基于多通道奇异谱分析的GNSS坐标时间序列共模误差的提取
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摘要
共模误差是区域连续GNSS网中存在的一种与时空相关的主要误差源.为了有效的剔除共模误差,提高坐标时间序列的精度,本文提出了利用多通道奇异谱分析(Multi-channel Singular Spectrum Analysis,MSSA)提取共模误差的新思路,并利用实验区域18个测站9年(2002年到2010年)的GPS坐标时间序列进行实验,分析了共模误差对时间序列的影响和测站噪声特性的影响,并对共模误差序列进行周期探测,结果显示:通过MSSA能够有效的剔除共模误差,提高坐标时间序列的精度.
The spatially and temporally correlated common mode errors(CMEs) are the primary error sources in daily GPS solutions in the regional GPS network. In order to effectively remove these errors and improve the accuracy of the coordinate time series, this paper proposes a new idea to extract the common mode error by multi-channel singular spectrum analysis(MSSA). Experiments on this method are carried out using the data of 18 GPS stations from 2002 to 2010 in the west coast of the United States. The results show that the MSSA can effectively eliminate the common mode errors and enhance the accuracy of the coordinate time series.
The spatially and temporally correlated common mode errors(CMEs) are the primary error sources in daily GPS solutions in the regional GPS network. In order to effectively remove these errors and improve the accuracy of the coordinate time series, this paper proposes a new idea to extract the common mode error by multi-channel singular spectrum analysis(MSSA). Experiments on this method are carried out using the data of 18 GPS stations from 2002 to 2010 in the west coast of the United States. The results show that the MSSA can effectively eliminate the common mode errors and enhance the accuracy of the coordinate time series.
引文
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Chen Q, van Dam T, Sneeuw N, et al. 2013. Singular spectrum analysis for modeling seasonal signals from GPS time series. Journal of Geodynamics, 72: 25-35, doi: 10.1016/j.jog.2013.05.005.
Dong D, Fang P, Bock Y, et al. 2006. Spatiotemporal filtering using principal component analysis and Karhunen-Loeve expansion approaches for regional GPS network analysis. Journal of Geophysical Research, 111(B3): B03405, doi: 10.1029/2005JB003806.
Freed A M, Bürgmann R, Calais E, et al. 2006. Implications of deformation following the 2002 Denali, Alaska, earthquake for postseismic relaxation processes and lithospheric rheology. Journal of Geophysical Research, 111(B1): B01401, doi: 10.1029/2005JB003894.
Guo J Y, Gao W Z, Yu H J, et al. 2018. Gravity tides extracted from relative gravimetric data with singular spectrum analysis. Chinese Journal of Geophysics (in Chinese), 61(10): 3889-3902, doi: 10.6038/cjg2018L0460.
Guo J Y, Yang L, Liu X, et al. 2012. On temporal-spatial distribution of backscatter coefficients over China determined by TOPEX/Poseidon mission. Science China Earth Sciences, 55(12): 2068-2083, doi: 10.1007/s11430-012-4524-y.
Guo J Y, Li W D, Chang X T, et al. 2018. Terrestrial water storage changes over Xinjiang extracted by combining Gaussian filter and multichannel singular spectrum analysis from GRACE. Geophysical Journal International, 213(1): 397-407, doi: 10.1093/gji/ggy006.
Hassani H. 2007. Singular spectrum analysis: Methodology and comparison. Journal of Data Science, 5(2): 239-257.
Hu S C, Wu J C, Sun Y F. 2009. Comparison among three spatiotemporal filtering methods for regional GPS networks analysis. Journal of Geodesy and Geodynamics (in Chinese), 29(3): 95-99.
Huang L R. 2006. Noise properties in time series of coordinate component at GPS fiducial stations. Journal of Geodesy and Geodynamics (in Chinese), 26(2): 31-33, 38.
Huang L R, Fu Y. 2007. Analysis on the noises from continuously monitoring GPS sites. Acta Seismologica Sinica (in Chinese), 29(2): 197-202.
Jiang Z H, Zhang P, Bi J Z, et al. 2010. Velocity estimation on the colored noise properties of CORS network in China based on the CGCS2000 Frame. Acta Geodaetica et Cartographica Sinica (in Chinese), 39(4): 355-363.
