journal of Geophysical Research:Solid Earth(1978~2012),1997,102(B8):18035-18055.
[3]TEUNISSEN P J G,AMIRI-SIMKOOEI A R.Leastsquares variance component estimation[J].Journal of Geodesy,2008,82(2):65-82.
[4]DONG D,FANG P,BOCK Y,et al.Anatomy of apparent seasonal variations from GPS‐derived site position time series[J].Journal of Geophysical Research:Solid Earth(1978-2012),2002,107(B4):ETG 9-1-ETG 9-16.
[5]袁林果,丁晓利,陈武,等.香港GPS基准站坐标序列特征分析[J].地球物理学报,2008,51(5):1372-1384.
[6]蒋志浩,张鹏,秘金钟,等.顾及有色噪声影响的CGCS2000下我国CORS站速度估计[J].测绘学报,2010,39(4):355.
[7]章浙涛,朱建军,卢骏,等.小波变换在时间序列特征提取中的应用[J].测绘工程,2014,23(6):21-26.
[8]WU Z,HUANG N E.Ensemble empirical mode decomposition:a noise-assisted data analysis method[J].Advances in adaptive data analysis,2009,1(1):1-41.
[9]MONTILLET J P,TREGONING P,MCCLUSKY S,et al.Extracting white noise statistics in GPS coordinate time series[J].Geoscience and Remote Sensing Letters,IEEE,2013,10(3):563-567.
[10]HUANG N E,SHEN Z,LONG S R,et al.The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis[J].Proceedings of the Royal Society of London.Series A:Mathematical,Physical and Engineering Sciences,1998,454(1971):903-995.
[11]AGNEW D C.The time-domain behavior of power‐law noises[J].Geophysical research letters,1992,19(4):333-336.
[12]黄立人.GPS基准站坐标分量时间序列的噪声特性分析[J].大地测量与地球动力学,2006,26(2):31-33.
[13]RODRIGUEZ E,ECHEVERRIA J C,ALVAREZRAMIREZ J.1/fαfractal noise generation from Grünwald-Letnikov formula[J].Chaos,Solitons&Fractals,2009,39(2):882-888.
[14]田云锋,沈正康.GPS坐标时间序列中非构造噪声的剔除方法研究进展[J].地震学报,2009,31(1):68-81.
[15]WILLIAMS S D P.The effect of coloured noise on the uncertainties of rates estimated from geodetic time series[J].Journal of Geodesy,2003,76(9-10):483-494.
[16]荣敏,孙付平,贾小林,等.利用GPS基准站数据浅析我国地壳垂直运动[J].测绘工程,2009,18(4):7-9.
[17]GRECH D,MAZUR Z.On the scaling ranges of detrended fluctuation analysis for long-term memory correlated short series of data[J].Physica A:Statistical Mechanics and its Applications,2013,392(10):2384-2397
[18]WILLIAMS S D P.CATS:GPS coordinate time series analysis software[J].GPS solutions,2008,12(2):147-153.