胡顺强,王坦,管雅慧,杨振宇

• 1:首都师范大学资源环境与旅游学院
• 2:中国地震台网中心

摘要(Abstract)：

针对传统的GPS时间序列最小二乘(LS)谐波函数模型方法不能精确提取GPS垂向时间序列的周期项信号问题,该文以云南地区2011年1月—2017年6月连续观测的27个GPS基准站数据为例,使用主成分分析(PCA)获得27个测站的共模误差,然后分别使用奇异谱分析(SSA)和LS方法对PCA滤波前后的测站时间序列进行周期项信号提取。实验结果表明,原始时间序列分别减去SSA、PCA-SSA、LS和PCA-LS提取周期项信号的RMS减少百分比平均为25.66%、17.23%、16.76%、16.76%;原始时间序列与4种方法提取周期项信号的相关系数平均为0.66、0.55、0.54、0.54,说明SSA提取的周期项信号要优于其他3种方法,将SSA应用于云南地区GPS垂向时间序列的周期项信号提取是可行和有效的。

关键词(KeyWords)： 最小二乘;奇异谱分析;周期项;时间序列

Abstract:

Keywords:

基金项目(Foundation): 国家自然科学基金项目(41672192)

作者(Author): 胡顺强,王坦,管雅慧,杨振宇

DOI: 10.16251/j.cnki.1009-2307.2021.08.006

参考文献(References)：

• [1] WANG Q,ZHANG P Z,FREYMUELLER J T,et al.Present-day crustal deformation in China constrained by global positioning system measurements[J].Science,2001,294(5542):574-577.
• [2] GAN W,ZHANG P,SHEN Z,et al.Present-day crustal motion within the Tibetan Plateau inferred from GPS measurements[J].J Geophys Res,2007,112(B8):416-429.
• [3] DONG D,HERRING T A,KING R W.Estimating regional deformation from a combination of space and terrestrial geodetic data[J].J Geod,1998,72(4):200-214.
• [4] NIKOLAIDIS R.Observation of geodetic and seismic deformation with the global positioning system[D].San Diego:University of California,2002.
• [5] 盛传贞，甘卫军，梁诗明，等.滇西地区GPS时间序列中陆地水载荷形变干扰的GRACE分辨与剔除[J].地球物理学报，2014,57(1):42-52.(SHENG Chuanzhen,GAN Weijun,LIANG Shiming,et al.Identification and elimination of non-tectonic crustal deformation caused by land water from GPS time series in the western Yunnan province based on GRACE observation[J].Chinese Journal of Geophysics,2014,57(1):42-52.)
• [6] 张双成，李振宇，何月帆，等.GNSS高程时间序列周期项的经验模态分解提取[J].测绘科学，2018,43(8):80-84.(ZHANG Shuangcheng,LI Zhenyu,HE Yuefan,et al.Extracting of periodic component of GNSS vertical time series using EMD[J].Science of Surveying and Mapping,2018,43(8):80-84.)
• [7] BOGUSA J,KLOS A.On the significance of periodic signals in noise analysis of GPS station coordinates time series[J].GPS Solutions,2016,20(4):655-664.
• [8] 李昭，姜卫平，刘鸿飞，等.中国区域IGS基准站坐标时间序列噪声模型建立与分析[J].测绘学报，2012,41(4):496-503.(LI Zhao,JIANG Weiping,LIU Hongfei,et al.Noise model establishment and analysis of IGS reference station coordinate time series inside China[J].Acta Geodaetica et Cartographica Sinica,2012,41(4):496-503.)
• [9] RAY J,ALTAMIMI Z,COLLILIEUX X,et al.Anomalous harmonics in the spectra of GPS position estimates[J].GPS Solutions,2008,12(1):55-64.
• [10] RANGELOVA E,SIDERIS M G,KIM J W.On the capabilities of the multi-channel singular spectrum method for extracting the main periodic and non-periodic variability from weekly GRACE data[J].Journal of Geodynamics,2012,54(2):64-78.
• [11] BENNETT R A.Instantaneous deformation from continuous GPS:contributions from quasi-periodic loads[J].Geophysical Journal International,2008,174(3):1052-1064.
