时空Kalman滤波在变形分析中的应用研究

doi:10.11947/j.AGCS.2022.20220292

测绘学报 ›› 2022, Vol. 51 ›› Issue (10): 2125-2138.doi: 10.11947/j.AGCS.2022.20220292

时空Kalman滤波在变形分析中的应用研究

石强^1,2,3, 戴吾蛟^1,3, 晏慧能^1,3, 刘宁¹

1. 中南大学测绘与遥感科学系,湖南长沙 410083;
2. 江苏海洋大学海洋技术与测绘学院,江苏连云港 222005;
3. 湖南省精密工程测量与形变灾害监测重点实验室,湖南长沙 410083

收稿日期:2022-05-05 修回日期:2022-08-21 发布日期:2022-11-05
通讯作者: 戴吾蛟 E-mail:wjdai@csu.edu.cn
作者简介:石强(1992—),男,博士生,讲师,研究方向为变形监测与分析。E-mail:qiangshi@jou.edu.cn
基金资助:
国家自然科学基金(42174053);湖南省自然科学基金(2021JJ30805)

Research on application of spatio-temporal Kalman filter in deformation analysis

SHI Qiang^1,2,3, DAI Wujiao^1,3, YAN Huineng^1,3, LIU Ning¹

1. Department of Surveying Engineering & Geo-Informatics, Central South University, Changsha 410083, China;
2. School of Marine Technology and Geomatics, Jiangsu Ocean University, Lianyungang 222005, China;
3. Key Laboratory of Precise Engineering Surveying & Deformation Disaster Monitoring of Hunan Province, Changsha 410083, China

Received:2022-05-05 Revised:2022-08-21 Published:2022-11-05
Supported by:
The National Natural Science Foundation of China (Nos. 42174053); The Hunan Natural Science Foundation (No. 2021JJ30805)

摘要/Abstract

摘要： 时空Kalman滤波可对变形监测数据进行时空滤波去噪、数据插补和变形预测,本文利用时空Kalman滤波进行变形分析,从模型原理及试验两方面比较分析了Kriged Kalman filter(KKF)、space time Kalman filter(STKF)和spatio-temporal mixed effects(STME) 3种典型时空Kalman滤波模型的性能和适用性。结果表明:3种时空Kalman滤波模型均基于空间基函数及动力学模型组合形式描述时空数据的时空相关性,其主要差异在于空间变异的描述形式不同、空间基函数和状态转移矩阵构造过程不同及模型降维方法不同。在适用性方面,KKF模型更适合于稀疏测站的变形分析,STKF模型及STME模型更适合于海量测站的变形分析。在变形分析应用效果方面,3种时空Kalman滤波模型均具有较高精度的时空滤波去噪、数据插补和变形预测性能,其滤波结果相对于普通Kalman滤波结果的平均改善率为21.1%,其缺失数据插补结果相对于Hermite时间插值结果的平均改善率为42.4%,其空间预测结果相对于Kriging空间插值结果的平均改善率为65.3%,其对已知测站未来变形的时空预测结果相对于普通Kalman滤波时间预测结果的平均改善率为20.6%,其对非观测站点未来变形的时空预测结果相对于Kalman滤波+Kriging组合模型预测结果的平均改善率为20.5%。

关键词: 变形分析, 滤波去噪, 数据插补, 变形预测, 时空Kalman滤波

Abstract: Spatio-temporal Kalman filter can be used for spatio-temporal data denoising, interpolation and deformation prediction. In order to use the spatio-temporal Kalman filter model for spatio-temporal deformation analysis, the performance and applicability of three typical spatio-temporal Kalman filter models, namely Kriged Kalman filter (KKF), space time Kalman filter (STKF) and spatio-temporal mixed effects (STME), are compared and analyzed from the aspects of principles and experiments. The results show that: in theory, the three spatio-temporal Kalman filter models are based on the combination of spatial basis function and dynamic model to describe the spatio-temporal correlation. The main difference lies in the expression of spatial data, such as trend term, fine-scale variation, observation noise and spatial basis function. In terms of applicability, the KKF model is more suitable for the spatio-temporal deformation analysis of sparse stations, while the STKF model and STME model are more suitable for the spatio-temporal deformation analysis of massive stations. In terms of application effects of spatio-temporal deformation analysis, the three spatio-temporal Kalman filter models have high-precision effect in denoising, data interpolation and deformation prediction performance. The average improvement rate of denoising results compared with ordinary Kalman model is 21.1%, the average improvement rate of interpolation results compared with Hermite time interpolation results is 42.4%, the average improvement rate of its spatio-temporal prediction results relative to Kriging spatial interpolation results is 65.3%, the average improvement rate of its spatio-temporal prediction results for observation stations relative to the time prediction results of ordinary Kalman filter is 20.6%, and the average improvement rate of its spatio-temporal prediction results for non-observation stations relative to the prediction results of Kalman filter+Kriging model is 20.5%.

