GPS动态变形监测数据的多尺度分析
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摘要
GPS不仅具有自动化程度高、能够全天候观测、无需通视等优点,而且它还能获得大型工程结构物在风、温度等外力荷载作用下的高频振动位移和低频(似静态)的整体惯性偏移,因此GPS技术已成为工程结构健康监测一项重要手段。但GPS监测数据中不仅包含各种外力因素引起的变形,还含有多路径效应、残余对流层延迟等系统性误差影响。为此,本文利用小波分析及经验模式分解两种方法对GPS动态变形监测数据进行多尺度分析,以实现数据的滤波去噪、多路径效应等系统误差及变形特征提取等功能。具体内容有:
1.GPS动态变形监测的数据特征分析:GPS动态变形监测数据中含有非线性、非平稳、复杂周期性变形信息以及噪声和系统误差等。
2.小波多尺度和经验模式分解的基本理论:论述连续小波、离散小波变换、希尔伯特-黄变换中本征模态函数和经验模式分解的基本方法以及多尺度分析理论。
3.基于小波分析的GPS动态变形监测多尺度分析方法,包括:预处理、时频域处理,并利用小波多尺度分析的方法实现振动数据的去噪、滤波和振动变形特征提取。
4.基于经验模式分解的GPS动态变形监测多尺度分析方法的探讨。对模拟算例和实验数据加以分析,讨论基于经验模式分解的多尺度变形分析方法,并与小波多尺度分析方法进行了比较。
5.建立基于小波和经验模式分解的组合多尺度变形分析方法。该方法克服了直接运用经验模式分解方法由大量噪声带来的不必要的干扰,减少了经营模式分解存在的边界效应和分解层数,提高了变形特征提取的准确性和时效性。
Compared with traditional instruments, GPS has many advantages such as no weather condition and line-of-sight limited. The most important advantage is that GPS can measure both the high frequency and quasi-static displacement of large engineering structure under abnormal loading conditions such as during wind and temperature etc. So GPS has been increasingly used in structure health monitoring. However the GPS measurements include not only the real displacements of the structures, but also the quasi-system errors such as multipath and residual tropospheric delay. In order to filter the noise, mitigate the quasi-system errors and analyze the displacements, two multi-scale analysis methods, i.e. wavelet analysis and empirical mode decomposition are used in using GPS dynamic defomation monitoring. Following are the main contents of the thesis:
1. Data characters analyse of dynamic deformation monitoring using GPS. It includes non-linearity, non-stationary, complex periodicity deformation, noises, system error and et al.
2. The basic theories of muti-scale analysis, wavelet transform and empirical mode decomposition. The continue wavelet transform, discrete wavelet transform and empirical mode decomposition were discussed first. Then the basic theories of muti-scale analysis were discussed in detail.
3. The multi-scale analysis method based on wavelet and its application in dynamic deformation monitoring. It includes denoising, data analysis in time-frequency domain, and extracting the properties of the dynamic deformations.
4. The multi-scale analysis method based on empirical mode decomposition and its application in dynamic deformation monitoring. Simulated experiments and real GPS data were analyzed using empirical mode decomposition. The corresponding results were compared with the ones from wavelet method .
5. A new multi-analysis method based on the combination of wavelet and empirical mode decomposition was developed. This method can overcome the disturb of noise using empirical mode decomposition, reduce the boundary effect and decomposition number, and improve the accuracy of the extracted properties of deformation.
1.GPS动态变形监测的数据特征分析:GPS动态变形监测数据中含有非线性、非平稳、复杂周期性变形信息以及噪声和系统误差等。
2.小波多尺度和经验模式分解的基本理论:论述连续小波、离散小波变换、希尔伯特-黄变换中本征模态函数和经验模式分解的基本方法以及多尺度分析理论。
3.基于小波分析的GPS动态变形监测多尺度分析方法,包括:预处理、时频域处理,并利用小波多尺度分析的方法实现振动数据的去噪、滤波和振动变形特征提取。
4.基于经验模式分解的GPS动态变形监测多尺度分析方法的探讨。对模拟算例和实验数据加以分析,讨论基于经验模式分解的多尺度变形分析方法,并与小波多尺度分析方法进行了比较。
5.建立基于小波和经验模式分解的组合多尺度变形分析方法。该方法克服了直接运用经验模式分解方法由大量噪声带来的不必要的干扰,减少了经营模式分解存在的边界效应和分解层数,提高了变形特征提取的准确性和时效性。
Compared with traditional instruments, GPS has many advantages such as no weather condition and line-of-sight limited. The most important advantage is that GPS can measure both the high frequency and quasi-static displacement of large engineering structure under abnormal loading conditions such as during wind and temperature etc. So GPS has been increasingly used in structure health monitoring. However the GPS measurements include not only the real displacements of the structures, but also the quasi-system errors such as multipath and residual tropospheric delay. In order to filter the noise, mitigate the quasi-system errors and analyze the displacements, two multi-scale analysis methods, i.e. wavelet analysis and empirical mode decomposition are used in using GPS dynamic defomation monitoring. Following are the main contents of the thesis:
1. Data characters analyse of dynamic deformation monitoring using GPS. It includes non-linearity, non-stationary, complex periodicity deformation, noises, system error and et al.
