大地测量信号小波相关性研究
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摘要
本文在简述小波分析基本理论的基础上,详细介绍了小波谱分析、小波熵分析以及小波相关性分析,并结合CASH、RIZH、TAIN、WUDI四个监测站的GPS坐标时间序列信号以及CASH、JIMO、RIZH、WUDI四个监测站的对流层延迟改正数据,根据小波谱、小波熵和小波相关性、相干性分析方法的有效性,对大地测量信号中的GPS坐标时间序列信号和对流层延迟改正数据的特征信息、相关性、相干性等问题进行了研究。全文的主要研究内容如下：
围绕Fourier谱、小波谱以及小波熵分析理论,分别进行仿真信号分析,验证各种方法的有效性,结合CASH、RIZH、TAIN、WUDI四个监测站GPS坐标时间序列最新观测数据,分别对其进行小波谱分析、小波熵分析。结果表明,在整个时间域内,小波谱分析能够有效地探测到时间序列信号中存在的周期性信息,这些周期性信息能够从侧面表明CASH、RIZH、TAIN、WUDI四个监测站的数据背后存在着相关性；在小波熵图谱中,四个监测站的分析结果基本上是一致的,表明四个监测站在同方向上的数据规律性基本相同,复杂程度也基本相同。
应用GAMIT软件解算了CASH、JIMO、RIZH、WUDI四个监测站的对流层延迟改正数据,利用小波相关性分析理论,对数据进行小波相关性分析。结果表明,山东监测站站间相关延迟量比较接近,没有出现较大的浮动,最小相关延迟为向前延迟,发生在CASH-RIZH,最大相关延迟为向后延迟,发生在RIZH-JIMO。
探讨了小波相干性分析方法及其理论,对CASH、RIZH、TAIN、WUDI四个监测站的GPS时间序列信号东方向、北方向、垂直方向分别作相干性分析以及相位相干性分析。结果表明,两两站间北方向的月周期、季节周期其小波相干性较强,表明月周期较强,影响因素有一定的规律性；各监测站间季节周期东方向的相位相干性较弱,半年周期东方向的相位相干性较强。
Based on the basic theory of wavelet analysis, this paper introduced wavelet spectrum analysis, wavelet entropy analysis and wavelet correlation analysis in detail. Combined with GPS coordinates time series signal of CASH、RIZH、TAIN、WUDI and troposphere delay correction data of CASH、JIMO、RIZH、WUDI, this paper explored the question of characteristics information,correlation and coherence according to the effectiveness of wavelet spectrum, wavelet entropy and wavelet correlation,coherence analysis to GPS coordinates time series signal and troposphere delay correction data. The main contents of the paper were following:
Around the Fourier spectral, wavelet spectrum and wavelet entropy analysis theory, the simulation signal analysis respectively, verify the effectiveness of various methods. Put the GPS coordinates time series signal of CASH、RIZH、TAIN、WUDI into wavelet spectrum analysis and wavelet entropy analysis, the results show that wavelet spectrum analysis can effectively detect the time series of the existence of periodic signal of the information in the time domain. These cyclical information can from the side that CASH、 RIZH、TAIN、WUDI four stations are behind the correlation of the data; Four monitoring stations analysis results are basically the same in the map of wavelet entropy. Four stations that forces the same basic data up regularity, basically the same complexity.
Troposphere delay correct data of CASH、JIMO、RIZH、WUDI were obtained through the GAMIT software. By using wavelet theory of correlation analysis, put the data into correlation analysis of wavelet. The results show that Shandong monitoring carried related delay between quantity is close, not appear larger float. Minimum related delay for forward delay, in the CASH-RIZH, the biggest related delay for backward delayed, took place in the RIZH-JIMO.
Discussed the wavelet coherence analysis method. Put the east direction、north direction and vertical direction of GPS coordinates time series signal of CASH、RIZH. TAIN、WUDI into coherence analysis and phase correlation analysis. The results show that north of the direction of between the lunar cycle, seasonal cycle the wavelet coherence is stronger, show that the lunar cycle is stronger, the influence factors have certain regularity; The monitoring stations seasonal cycle of direction between the phase coherence is weak, the half year cycle the direction of the coherence of the phase is stronger.