Kondrashov D, Ghil M. 2006. Spatio-temporal filling of missing points in geophysical data sets. Nonlinear Processes in Geophysics, 13(2): 151-159, doi: 10.5194/npg-13-151-2006.
Kondrashov D, Shprits Y, Ghil M. 2010. Gap filling of solar wind data by singular spectrum analysis. Geophysical Research Letters, 37(15): L15101, doi: 10.1029/2010GL044138.
Kondrashov D, Berloff P. 2015. Stochastic modeling of decadal variability in ocean gyres.Geophysical Research Letters, 42(5): 1543-1553, doi: 10.1002/2014GL062871.
Liu G, Li G, Tan K, et al. 2012. Improvement of instantaneous positioning by spatial stacking and modified sidereal filtering methods with application to the 2008 Ms8.0 Wenchuan earthquake. Geodesy and Geodynamics, 3(1): 13-18, doi: 10.3724/SP.J.1246.2012.00013.
Ma C, Li F, Zhang S K, et al. 2016. The coordinate time series analysis of continuous GPS stations in the Antarctic Peninsula with consideration of common mode error. Chinese Journal of Geophysics (in Chinese), 59(8): 2783-2795, doi: 10.6038/cjg20160806.
Márquez-Azúa B, DeMets C. 2003. Crustal velocity field of Mexico from continuous GPS measurements, 1993 to June 2001: Implications for the Neotectonics of Mexico. Journal of Geophysical Research, 108(B9): 2450, doi: 10.1029/2002JB002241.
Mazzotti S, Dragert H, Henton J, et al. 2003. Current tectonics of northern Cascadia from a decade of GPS measurements. Journal of Geophysical Research, 108(B12): 2554, doi: 10.1029/2003JB002653.
Meade B J, Hager B H. 2005. Block models of crustal motion in southern California constrained by GPS measurements. Journal of Geophysical Research, 110(B3): B03403, doi: 10.1029/2004JB003209.
Melbourne T I, Webb F H, Stock J M, et al. 2002. Rapid postseismic transients in subduction zones from continuous GPS.Journal of Geophysical Research, 107(B10): 2241, doi: 10.1029/2001JB000555.
Melbourne T I, Szeliga W M, Miller M M, et al. 2005. Extent and duration of the 2003 Cascadia slow earthquake. Geophysical Research Letters, 32(4): L04301, doi: 10.1029/2004GL021790.
Nikolaidis R. 2002. Observation of geodetic and seismic deformation with the Global Positioning System[Ph. D. thesis]. San Diego: University of California, 249.
Prawirodirdjo L, Bock Y. 2004. Instantaneous global plate motion model from 12 years of continuous GPS observations. Journal of Geophysical Research, 109(B8): B08405, doi: 10.1029/2003JB002944.
Santamaría-Gómez A, Gravelle M, Collilieux X, et al. 2012. Mitigating the effects of vertical land motion in tide gauge records using a state-of-the-art GPS velocity field. Global and Planetary Change, 98-99: 6-17, doi: 10.1016/j.gloplacha.2012.07.007.
Schoellhamer D H. 2001. Singular spectrum analysis for time series with missing data. Geophysical Research Letters, 28(16): 3187-3190, doi: 10.1029/2000GL012698.
Sella G F, Stein S, Dixon T H, et al. 2007. Observation of glacial isostatic adjustment in “stable” North America with GPS. Geophysical Research Letters, 34(2): L02306, doi: 10.1029/2006GL027081.
Shen Y, Guo J Y, Liu X, et al. 2017. One hybrid model combining singular spectrum analysis and LS+ARMA for polar motion prediction. Advances in Space Research, 59(2): 513-523, doi: 10.1016/j.asr.2016.10.023.
Shen Y, Guo J Y, Liu X, et al. 2018. Long-term prediction of polar motion using a combined SSA and ARMA model. Journal of Geodesy, 92(2): 333-343, doi: 10.1007/s00190-017-1065-3.
Shen Y Z, Li W W, Xu G C, et al. 2014. Spatiotemporal filtering of regional GNSS network′s position time series with missing data using principle component analysis. Journal of Geodesy, 88(1): 1-12, doi: 10.1007/s00190-013-0663-y.
Szeliga W, Melbourne T I, Miller M M, et al. 2004. Southern Cascadia episodic slow earthquakes. Geophysical Research Letters, 31(16): L16602. doi: 10.1029/2004GL020824.