2. The basic theories of muti-scale analysis, wavelet transform and empirical mode decomposition. The continue wavelet transform, discrete wavelet transform and empirical mode decomposition were discussed first. Then the basic theories of muti-scale analysis were discussed in detail.
3. The multi-scale analysis method based on wavelet and its application in dynamic deformation monitoring. It includes denoising, data analysis in time-frequency domain, and extracting the properties of the dynamic deformations.
4. The multi-scale analysis method based on empirical mode decomposition and its application in dynamic deformation monitoring. Simulated experiments and real GPS data were analyzed using empirical mode decomposition. The corresponding results were compared with the ones from wavelet method .
5. A new multi-analysis method based on the combination of wavelet and empirical mode decomposition was developed. This method can overcome the disturb of noise using empirical mode decomposition, reduce the boundary effect and decomposition number, and improve the accuracy of the extracted properties of deformation.
引文
[1]贡建兵.隔河岩大坝外部变形GPS自动化监测系统概况[J].湖北水力发电,2003,(1):55-57
[2]陈永奇.变形观测数据处理[M].北京:测绘出版社,1988
[3]徐良,江见鲸,过静珺.广州虎门悬索桥的模态分析[J].土木工程学报,2002,35(1):25-27
[4]Lovse,J.,W.F.Teskey,G.Lachapelle & M.E.Cannon.Dynamic deformation monitoring of tall structures using GPS technology[J].Journal of Surveying Engineering,1995,121(1),35-40
[5]李征航,黄劲松.GPS测量与数据处理[M].武汉:武汉大学出版社,2005
[6]Celebi,M.and A.Sanli.GPS in Pioneering Dynamic Monitoring of Long-Period Structures[J],Earthquake Spectra,2002,18(i):47-61
[7]过静瑶,戴连君,卢云川.虎门大桥GPS(RTK)实时位移监测方法研究[J].测绘通报,2000,12:4-12
[8]罗志才,陈永奇,刘焱雄.GPS用于监测高层建筑物动态特征的模拟研究[J].武汉测绘科技大学学报,2000(25):100-104
[9]黄丁发,陈永奇,丁晓利,朱建军,杨喜中,刘国祥.GPS高层建筑物常荷载振动测试的小波分析[J].振动与冲击,2001,20(1):12-15
[10]Chan W.S.,Xu Y.L.,Ding X.L.,Xiong Y.L.,Dai W.J.Dynamic displacement measurement accuracy of GPS for monitoring large civil engineering structures[A],Proceedings of SPIE[C],No.5765,2005:54-65
[11]Chan W.S.,Xu Y.L.,Ding X.L.,Dai W.J.Calibration of GPS for Dynamic Displacement Measurement of Long Span Cable-Supported Bridges in Vertical Direction[A],Proceedings of SPIE[C],No.5770,2005:168-179
[12]戴吾蛟.GPS精密动态变形监测的数据处理方法研究[D].长沙:中南大学,2007
[13]徐绍铨,李征航,刘经南等.隔河岩大坝外观变形GPS自动化监测系统的可靠性分析[J].全球定位系统,2000,25(1):25-28
