时空Kalman滤波及其在地面沉降监测数据处理中的应用
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摘要
对地面沉降监测数据序列进行滤波与预测是地面沉降数据分析的重要内容,但传统方法是针对单个沉降点进行处理,无法进行区域整体分析,为此将时空Kalman滤波应用于GPS地面沉降数据处理,并根据GPS地面沉降监测数据特点,重点探讨了地面沉降时空Kalman滤波的空间场确定方法以及迭代滤波算法。模拟实验及天津CORS站沉降数据分析结果表明,时空Kalman滤波比单点Kalman滤波精度更高,且更稳健,同时由于其可以同时在时间域和空间域进行滤波与预测,因而实现了地面沉降数据的整体分析。
Filtering and predicting the land subsidence monitoring data series is an important content of land subsidence monitoring data analysis. But the traditional methods are mostly targeted at single settlement point, so an overall analysis of the section is unavailable. According to the characteristic of GPS land subsidence monitoring data, this paper mainly discusses the determination of the Kriging space fields of space-time Kalman filter and the iterative filtering algorithm. Simulation experiment and land subsidence monitoring data analysis of Tianjin CORS show that space-time Kalman filter are more accurate and robust than single-point Kalman Filter. Meanwhile, this method allows predictions in time as well as in space, so an overall analysis of land subsidence monitoring data is achieved.
Filtering and predicting the land subsidence monitoring data series is an important content of land subsidence monitoring data analysis. But the traditional methods are mostly targeted at single settlement point, so an overall analysis of the section is unavailable. According to the characteristic of GPS land subsidence monitoring data, this paper mainly discusses the determination of the Kriging space fields of space-time Kalman filter and the iterative filtering algorithm. Simulation experiment and land subsidence monitoring data analysis of Tianjin CORS show that space-time Kalman filter are more accurate and robust than single-point Kalman Filter. Meanwhile, this method allows predictions in time as well as in space, so an overall analysis of land subsidence monitoring data is achieved.
引文
[1] 张永红,龚文瑜,张继贤等.基于SAR干涉点目标分析技术的城市地表形变监测[J].测绘学报,2009,38(6):482～487,493.Zhang Yonghong,Gong Wenyu,Zhang Jixian et al.Monitoring urban subsidence based on SAR interferometric point target analysis [J].Acta Geodaetica et Cartographica Sinica,2009,38(6):482～487,493.(in Chinese)
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[12] Wikle.C.K,Cressie N.A dimension-reduced approach to space-time Kalman filtering[J].Biometrika,1999,4 (86):815～829.
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[14] Jorge Cort'es.Distributed Kriged Kalman filter for spatial estimation.IEEE transactions on automatic control.2009,12(54):2816～2827.
[15] Sujit K.Sahu & Kanti V.Mardia.A Bayesian Kriged Kalman model for short-term forecasting of air pollution levels[J].Appl.Statist,2005,1(54):223～244.
[16] Jona Lasinio G,Sahu S K,Mardia K V.Modeling rainfall data using a Bayesian Kriged-Kalman model[J].2007.
[17] Al-Awadhi F A,Alhajraf A.Prediction of non-methane hydrocarbons in Kuwait using regression and Bayesian Kriged Kalman model[J].Environmental and Ecological Statistics,2012,19(3):393～412.
[18] 戴吾蛟,伍锡锈.变形监测中 Kalman 滤波状态模型的比较分析[J].大地测量与地球动力学,2009,29(6):88～92.Dai Wujiao,Wu Xixiu.Comparative analysis of state models of Kalman filtering in deformation monitoring [J].Journal of Geodesy and Geodynamics,2009,29(6):88～92.(in Chinese)
[19] Bookstein F L.Principal warps:Thin-plate splines and the decomposition of deformations[J].Pattern Analysis and Machine Intelligence,IEEE Transactions on,1989,11(6):567～585.
[20] Shumway R H,Stoffer D S.An approach to time series smoothing and forecasting using the EM algorithm[J].Journal of time series analysis,1982,3(4):253～264.
[21] Watson M W,Engle R F.Alternative algorithms for the estimation of dynamic factor,mimic and varying coefficient regression models[J].Journal of Econometrics,1983,23(3):385～400.
[22] 黄声享,尹晖,蒋征.变形监测数据处理(第二版)[M].武汉:武汉大学出版社,2010.Huang Shengxiang,Yin Hui,Jiang Zheng.Deformation monitoring data processing (edition second)[M].Wuhan:Wuhan University Press,2010.(in Chinese)
[23] Cressie N.Statistics for spatial data[M].John Wiley & Sons,2015.
[24] Subba Rao T.Spatial statistics and spatio-temporal data[J].Journal of Time Series Analysis,2012.
[25] 李增科,高井祥,王坚等.地质统计学模型在变形序列分析中的应用[J].大地测量与地球动力学,2012,32(4):99～102.Li Zengke,Gao Jingxiang,Wang Jian et al.Application of geostatistics model in analysis of GPS deformation sequence [J].Journal of Geodesy and Geodynamics,2012,32(4):99～102.(in Chinese)
[26] Dai W,Liu N,Santerre R et al.Dam deformation monitoring data analysis using space-time Kalman filter[J].ISPRS International Journal of Geo-Information,2016,5(12):236.
[27] Liu N,Dai W,Santerre R et al.A MATLAB-based Kriged Kalman filter software for interpolating missing data in GNSS coordinate time series[J].GPS Solutions,2018,22(1):25.