Vautard R, Yiou P, Ghil M. 1992. Singular-spectrum analysis: A toolkit for short, noisy chaotic signals. Physica D: Nonlinear Phenomena, 58(1-4): 95-126, doi: 10.1016/0167-2789(92)90103-T.
Wdowinski S, Bock Y, Zhang J, et al. 1997. Southern California permanent GPS geodetic array: Spatial filtering of daily positions for estimating coseismic and postseismic displacements induced by the 1992 Landers earthquake. Journal of Geophysical Research, 102(B8): 18057-18070, doi: 10.1029/97JB01378.
Williams S D P. 2008. CATS: GPS coordinate time series analysis software. GPS Solutions, 12(2): 147-153, doi: 10.1007/s10291-007-0086-4.
Wu H B, Wu L. 2005. Methods for Diagnosing and Forecasting Climate Variability (in Chinese). Beijing: China Meteorological Press.
Wyatt M G, Kravtsov S, Tsonis A A. 2012. Atlantic multidecadal oscillation and northern hemisphere′s climate variability. Climate Dynamics, 38(5-6): 929-949, doi: 10.1007/s00382-011-1071-8.
Yang B, Zhan W, Liu Z G, et al. 2014. The identification of GNSS large space domain common-mode error based on multi-kernel function method. Journal of Geomatics Science and Technology (in Chinese), 31(2): 127-132.
Zabalza J, Ren J C, Wang Z, et al. 2014. Singular spectrum analysis for effective feature extraction in hyperspectral imaging. IEEE Geoscience and Remote Sensing Letters, 11(11): 1886-1890, doi: 10.1109/LGRS.2014.2312754.
郭金运,高文宗,于红娟等. 2018. 基于奇异谱分析的静态相对重力观测重力固体潮提取.地球物理学报,61(10):3889-3902, doi:10.6038/cjg2018L0460.
胡守超, 伍吉仓, 孙亚峰. 2009. 区域GPS网三种时空滤波方法的比较. 大地测量与地球动力学, 29(3): 95-99.
黄立人. 2006. GPS基准站坐标分量时间序列的噪声特性分析. 大地测量与地球动力学, 26(2): 31-33, 38.
黄立人, 符养. 2007. GPS连续观测站的噪声分析. 地震学报, 29(2): 197-202.
蒋志浩, 张鹏, 秘金钟等. 2010. 顾及有色噪声影响的CGCS2000下我国CORS站速度估计. 测绘学报, 39(4): 355-363.
马超, 李斐, 张胜凯等. 2016. 顾及共性误差的南极半岛地区连续GPS站坐标时间序列分析. 地球物理学报, 59(8): 2783-2795, doi: 10.6038/cjg20160806.
吴洪宝, 吴蕾. 2005. 气候变率诊断和预测方法. 北京: 气象出版社.
杨博, 占伟, 刘志广等. 2014. 多核函数法对GNSS大空间域共模误差的识别. 测绘科学技术学报, 31(2): 127-132.
Chen Q, van Dam T, Sneeuw N, et al. 2013. Singular spectrum analysis for modeling seasonal signals from GPS time series. Journal of Geodynamics, 72: 25-35, doi: 10.1016/j.jog.2013.05.005.
Dong D, Fang P, Bock Y, et al. 2006. Spatiotemporal filtering using principal component analysis and Karhunen-Loeve expansion approaches for regional GPS network analysis. Journal of Geophysical Research, 111(B3): B03405, doi: 10.1029/2005JB003806.
Freed A M, Bürgmann R, Calais E, et al. 2006. Implications of deformation following the 2002 Denali, Alaska, earthquake for postseismic relaxation processes and lithospheric rheology. Journal of Geophysical Research, 111(B1): B01401, doi: 10.1029/2005JB003894.
Guo J Y, Gao W Z, Yu H J, et al. 2018. Gravity tides extracted from relative gravimetric data with singular spectrum analysis. Chinese Journal of Geophysics (in Chinese), 61(10): 3889-3902, doi: 10.6038/cjg2018L0460.
Guo J Y, Yang L, Liu X, et al. 2012. On temporal-spatial distribution of backscatter coefficients over China determined by TOPEX/Poseidon mission. Science China Earth Sciences, 55(12): 2068-2083, doi: 10.1007/s11430-012-4524-y.