[14]徐绍铨.隔河岩大坝GPS自动化监测系统[J].铁路航测,2001,(4):42-44
[15]夏禾,徐幼麟,阎全胜.大跨度悬索桥在风与列车荷载同时作用下的动力响应分析[J].铁道学报,2002,24(4):83-91
[16]过静珺,戴连君,卢云川.虎门大桥GPS(RTK)实时位移监测方法研究[J].测绘通报,2000(12):4-5转12
[17]黄声享,刘经南,柳响林.小波分析在高层建筑动态监测中的应用[J].测绘学报,2003,32(2):153-157
[18]钱稼如,过静瑁,陈志鹏.地王大厦动力特性及大风时楼顶位移和加速度实测研究[J].土木工程学报,1998,31(6):30-39
[19]过静珺,商瑞斌,葛胜杰,谢宝童,白涛.利用GPS监测高大建筑物动态位移法研究[J].工程勘察,1997,3:48-51
[20]Michael Kochly,Tracy Kijewski-Correa,James Stowell.GPS monitoring in urban zones:calibration and quantification of multipath effects[A].SPIE[C],2005
[21]Robert S.Radovanovic,High Accuracy Deformation Monitoring Via Multipath Mitigation by Day-To-Day Correlation Analysis[A].ION GPS 2000[C],19-22 September 2000,Salt Lake City,UT:35-44
[22]Roberts Gethin Wyn,Meng Xiaolin,and Dodson Alan Henry,Integrating a Global Positioning System and Accelerometers to Monitor the Deflection of Bridges[J].Journal of Surveying Engineering,2004,130(2):65-72
[23]Shun-ichi Nakamura.GPS MEASUREMENT OF WIND-INDUCED SUSPENSION BRIDGE GIRDER DISPLACEMENTS[J].JOURNAL OF STRUCTURAL ENGINEERING,2000,126(12):1413-1419
[24]Satoshi Kashima,Yukikazu Yanaka,Shuichi Suzuki et al.Monitoring the Akashi Kaikyo Bridge:First Experiences[J].Structural Engineering International,2001(2):120-123
[25]Chen Yongqi,Huang Dingfa,Ding Xiaoli.Measurement of vibration of tall building with GPS:a case study[A].Proceedings of SPIE[C].No.4337,2001:477-483
[26]熊永良,丁晓利,黄丁发,戴吾蛟,陈慧珊.基于小波变换的单历元算 法及其在结构振动监测中的应用研究[J].测绘学报,2005,34(3):202-207
[27]葛茂荣,过静君,葛胜杰.GPS工程结构监测系统的建立及应用[J].解放军测绘学院学报,1999,16(2):79-82
[28]徐绍铨,隔河岩大坝GPS自动化监测系统[J].铁路航测,2001,第4期:42-44
[29]黄声享.变形数据分析方法研究及其在精密工程GPS自动监测系统中的应用[D].武汉:武汉大学,2001
[30]文鸿雁.基于小波理论的变形分析模型研究[D].武汉:武汉大学,2004
[31]朱建军,贺跃光,曾卓乔.变形观测的理论与方法[M].长沙:中南大学出版社,2004
[32]陈永奇,吴子安,吴中如.变形监测分析与预报[M].北京:测绘出版社,1998
[33]杨位钦,顾岚.时间序列分析与动态数据建模[M].北京:北京工业学院出版社,1986
[34]王文圣,丁晶,李跃清.水文小波分析[M].北京:化学工业出版社,2005
[35]向东.强噪声背景下弱信号特征提取的小波分析[D].武汉:武汉大学,2003
[36]郭亚.振动信号处理中的小波基选择研究[D].合肥:合肥工业大学,2003
[37]飞思科技产品研发中心.小波分析理论与MATLAB7实现[M].北京:电子工业出版社,2005
[38]熊永良,黄丁发,张献洲.一种可靠的含约束的GPS变形监测单历元求解算法[J].武汉大学学报·信息科学版,2001,26(1):51-57
[39]戴吾蛟,丁晓利,朱建军.GPS振动变形监测中单一衍射或反射信号误差处理研究[J].工程勘察,2006(5):49-54
[40]戴吾蛟,丁晓利,朱建军,陈永奇,李志伟.基于经验模式分解的滤波去噪法及其在GPS多路径效应中的应用[J].测绘学报,2006,35(4):321-327
[41]黄丁发,丁晓利,陈永奇,龚涛,熊永良.GPS多路径效应影响与结构振动的小波滤波筛分研究[J].测绘学报,2001,30(1):36-41
