一种改进的GPS区域叠加滤波算法
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摘要
GPS时间序列的空间滤波可以提高观测数据的信噪比,有利于获取更高精度的地壳形变信息。区域叠加滤波算法的空间滤波结果随着测站数和空间尺度不同而不同,不利于研究GPS时间序列中的形变信息。为了削弱区域叠加滤波受空间尺度的影响,提出一种不以空间尺度作为约束条件,同时引入相关系数和距离因子的区域叠加滤波算法。采用2010—2017年中国区域260个GPS连续观测站的时间序列展开空间滤波方法的研究,计算结果表明,对比相关性区域叠加滤波算法,考虑GPS时间序列之间的相关系数和距离因子更有利于提取GPS时间序列中的共模误差,且受空间尺度的影响较小。对比3种不同距离因子的区域叠加滤波算法,可知引入距离反比的空间滤波算法可实现更优的空间滤波。采用该方法空间滤波后可使GPS时间序列残差降低30%～40%,GPS速度场精度提高30%～40%。此算法实现了更优的GPS形变场估计,为研究中国区域的地壳运动和其动力学机制提供了可靠的数据基础。
GPS(Global Positioning System) time series spatial filtering can improve the signal-to-noise ratio of the observations, which is beneficial to obtain more accurate deformation information. The spatial filtering result by using stacking filtering method is not unique, as the number of stations and the spatial scale are different. This is not good to study the deformation information in GPS time series. In order to weaken the influence of spatial scale on spatial filtering method, an improved stacking filtering algorithm is proposed. This method introduces correlation coefficient factor and distance factor as the weights, and it does not constraint by spatial scale. This method is applicable for the regions with different GPS station distribution. We study the spatial filtering method for 260 GPS continuous observing stations in China, and the observation time series is from 2010 to 2017. The results show that:(1) Compared with the correlation weighted stacking filtering algorithm, the method is more effective to extract the common-mode errors from the GPS time series. The stacking filtering method are less constraint by the spatial scale, which take the correlation coefficients between GPS stations and distance factors as weighted.(2) Compared three kinds of stacking filtering methods with different distance factors as weighted, the method with the inverse distance factor obtained the better spatial filtering result.(3) The residuals of GPS time series can be reduced by 30%-40% and the precision of GPS velocity field increased by 30%-40% after spatial filtering by this method. This spatial filtering method can obtain better GPS deformation field estimation. And it also provides a reliable data foundation for studying the crustal movement and its dynamic mechanism in China.
GPS(Global Positioning System) time series spatial filtering can improve the signal-to-noise ratio of the observations, which is beneficial to obtain more accurate deformation information. The spatial filtering result by using stacking filtering method is not unique, as the number of stations and the spatial scale are different. This is not good to study the deformation information in GPS time series. In order to weaken the influence of spatial scale on spatial filtering method, an improved stacking filtering algorithm is proposed. This method introduces correlation coefficient factor and distance factor as the weights, and it does not constraint by spatial scale. This method is applicable for the regions with different GPS station distribution. We study the spatial filtering method for 260 GPS continuous observing stations in China, and the observation time series is from 2010 to 2017. The results show that:(1) Compared with the correlation weighted stacking filtering algorithm, the method is more effective to extract the common-mode errors from the GPS time series. The stacking filtering method are less constraint by the spatial scale, which take the correlation coefficients between GPS stations and distance factors as weighted.(2) Compared three kinds of stacking filtering methods with different distance factors as weighted, the method with the inverse distance factor obtained the better spatial filtering result.(3) The residuals of GPS time series can be reduced by 30%-40% and the precision of GPS velocity field increased by 30%-40% after spatial filtering by this method. This spatial filtering method can obtain better GPS deformation field estimation. And it also provides a reliable data foundation for studying the crustal movement and its dynamic mechanism in China.