Guo J Y, Li W D, Chang X T, et al. 2018. Terrestrial water storage changes over Xinjiang extracted by combining Gaussian filter and multichannel singular spectrum analysis from GRACE. Geophysical Journal International, 213(1): 397-407, doi: 10.1093/gji/ggy006.
Hassani H. 2007. Singular spectrum analysis: Methodology and comparison. Journal of Data Science, 5(2): 239-257.
Hu S C, Wu J C, Sun Y F. 2009. Comparison among three spatiotemporal filtering methods for regional GPS networks analysis. Journal of Geodesy and Geodynamics (in Chinese), 29(3): 95-99.
Huang L R. 2006. Noise properties in time series of coordinate component at GPS fiducial stations. Journal of Geodesy and Geodynamics (in Chinese), 26(2): 31-33, 38.
Huang L R, Fu Y. 2007. Analysis on the noises from continuously monitoring GPS sites. Acta Seismologica Sinica (in Chinese), 29(2): 197-202.
Jiang Z H, Zhang P, Bi J Z, et al. 2010. Velocity estimation on the colored noise properties of CORS network in China based on the CGCS2000 Frame. Acta Geodaetica et Cartographica Sinica (in Chinese), 39(4): 355-363.
Kondrashov D, Ghil M. 2006. Spatio-temporal filling of missing points in geophysical data sets. Nonlinear Processes in Geophysics, 13(2): 151-159, doi: 10.5194/npg-13-151-2006.
Kondrashov D, Shprits Y, Ghil M. 2010. Gap filling of solar wind data by singular spectrum analysis. Geophysical Research Letters, 37(15): L15101, doi: 10.1029/2010GL044138.
Kondrashov D, Berloff P. 2015. Stochastic modeling of decadal variability in ocean gyres.Geophysical Research Letters, 42(5): 1543-1553, doi: 10.1002/2014GL062871.
Liu G, Li G, Tan K, et al. 2012. Improvement of instantaneous positioning by spatial stacking and modified sidereal filtering methods with application to the 2008 Ms8.0 Wenchuan earthquake. Geodesy and Geodynamics, 3(1): 13-18, doi: 10.3724/SP.J.1246.2012.00013.
Ma C, Li F, Zhang S K, et al. 2016. The coordinate time series analysis of continuous GPS stations in the Antarctic Peninsula with consideration of common mode error. Chinese Journal of Geophysics (in Chinese), 59(8): 2783-2795, doi: 10.6038/cjg20160806.
Márquez-Azúa B, DeMets C. 2003. Crustal velocity field of Mexico from continuous GPS measurements, 1993 to June 2001: Implications for the Neotectonics of Mexico. Journal of Geophysical Research, 108(B9): 2450, doi: 10.1029/2002JB002241.
Mazzotti S, Dragert H, Henton J, et al. 2003. Current tectonics of northern Cascadia from a decade of GPS measurements. Journal of Geophysical Research, 108(B12): 2554, doi: 10.1029/2003JB002653.
Meade B J, Hager B H. 2005. Block models of crustal motion in southern California constrained by GPS measurements. Journal of Geophysical Research, 110(B3): B03403, doi: 10.1029/2004JB003209.
Melbourne T I, Webb F H, Stock J M, et al. 2002. Rapid postseismic transients in subduction zones from continuous GPS.Journal of Geophysical Research, 107(B10): 2241, doi: 10.1029/2001JB000555.
Melbourne T I, Szeliga W M, Miller M M, et al. 2005. Extent and duration of the 2003 Cascadia slow earthquake. Geophysical Research Letters, 32(4): L04301, doi: 10.1029/2004GL021790.
Nikolaidis R. 2002. Observation of geodetic and seismic deformation with the Global Positioning System[Ph. D. thesis]. San Diego: University of California, 249.
Prawirodirdjo L, Bock Y. 2004. Instantaneous global plate motion model from 12 years of continuous GPS observations. Journal of Geophysical Research, 109(B8): B08405, doi: 10.1029/2003JB002944.
Santamaría-Gómez A, Gravelle M, Collilieux X, et al. 2012. Mitigating the effects of vertical land motion in tide gauge records using a state-of-the-art GPS velocity field. Global and Planetary Change, 98-99: 6-17, doi: 10.1016/j.gloplacha.2012.07.007.