[42]HUANG N.E.,SHEN Z.,and LONG S.R..The Emprical Mode Decomposition and Hilbert Spectrum for Nonlinear and Non-stationary Time series Analysis[J].Proceedings of the Royal Society of London SERIESA,1998,454:903-995
[43]HUANG N.E.,SHEN Z.,and LONG S.R..A new view of nonlinear water waves:The Hilbert spectrum[J].Ainu.8ev.Fluid Mech.,1999,31:417-457
[44]HUANG N.E.,Wu M.L.,Long S.R.,Shen S.P.,Qu W.D.A confidence limit for the empirical mode decomposition and Hilbert spectral analysis[J].The Royal Society,2003,459:2317-2345
[45]谭善文.多分辨率希尔伯特-黄(Hiibert-Huang)变换方法的研究[D].重庆:重庆大学,2001
[46]石春香.HHT变换及其在结构分析中的应用[D].上海:同济大学,2003
[47]程军圣.基于Hilbert-Huang变换的旋转机械故障诊断方法研究[D].长沙:湖南大学,2005
[48]禹丹江.土木工程结构模态参数识别—理论、实现与应用[D].福建:福州大学,2005
[49]刘大杰,施一民.全球定位系统的原理与数据处理[M].上海:同济大学出版社,1996
[50]魏子卿,葛茂荣.GPS相对定位的数学模型[M].北京:测绘出版社,1998
[51]郑作亚.GPS数据预处理和星载GPS运动学定轨研究及其软件实现[D].上海:中国科学院上海天文台,2005
[52]柴立合.多尺度科学的研究进展[J].化学进展,2005,17(2):186-191
[53]文成林,周东华.多尺度估计理论及其应用[M].北京:清华大学出版社,2002
[54]郑作亚,柳林涛,黄珹等.小波分析在我国地球物理测量中的应用[J].山东科技大学学报(自然科学版),2003,22(4):28-32
[55]崔锦泰.小波分析导论[M].西安:西安交通大学出版社,1997
[56]徐晨,赵瑞珍,甘小冰.小波分析应用算法[M].北京:科学出版社,2004
[57]张郁山.希尔伯特-黄变换(HHT)与地震动时程的希尔伯特谱方法与应用研究[D].北京:中国地震局地球物理研究所,2003
[58]张立振.快速滤波本征模态信号分解及其在海洋数据分析中的应用[D].青岛:中国海洋大学,2006
[59]Chan W.S.,Xu Y.L.,M.ASCE,Ding X.L.,Xiong Y.L.,Dai W.J.Assessment of Dynamic Measurement Accuracy of GPS in Three Directions[J].JOUNAL of SURVEYING ENGINEERING,2006,AUGUST:108-117
[60]王济,胡晓.MATLAB在振动信号处理中的应用[M].北京:中国水利水电出版社,知识产权出版社,2006
[61]Ogaja Clement,Rizos Chris,Wang Jinling,A DYNAMIC GPS SYSTEM FOR ON-LINE STRUCTURAL MONITORING[A].The 10th FIG International Symposium on Deformation Measurements[C].Orage,California,USA,2001
[62]夏林元.GPS观测值中的多路径效应理论研究及数值结果[D].武汉:武汉大学,2001
[63]葛哲学,陈仲生.Matlab时频分析技术及其应用[M].北京:人民邮电出版社,2006
[2]陈永奇.变形观测数据处理[M].北京:测绘出版社,1988
[3]徐良,江见鲸,过静珺.广州虎门悬索桥的模态分析[J].土木工程学报,2002,35(1):25-27
[4]Lovse,J.,W.F.Teskey,G.Lachapelle & M.E.Cannon.Dynamic deformation monitoring of tall structures using GPS technology[J].Journal of Surveying Engineering,1995,121(1),35-40
[5]李征航,黄劲松.GPS测量与数据处理[M].武汉:武汉大学出版社,2005
[6]Celebi,M.and A.Sanli.GPS in Pioneering Dynamic Monitoring of Long-Period Structures[J],Earthquake Spectra,2002,18(i):47-61
[7]过静瑶,戴连君,卢云川.虎门大桥GPS(RTK)实时位移监测方法研究[J].测绘通报,2000,12:4-12
[8]罗志才,陈永奇,刘焱雄.GPS用于监测高层建筑物动态特征的模拟研究[J].武汉测绘科技大学学报,2000(25):100-104
[9]黄丁发,陈永奇,丁晓利,朱建军,杨喜中,刘国祥.GPS高层建筑物常荷载振动测试的小波分析[J].振动与冲击,2001,20(1):12-15