• [12] 罗勇，匡翠林，卢辰龙，等.基于SSA的GPS坐标序列去噪及季节信号提取[J].大地测量与地球动力学，2015,35(3):391-395.(LUO Yong,KUANG Cuilin,LU Chenlong,et al.GPS coordinate series denoising and seasonal signal extraction based on SSA[J].Journal of Geodesy and Geodynamics,2015,35(3):391-395.)
• [13] HASSANI H,SOOFI A.Predicting daily exchange rate with singular spectrum analysis[J].Nonlinear Analysis:Real World Applications,2010,11:2023-2034.
• [14] 卢辰龙，匡翠林，易重海，等.奇异谱分析滤波法在消除GPS多路径中的应用[J].武汉大学学报(信息科学版),2015,40(7):924-931.(LU Chenlong,KUANG Cuilin,YI Zhonghai,et al.Singular spectrum analysis filter method for mitigation of GPS multipath errors[J].Geomatics and Information Science of Wuhan University,2015,40(7):924-931.)
• [15] KONDRASHOV D,BERLOFF P.Stochastic modeling of decadal variability in ocean gyres[J].Geophysical Research Letters,2015,42(5):1543-1553.
• [16] 李婉秋，王伟，章传银，等.基于奇异谱分析的CORS大地高时序形变信息提取[J].大地测量与地球动力学，2019,39(8):825-831.(LI Wanqiu,WANG Wei,ZHANG Chuanyin,et al.Deformation Signal extraction of geodetic height change time series of CORS based on singular spectrum analysis[J].Journal of Geodesy and Geodynamics,2019,39(8):825-831.)
• [17] 高文宗，郭金运，沈毅，等.基于多通道奇异谱分析的北京房山站2007—2015年坐标时变分析[J].中国科技论文，2018,13(3):358-364.(GAO Wenzong,GUO Jinyun,SHEN Yi,et al.Displacement analysis of BJFS station with MSSA from 2007 to 2015[J].China Sciencepaper,2018,13(3):358-364.)
• [18] DONG D,FANG P,BOCK Y,et al.Spatiotemporal filtering using principal component analysis and Karhunen-Loeve expansion approaches for regional GPS network analysis[J].Journal of Geophysical research(Solid Earth),2006,111(B3):B03405.
• [19] 王方超，吕志平，吕浩，等.基于RegEM算法的GPS坐标时间序列插值应用分析[J].大地测量与地球动力学，2020,40(1):45-50.(WANG Fangchao,LYU Zhiping,LYU Hao,et al.Application analysis of GPS coordinate times series interpolation based on RegEM algorithm[J].Journal of Geodesy and Geodynamics,2020,40(1):45-50.)
• [20] SCHNEIDER T.Analysis of incomplete climate data:estimation of mean values and covariance matrices and imputation of missing values[J].Journal of Climate,2001,14(5):853-871.
• [21] XIANG Y,YUE J P,TANG K,et al.Joint analysis of seasonal oscillations derived from GPS observations and hydrological loading for China's mainland[J].Adv Space Res,2018,62(11):3148-3161.
• [22] CHEN Q,DAM T V,SNEEUW N,et al.Singular spectrum analysis for modeling seasonal signals from GPS time series[J].J Geodyn,2013,72(12):25-35.
• [23] HASSANI H.Singular spectrum analysis:methodology and comparison[J].Journal of Data Science,2007,5(2):239-257.
• [24] 张为民，王勇.洱海水位变化对下关基准点绝对重力观测的影响[J].大地测量与地球动力学，2005,25(4):114-116.(ZHANG Weimin,WANG Yong.Effect of water level variations of Erhai lake on absolute gravity observation at Xiaguan station[J].Journal of Geodesy and Geodynamics,2005,25(4):114-116.)