Schoellhamer D H. 2001. Singular spectrum analysis for time series with missing data. Geophysical Research Letters, 28(16): 3187-3190, doi: 10.1029/2000GL012698.
Sella G F, Stein S, Dixon T H, et al. 2007. Observation of glacial isostatic adjustment in “stable” North America with GPS. Geophysical Research Letters, 34(2): L02306, doi: 10.1029/2006GL027081.
Shen Y, Guo J Y, Liu X, et al. 2017. One hybrid model combining singular spectrum analysis and LS+ARMA for polar motion prediction. Advances in Space Research, 59(2): 513-523, doi: 10.1016/j.asr.2016.10.023.
Shen Y, Guo J Y, Liu X, et al. 2018. Long-term prediction of polar motion using a combined SSA and ARMA model. Journal of Geodesy, 92(2): 333-343, doi: 10.1007/s00190-017-1065-3.
Shen Y Z, Li W W, Xu G C, et al. 2014. Spatiotemporal filtering of regional GNSS network′s position time series with missing data using principle component analysis. Journal of Geodesy, 88(1): 1-12, doi: 10.1007/s00190-013-0663-y.
Szeliga W, Melbourne T I, Miller M M, et al. 2004. Southern Cascadia episodic slow earthquakes. Geophysical Research Letters, 31(16): L16602. doi: 10.1029/2004GL020824.
Vautard R, Yiou P, Ghil M. 1992. Singular-spectrum analysis: A toolkit for short, noisy chaotic signals. Physica D: Nonlinear Phenomena, 58(1-4): 95-126, doi: 10.1016/0167-2789(92)90103-T.
Wdowinski S, Bock Y, Zhang J, et al. 1997. Southern California permanent GPS geodetic array: Spatial filtering of daily positions for estimating coseismic and postseismic displacements induced by the 1992 Landers earthquake. Journal of Geophysical Research, 102(B8): 18057-18070, doi: 10.1029/97JB01378.
Williams S D P. 2008. CATS: GPS coordinate time series analysis software. GPS Solutions, 12(2): 147-153, doi: 10.1007/s10291-007-0086-4.
Wu H B, Wu L. 2005. Methods for Diagnosing and Forecasting Climate Variability (in Chinese). Beijing: China Meteorological Press.
Wyatt M G, Kravtsov S, Tsonis A A. 2012. Atlantic multidecadal oscillation and northern hemisphere′s climate variability. Climate Dynamics, 38(5-6): 929-949, doi: 10.1007/s00382-011-1071-8.
Yang B, Zhan W, Liu Z G, et al. 2014. The identification of GNSS large space domain common-mode error based on multi-kernel function method. Journal of Geomatics Science and Technology (in Chinese), 31(2): 127-132.
Zabalza J, Ren J C, Wang Z, et al. 2014. Singular spectrum analysis for effective feature extraction in hyperspectral imaging. IEEE Geoscience and Remote Sensing Letters, 11(11): 1886-1890, doi: 10.1109/LGRS.2014.2312754.
郭金运,高文宗,于红娟等. 2018. 基于奇异谱分析的静态相对重力观测重力固体潮提取.地球物理学报,61(10):3889-3902, doi:10.6038/cjg2018L0460.
胡守超, 伍吉仓, 孙亚峰. 2009. 区域GPS网三种时空滤波方法的比较. 大地测量与地球动力学, 29(3): 95-99.
黄立人. 2006. GPS基准站坐标分量时间序列的噪声特性分析. 大地测量与地球动力学, 26(2): 31-33, 38.
黄立人, 符养. 2007. GPS连续观测站的噪声分析. 地震学报, 29(2): 197-202.
蒋志浩, 张鹏, 秘金钟等. 2010. 顾及有色噪声影响的CGCS2000下我国CORS站速度估计. 测绘学报, 39(4): 355-363.
马超, 李斐, 张胜凯等. 2016. 顾及共性误差的南极半岛地区连续GPS站坐标时间序列分析. 地球物理学报, 59(8): 2783-2795, doi: 10.6038/cjg20160806.
吴洪宝, 吴蕾. 2005. 气候变率诊断和预测方法. 北京: 气象出版社.
杨博, 占伟, 刘志广等. 2014. 多核函数法对GNSS大空间域共模误差的识别. 测绘科学技术学报, 31(2): 127-132.