引文
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[7] Tian Yunfeng,Shen Zhengkang. Extracting the Regional Common-Mode Component of GPS Station Position Time Series from Dense Continuous Network[J]. Journal of Geophysical Research:Solid Earth,2016,121(2):1 080-1 096
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[9] Bogusz J,Gruszczynski M,Figurski M,et al. SpatioTemporal Filtering for Determination of Common Mode Error in Regional GNSS Networks[J]. Open Geosciences,2015,7(1):140-148
[10] He Xiaoxing,Montillet J P,Fernandes R,et al. Review of Current GPS Methodologies for Producing Accurate Time Series and Their Error Sources[J].Journal of Geodynamics,2017,106(1):12-29
[11] Ma Chao,Li Fei,Zhang Shengkai,et al. The Coordinate Time Series Analysis of Continuous GPS Stations in the Antarctic Peninsula with Consideration of Common Mode Error[J]. Chinese Journal of Geophysics,2016,59(8):2 783-2 795(马超,李斐,张胜凯,等.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[J].地球物理学报,2016,59(8):2 783-2 795)
[12] Yin Haitao,Gan Weijun,Xiong Yongliang,et al.Study on the Effect of PCA Spatial Filtering on Highrate GPS Positioning[J]. Geomatics and Information Science of Wuhan University,2011,36(7):825-829(殷海涛,甘卫军,熊永良,等. PCA空间滤波在高频GPS定位中的应用研究[J].武汉大学学报·信息科学版,2011,36(7):825-829)
[13] Bos M S,Fernandes R M S,Williams S D P,et al.Fast Error Analysis of Continuous GPS Observations[J]. Journal of Geodesy,2008,82(3):157-166
[14] Klos A,Bogusz J,Figurski M,et al. Error Analysis for European IGS Stations[J]. Studia Geophysica et Geodaetica,2016,60(1):17-34
[15] Williams S D P,Bock Y,Fang P,et al. Error Analysis of Continuous GPS Position Time Series[J]. Journal of Geophysical Research:Solid Earth,2004,109(B):3 412-3 431
[16] Lyard F,Lefevre F,Letellier T,et al. Modelling the Global Ocean Tides:Modern Insights from FES2004[J]. Ocean Dynamics,2006,56(5-6):394-415
[17] Boehm J, Niell A, Tregoning P, et al. Global Mapping Function(GMF):A New Empirical Mapping Function Based on Numerical Weather Model Data[J]. Geophysical Research Letters,2006,33(4):7 304-7 307
[2] 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):3 405-3 421
[3] 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,2002,107(B4):2 156-2 202
[4] Nikolaidis R. Observation of Geodetic and Seismic Deformation with the Global Positioning System[D]. San Diego:University of California,2002
[5] Tian Yunfeng,Shen Zhengkang. Correlation Weighted Stacking Filtering of Common-Mode Component in GPS Observation Network[J]. Acta Seismologica Sinica,2011,33(2):198-208(田云锋,沈正康.GPS观测网络中共模分量的相关加权叠加滤波[J].地震学报,2011,33(2):198-208)
[6] Xie Shuming,Pan Pengfei,Zhou Xiaohui. Research on Common Mode Error Extraction Method for LargeScale GPS Network[J]. Geomatics and Information Science of Wuhan University,2014,39(10):1 168-1 173(谢树明,潘鹏飞,周晓慧.大空间尺度GPS网共模误差提取方法研究[J].武汉大学学报·信息科学版,2014,39(10):1 168-1 173)
[7] Tian Yunfeng,Shen Zhengkang. Extracting the Regional Common-Mode Component of GPS Station Position Time Series from Dense Continuous Network[J]. Journal of Geophysical Research:Solid Earth,2016,121(2):1 080-1 096
[8] Bogusz J,Klos A,Figurski M,et al. Investigation of Long-range Dependencies in the Stochastic Part of Daily GPS Solutions[J]. Survey Review,2016,48(347):140-147
[9] Bogusz J,Gruszczynski M,Figurski M,et al. SpatioTemporal Filtering for Determination of Common Mode Error in Regional GNSS Networks[J]. Open Geosciences,2015,7(1):140-148
[10] He Xiaoxing,Montillet J P,Fernandes R,et al. Review of Current GPS Methodologies for Producing Accurate Time Series and Their Error Sources[J].Journal of Geodynamics,2017,106(1):12-29
[11] Ma Chao,Li Fei,Zhang Shengkai,et al. The Coordinate Time Series Analysis of Continuous GPS Stations in the Antarctic Peninsula with Consideration of Common Mode Error[J]. Chinese Journal of Geophysics,2016,59(8):2 783-2 795(马超,李斐,张胜凯,等.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[J].地球物理学报,2016,59(8):2 783-2 795)
[12] Yin Haitao,Gan Weijun,Xiong Yongliang,et al.Study on the Effect of PCA Spatial Filtering on Highrate GPS Positioning[J]. Geomatics and Information Science of Wuhan University,2011,36(7):825-829(殷海涛,甘卫军,熊永良,等. PCA空间滤波在高频GPS定位中的应用研究[J].武汉大学学报·信息科学版,2011,36(7):825-829)
[13] Bos M S,Fernandes R M S,Williams S D P,et al.Fast Error Analysis of Continuous GPS Observations[J]. Journal of Geodesy,2008,82(3):157-166
[14] Klos A,Bogusz J,Figurski M,et al. Error Analysis for European IGS Stations[J]. Studia Geophysica et Geodaetica,2016,60(1):17-34
[15] Williams S D P,Bock Y,Fang P,et al. Error Analysis of Continuous GPS Position Time Series[J]. Journal of Geophysical Research:Solid Earth,2004,109(B):3 412-3 431
[16] Lyard F,Lefevre F,Letellier T,et al. Modelling the Global Ocean Tides:Modern Insights from FES2004[J]. Ocean Dynamics,2006,56(5-6):394-415
[17] Boehm J, Niell A, Tregoning P, et al. Global Mapping Function(GMF):A New Empirical Mapping Function Based on Numerical Weather Model Data[J]. Geophysical Research Letters,2006,33(4):7 304-7 307