Key words: deformation analysis, filtering denoising, data interpolation, deformation prediction, spatio-temporal Kalman filter

中图分类号:

P227

石强, 戴吾蛟, 晏慧能, 刘宁. 时空Kalman滤波在变形分析中的应用研究[J]. 测绘学报, 2022, 51(10): 2125-2138.

SHI Qiang, DAI Wujiao, YAN Huineng, LIU Ning. Research on application of spatio-temporal Kalman filter in deformation analysis[J]. Acta Geodaetica et Cartographica Sinica, 2022, 51(10): 2125-2138.

参考文献

[1] 张勤, 黄观文, 杨成生. 地质灾害监测预警中的精密空间对地观测技术[J]. 测绘学报, 2017, 46(10): 1300-1307. DOI: 10.11947/j.AGCS.2017.20170453. ZHANG Qin, HUANG Guanwen, YANG Chengsheng. Precision space observation technique for geological hazard monitoring and early warning[J]. Acta Geodaetica et Cartographica Sinica, 2017, 46(10): 1300-1307. DOI: 10.11947/j.AGCS.2017.20170453.
[2] 许强, 朱星, 李为乐, 等. “天-空-地”协同滑坡监测技术进展[J]. 测绘学报,2022,51(7):1416-1436. DOI: 10.11947/j.AGCS.2022.20220320. XU Qiang, ZHU Xing, LI Weile, et al. Technical progress of space-air-ground collaborative monitoring of landslide[J]. Acta Geodaetica et Cartographica Sinica, 2022, 51(7): 1416-1436. DOI: 10.11947/j.AGCS.2022.20220320.
[3] ZHOU Lü, ZHAO Yizhan, ZHU Zilin, et al. Spatial and temporal evolution of surface subsidence in Tianjin from 2015 to 2020 based on SBAS-InSAR technology[J]. Journal of Geodesy and Geoinformation Science, 2022, 5(1): 60-72. DOI: 10.11947/j.JGGS.2022.0107.
[4] 尹晖. 时空变形分析与预报的理论和方法[M]. 北京: 测绘出版社, 2002. YIN Hui. Theory and method of spatio-temporal deformation analysis and prediction[M]. Beijing: Surveying and Mapping Press, 2002.
[5] 王建民, 张锦, 邓增兵, 等. 时空Kriging插值在边坡变形监测中的应用[J]. 煤炭学报, 2014, 39(5): 874-879. WANG Jianmin, ZHANG Jin, DENG Zengbing, et al. Slope deformation analyses with space-time Kriging interpolation method[J]. Journal of China Coal Society, 2014, 39(5): 874-879.
[6] 王建民. 矿山边坡变形监测数据的高斯过程智能分析与预测[D]. 太原: 太原理工大学, 2016. WANG Jianmin. Intelligent analysis and prediction of mine slope deformation monitoring data based on Gaussian process[D]. Taiyuan:Taiyuan University of Technology, 2016.
[7] 张可能, 胡达, 何杰, 等. 基于Kriging时空统一模型的隧道动态施工位移预测[J]. 中南大学学报(自然科学版), 2017, 48(12): 3328-3334. ZHANG Keneng, HU Da, HE Jie, et al. Tunnel construction of dynamic displacement prediction based on unified space-time Kriging model[J]. Journal of Central South University (Science and Technology), 2017, 48(12): 3328-3334.
[8] 李广春, 戴吾蛟, 杨国祥, 等. 时空自回归模型在大坝变形分析中的应用[J]. 武汉大学学报(信息科学版), 2015, 40(7): 877-881. LI Guangchun, DAI Wujiao, YANG Guoxiang, et al. Application of space-time auto-regressive model in dam deformation analysis[J]. Geomatics and Information Science of Wuhan University, 2015, 40(7): 877-881.
[9] 杨志佳, 戴吾蛟, 陈必焰, 等. 克里金时空自回归模型在变形建模中的应用[J]. 测绘科学, 2019, 44(7): 40-45. YANG Zhijia, DAI Wujiao, CHEN Biyan, et al. The application of Kriging's space-time auto-regressive model in deformation modeling[J]. Science of Surveying and Mapping, 2019, 44(7): 40-45.
[10] 孙志鹏, 郭玉平. 基于时空自回归模型的大型桥梁变形监测分析与预报[J]. 全球定位系统, 2015, 40(6): 83-85. SUN Zhipeng, GUO Yuping. Large-scale bridge deformation monitoring analysis and forecasting based on space-time auto-regressive model[J]. GNSS World of China, 2015, 40(6): 83-85.