[2] 郑铣鑫,武强,侯艳声等.关于城市地面沉降研究的几个前沿问题[J].地球学报,2002,23(3):279～282.Zheng Xianxin,Wu Qiang,Hou Yansheng et al.Some frontier problems on land subsidence research [J].Acta Geoscientica Sinica,2002,23(3):279～282.(in Chinese)
[3] Cankut D.Ince and Muhammed Sahin.Real-time deformation monitoring with GPS and Kalman Filter [J].Earth Planets Space,2000,52(10):837～840.
[4] 吴吉贤,杜海燕,张耀文.Kalman 滤波在沉降监测数据处理中的应用[J].高原地震,2010,(1):42～45.Wu Jixian,Du Haiyan,Zhang Yaowen.Application of discrete Kalman filtering to data processing of deformation observation [J].Plateau Earthquake Research,2010,(1):42～45.(in Chinese)
[5] L.Li and H.Kuhlmann.Real-time deformation measurements using time series of GPS coordinates processed by Kalman filter with shaping filter [J].Survey Review,2012,44(326):189～197.
[6] 伍锡锈,戴吾蛟,罗飞雪.抗差自适应 Kalman 滤波在动态变形监测中的应用研究[J].防灾减灾工程学报,2011,31(1):102～106.Wu Xixiu,Dai Wujiao,Luo Feixue.Research on adaptively robust Kalman filtering for dynamic deformation monitoring applications [J].Journal of Disaster Prevention and Mitigation Engineering,2011,31(1):102～106.(in Chinese)
[7] 王佳璆,邓敏,程涛等.时空序列数据分析和建模[M].北京:科学出版社,2012.Wang Jiaqiu,Deng Min,Cheng Tao et al.Spatio-temporal data analysis and modeling [M].Beijing:Science Press,2012.(in Chinese)
[8] Cressie N.Comment on‘An approach to statistical spatial-temporal modeling of meteorological fields’ by M.S.Handcock and J.R.Wallis[J].Journal of the American Statistical Association,1994,(89):379～382.
[9] Goodall C,Mardia K V.Challenges in multivariate spatio-temporal modeling[C].Proceedings of the XVIIth International Biometric Conference,1994:1～17.
[10] Huang H-C,Cressie N.Spatial-temporal prediction of snow water equivalent using the Kalman filter[J].Computational Statistics & Data Analysis,1996,(22):159～175.
[11] Mardia K V,Goodall C,Redfern E J et al.The Kriged Kalman filter [J].Test,1998,7(2):217～285.
[12] Wikle.C.K,Cressie N.A dimension-reduced approach to space-time Kalman filtering[J].Biometrika,1999,4 (86):815～829.
[13] Noel Cressie & Christopher K.Wikle.Space-time Kalman filter.Encyclopedia of Environmetrics[J].2002,4:2045～2049.
[14] Jorge Cort'es.Distributed Kriged Kalman filter for spatial estimation.IEEE transactions on automatic control.2009,12(54):2816～2827.
[15] Sujit K.Sahu & Kanti V.Mardia.A Bayesian Kriged Kalman model for short-term forecasting of air pollution levels[J].Appl.Statist,2005,1(54):223～244.
[16] Jona Lasinio G,Sahu S K,Mardia K V.Modeling rainfall data using a Bayesian Kriged-Kalman model[J].2007.
[17] Al-Awadhi F A,Alhajraf A.Prediction of non-methane hydrocarbons in Kuwait using regression and Bayesian Kriged Kalman model[J].Environmental and Ecological Statistics,2012,19(3):393～412.
[18] 戴吾蛟,伍锡锈.变形监测中 Kalman 滤波状态模型的比较分析[J].大地测量与地球动力学,2009,29(6):88～92.Dai Wujiao,Wu Xixiu.Comparative analysis of state models of Kalman filtering in deformation monitoring [J].Journal of Geodesy and Geodynamics,2009,29(6):88～92.(in Chinese)
[19] Bookstein F L.Principal warps:Thin-plate splines and the decomposition of deformations[J].Pattern Analysis and Machine Intelligence,IEEE Transactions on,1989,11(6):567～585.
[20] Shumway R H,Stoffer D S.An approach to time series smoothing and forecasting using the EM algorithm[J].Journal of time series analysis,1982,3(4):253～264.
[21] Watson M W,Engle R F.Alternative algorithms for the estimation of dynamic factor,mimic and varying coefficient regression models[J].Journal of Econometrics,1983,23(3):385～400.
[22] 黄声享,尹晖,蒋征.变形监测数据处理(第二版)[M].武汉:武汉大学出版社,2010.Huang Shengxiang,Yin Hui,Jiang Zheng.Deformation monitoring data processing (edition second)[M].Wuhan:Wuhan University Press,2010.(in Chinese)
[23] Cressie N.Statistics for spatial data[M].John Wiley & Sons,2015.
[24] Subba Rao T.Spatial statistics and spatio-temporal data[J].Journal of Time Series Analysis,2012.
[25] 李增科,高井祥,王坚等.地质统计学模型在变形序列分析中的应用[J].大地测量与地球动力学,2012,32(4):99～102.Li Zengke,Gao Jingxiang,Wang Jian et al.Application of geostatistics model in analysis of GPS deformation sequence [J].Journal of Geodesy and Geodynamics,2012,32(4):99～102.(in Chinese)
[26] Dai W,Liu N,Santerre R et al.Dam deformation monitoring data analysis using space-time Kalman filter[J].ISPRS International Journal of Geo-Information,2016,5(12):236.
[27] Liu N,Dai W,Santerre R et al.A MATLAB-based Kriged Kalman filter software for interpolating missing data in GNSS coordinate time series[J].GPS Solutions,2018,22(1):25.