[10]Chan W.S.,Xu Y.L.,Ding X.L.,Xiong Y.L.,Dai W.J.Dynamic displacement measurement accuracy of GPS for monitoring large civil engineering structures[A],Proceedings of SPIE[C],No.5765,2005:54-65
[11]Chan W.S.,Xu Y.L.,Ding X.L.,Dai W.J.Calibration of GPS for Dynamic Displacement Measurement of Long Span Cable-Supported Bridges in Vertical Direction[A],Proceedings of SPIE[C],No.5770,2005:168-179
[12]戴吾蛟.GPS精密动态变形监测的数据处理方法研究[D].长沙:中南大学,2007
[13]徐绍铨,李征航,刘经南等.隔河岩大坝外观变形GPS自动化监测系统的可靠性分析[J].全球定位系统,2000,25(1):25-28
[14]徐绍铨.隔河岩大坝GPS自动化监测系统[J].铁路航测,2001,(4):42-44
[15]夏禾,徐幼麟,阎全胜.大跨度悬索桥在风与列车荷载同时作用下的动力响应分析[J].铁道学报,2002,24(4):83-91
[16]过静珺,戴连君,卢云川.虎门大桥GPS(RTK)实时位移监测方法研究[J].测绘通报,2000(12):4-5转12
[17]黄声享,刘经南,柳响林.小波分析在高层建筑动态监测中的应用[J].测绘学报,2003,32(2):153-157
[18]钱稼如,过静瑁,陈志鹏.地王大厦动力特性及大风时楼顶位移和加速度实测研究[J].土木工程学报,1998,31(6):30-39
[19]过静珺,商瑞斌,葛胜杰,谢宝童,白涛.利用GPS监测高大建筑物动态位移法研究[J].工程勘察,1997,3:48-51
[20]Michael Kochly,Tracy Kijewski-Correa,James Stowell.GPS monitoring in urban zones:calibration and quantification of multipath effects[A].SPIE[C],2005
[21]Robert S.Radovanovic,High Accuracy Deformation Monitoring Via Multipath Mitigation by Day-To-Day Correlation Analysis[A].ION GPS 2000[C],19-22 September 2000,Salt Lake City,UT:35-44
[22]Roberts Gethin Wyn,Meng Xiaolin,and Dodson Alan Henry,Integrating a Global Positioning System and Accelerometers to Monitor the Deflection of Bridges[J].Journal of Surveying Engineering,2004,130(2):65-72
[23]Shun-ichi Nakamura.GPS MEASUREMENT OF WIND-INDUCED SUSPENSION BRIDGE GIRDER DISPLACEMENTS[J].JOURNAL OF STRUCTURAL ENGINEERING,2000,126(12):1413-1419
[24]Satoshi Kashima,Yukikazu Yanaka,Shuichi Suzuki et al.Monitoring the Akashi Kaikyo Bridge:First Experiences[J].Structural Engineering International,2001(2):120-123
[25]Chen Yongqi,Huang Dingfa,Ding Xiaoli.Measurement of vibration of tall building with GPS:a case study[A].Proceedings of SPIE[C].No.4337,2001:477-483
[26]熊永良,丁晓利,黄丁发,戴吾蛟,陈慧珊.基于小波变换的单历元算 法及其在结构振动监测中的应用研究[J].测绘学报,2005,34(3):202-207
[27]葛茂荣,过静君,葛胜杰.GPS工程结构监测系统的建立及应用[J].解放军测绘学院学报,1999,16(2):79-82
[28]徐绍铨,隔河岩大坝GPS自动化监测系统[J].铁路航测,2001,第4期:42-44
[29]黄声享.变形数据分析方法研究及其在精密工程GPS自动监测系统中的应用[D].武汉:武汉大学,2001
[30]文鸿雁.基于小波理论的变形分析模型研究[D].武汉:武汉大学,2004
[31]朱建军,贺跃光,曾卓乔.变形观测的理论与方法[M].长沙:中南大学出版社,2004
[32]陈永奇,吴子安,吴中如.变形监测分析与预报[M].北京:测绘出版社,1998