[11] 柳新强, 王涛. 时空序列模型在地下管线沉降监测中的应用[J]. 北京测绘, 2018, 32(7): 809-813. LIU Xinqiang, WANG Tao. Application of space-time series model in subsidence monitoring of underground pipeline[J]. Beijing Surveying and Mapping, 2018, 32(7): 809-813.
[12] 柳新强, 王涛, 胡泊. 时空序列模型在沉降监测中的应用[J]. 测绘与空间地理信息, 2019, 42(2): 86-89, 93. LIU Xinqiang, WANG Tao, HU Bo. Application of space-time series model in subsidence monitoring[J]. Geomatics & Spatial Information Technology, 2019, 42(2): 86-89, 93.
[13] YANG Zhijia, DAI Wujiao, SANTERRE R, et al. A spatiotemporal deformation modelling method based on geographically and temporally weighted regression[J]. Mathematical Problems in Engineering, 2019: 4352396.
[14] YANG Zhijia, DAI Wujiao, YU Wenkun, et al. Mixed geographically and temporally weighted regression for spatio-temporal deformation modelling[J]. Survey Review, 2022, 54(385): 290-300. DOI: 10.1080/00396265.2021.1935578.
[15] ZHUANG Lili, CRESSIE N. Bayesian hierarchical statistical SIRS models[J]. Statistical Methods & Applications, 2014, 23(4): 601-646.
[16] NGUYEN H, KATZFUSS M, CRESSIE N, et al. Spatio-temporal data fusion for very large remote sensing datasets[J]. Technometrics, 2014, 56(2): 174-185.
[17] ZAMMIT-MANGION A, CRESSIE N, GANESAN A L, et al. Spatio-temporal bivariate statistical models for atmospheric trace-gas inversion[J]. Chemometrics and Intelligent Laboratory Systems, 2015, 149: 227-241.
[18] ZHANG Bohai, CRESSIE N. Bayesian inference of spatio-temporal changes of Arctic sea ice[J]. Bayesian Analysis, 2020, 15(2): 605-631.
[19] HUANG H C, CRESSIE N. Spatio-temporal prediction of snow water equivalent using the Kalman filter[J]. Computational Statistics & Data Analysis, 1996, 22(2): 159-175.
[20] MARDIA K V, GOODALL C, REDFERN E J, et al. The Kriged Kalman filter[J]. Test, 1998, 7(2): 217-282.
[21] WIKLE C K, CRESSIE N. A dimension-reduced approach to space-time Kalman filtering[J]. Biometrika, 1999, 86(4): 815-829.
[22] CRESSIE N, SHI Tao, KANG E L. Fixed rank filtering for spatio-temporal data[J]. Journal of Computational and Graphical Statistics, 2010, 19(3): 724-745.
[23] KANG E L, CRESSIE N, SHI Tao. Using temporal variability to improve spatial mapping with application to satellite data[J]. Canadian Journal of Statistics, 2010, 38(2): 271-289.
[24] LIU Ning, DAI Wujiao, 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.
[25] LIU Ning, DAI Wujiao, SANTERRE R, et al. High spatio-temporal resolution deformation time series with the fusion of InSAR and GNSS data using spatio-temporal random effect model[J]. IEEE Transactions on Geoscience and Remote Sensing, 2019, 57(1): 364-380.
[26] DAI Wujiao, LIU Ning, 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] 刘宁, 戴吾蛟, 刘斌. 一种抗差的形变数据插补方法[J]. 测绘科学, 2017, 42(9): 126-131, 190. LIU Ning, DAI Wujiao, LIU Bin. A interpolation method of deformation monitoring data series[J]. Science of Surveying and Mapping, 2017, 42(9): 126-131, 190.
[28] CRESSIE N A, WIKLE C. Strategies for dynamic space-time statistical modeling: discussion of “the Kriged Kalman filter” by Mardia et al[J]. Test, 1998, 7(2): 257-264.

时空Kalman滤波在变形分析中的应用研究

Research on application of spatio-temporal Kalman filter in deformation analysis

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