[33]杨位钦,顾岚.时间序列分析与动态数据建模[M].北京:北京工业学院出版社,1986
[34]王文圣,丁晶,李跃清.水文小波分析[M].北京:化学工业出版社,2005
[35]向东.强噪声背景下弱信号特征提取的小波分析[D].武汉:武汉大学,2003
[36]郭亚.振动信号处理中的小波基选择研究[D].合肥:合肥工业大学,2003
[37]飞思科技产品研发中心.小波分析理论与MATLAB7实现[M].北京:电子工业出版社,2005
[38]熊永良,黄丁发,张献洲.一种可靠的含约束的GPS变形监测单历元求解算法[J].武汉大学学报·信息科学版,2001,26(1):51-57
[39]戴吾蛟,丁晓利,朱建军.GPS振动变形监测中单一衍射或反射信号误差处理研究[J].工程勘察,2006(5):49-54
[40]戴吾蛟,丁晓利,朱建军,陈永奇,李志伟.基于经验模式分解的滤波去噪法及其在GPS多路径效应中的应用[J].测绘学报,2006,35(4):321-327
[41]黄丁发,丁晓利,陈永奇,龚涛,熊永良.GPS多路径效应影响与结构振动的小波滤波筛分研究[J].测绘学报,2001,30(1):36-41
[42]HUANG N.E.,SHEN Z.,and LONG S.R..The Emprical Mode Decomposition and Hilbert Spectrum for Nonlinear and Non-stationary Time series Analysis[J].Proceedings of the Royal Society of London SERIESA,1998,454:903-995
[43]HUANG N.E.,SHEN Z.,and LONG S.R..A new view of nonlinear water waves:The Hilbert spectrum[J].Ainu.8ev.Fluid Mech.,1999,31:417-457
[44]HUANG N.E.,Wu M.L.,Long S.R.,Shen S.P.,Qu W.D.A confidence limit for the empirical mode decomposition and Hilbert spectral analysis[J].The Royal Society,2003,459:2317-2345
[45]谭善文.多分辨率希尔伯特-黄(Hiibert-Huang)变换方法的研究[D].重庆:重庆大学,2001
[46]石春香.HHT变换及其在结构分析中的应用[D].上海:同济大学,2003
[47]程军圣.基于Hilbert-Huang变换的旋转机械故障诊断方法研究[D].长沙:湖南大学,2005
[48]禹丹江.土木工程结构模态参数识别—理论、实现与应用[D].福建:福州大学,2005
[49]刘大杰,施一民.全球定位系统的原理与数据处理[M].上海:同济大学出版社,1996
[50]魏子卿,葛茂荣.GPS相对定位的数学模型[M].北京:测绘出版社,1998
[51]郑作亚.GPS数据预处理和星载GPS运动学定轨研究及其软件实现[D].上海:中国科学院上海天文台,2005
[52]柴立合.多尺度科学的研究进展[J].化学进展,2005,17(2):186-191
[53]文成林,周东华.多尺度估计理论及其应用[M].北京:清华大学出版社,2002
[54]郑作亚,柳林涛,黄珹等.小波分析在我国地球物理测量中的应用[J].山东科技大学学报(自然科学版),2003,22(4):28-32
[55]崔锦泰.小波分析导论[M].西安:西安交通大学出版社,1997
[56]徐晨,赵瑞珍,甘小冰.小波分析应用算法[M].北京:科学出版社,2004
[57]张郁山.希尔伯特-黄变换(HHT)与地震动时程的希尔伯特谱方法与应用研究[D].北京:中国地震局地球物理研究所,2003
[58]张立振.快速滤波本征模态信号分解及其在海洋数据分析中的应用[D].青岛:中国海洋大学,2006
[59]Chan W.S.,Xu Y.L.,M.ASCE,Ding X.L.,Xiong Y.L.,Dai W.J.Assessment of Dynamic Measurement Accuracy of GPS in Three Directions[J].JOUNAL of SURVEYING ENGINEERING,2006,AUGUST:108-117
[60]王济,胡晓.MATLAB在振动信号处理中的应用[M].北京:中国水利水电出版社,知识产权出版社,2006
[61]Ogaja Clement,Rizos Chris,Wang Jinling,A DYNAMIC GPS SYSTEM FOR ON-LINE STRUCTURAL MONITORING[A].The 10th FIG International Symposium on Deformation Measurements[C].Orage,California,USA,2001
[62]夏林元.GPS观测值中的多路径效应理论研究及数值结果[D].武汉:武汉大学,2001
[63]葛哲学,陈仲生.Matlab时频分析技术及其应用[M].北京:人民邮电出版社,2006
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