围绕Fourier谱、小波谱以及小波熵分析理论,分别进行仿真信号分析,验证各种方法的有效性,结合CASH、RIZH、TAIN、WUDI四个监测站GPS坐标时间序列最新观测数据,分别对其进行小波谱分析、小波熵分析。结果表明,在整个时间域内,小波谱分析能够有效地探测到时间序列信号中存在的周期性信息,这些周期性信息能够从侧面表明CASH、RIZH、TAIN、WUDI四个监测站的数据背后存在着相关性；在小波熵图谱中,四个监测站的分析结果基本上是一致的,表明四个监测站在同方向上的数据规律性基本相同,复杂程度也基本相同。
应用GAMIT软件解算了CASH、JIMO、RIZH、WUDI四个监测站的对流层延迟改正数据,利用小波相关性分析理论,对数据进行小波相关性分析。结果表明,山东监测站站间相关延迟量比较接近,没有出现较大的浮动,最小相关延迟为向前延迟,发生在CASH-RIZH,最大相关延迟为向后延迟,发生在RIZH-JIMO。
探讨了小波相干性分析方法及其理论,对CASH、RIZH、TAIN、WUDI四个监测站的GPS时间序列信号东方向、北方向、垂直方向分别作相干性分析以及相位相干性分析。结果表明,两两站间北方向的月周期、季节周期其小波相干性较强,表明月周期较强,影响因素有一定的规律性；各监测站间季节周期东方向的相位相干性较弱,半年周期东方向的相位相干性较强。
Based on the basic theory of wavelet analysis, this paper introduced wavelet spectrum analysis, wavelet entropy analysis and wavelet correlation analysis in detail. Combined with GPS coordinates time series signal of CASH、RIZH、TAIN、WUDI and troposphere delay correction data of CASH、JIMO、RIZH、WUDI, this paper explored the question of characteristics information,correlation and coherence according to the effectiveness of wavelet spectrum, wavelet entropy and wavelet correlation,coherence analysis to GPS coordinates time series signal and troposphere delay correction data. The main contents of the paper were following:
Around the Fourier spectral, wavelet spectrum and wavelet entropy analysis theory, the simulation signal analysis respectively, verify the effectiveness of various methods. Put the GPS coordinates time series signal of CASH、RIZH、TAIN、WUDI into wavelet spectrum analysis and wavelet entropy analysis, the results show that wavelet spectrum analysis can effectively detect the time series of the existence of periodic signal of the information in the time domain. These cyclical information can from the side that CASH、 RIZH、TAIN、WUDI four stations are behind the correlation of the data; Four monitoring stations analysis results are basically the same in the map of wavelet entropy. Four stations that forces the same basic data up regularity, basically the same complexity.
Troposphere delay correct data of CASH、JIMO、RIZH、WUDI were obtained through the GAMIT software. By using wavelet theory of correlation analysis, put the data into correlation analysis of wavelet. The results show that Shandong monitoring carried related delay between quantity is close, not appear larger float. Minimum related delay for forward delay, in the CASH-RIZH, the biggest related delay for backward delayed, took place in the RIZH-JIMO.
Discussed the wavelet coherence analysis method. Put the east direction、north direction and vertical direction of GPS coordinates time series signal of CASH、RIZH. TAIN、WUDI into coherence analysis and phase correlation analysis. The results show that north of the direction of between the lunar cycle, seasonal cycle the wavelet coherence is stronger, show that the lunar cycle is stronger, the influence factors have certain regularity; The monitoring stations seasonal cycle of direction between the phase coherence is weak, the half year cycle the direction of the coherence of the phase is stronger.
引文
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[2]党亚民,秘金钟,成英燕.全球导航卫星系统原理与应用[M].北京：测绘出版社,2007.
[3]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.
[4]赵斌.基于小波分析的RINEX级GPS数据处理方法研究及其软件开发[D].硕士论文.中国地质大学,2007.
[5]朱习军.丛于小波分析的高精度GPS测量质量控制研究[D].硕士论文.山东科技大学,2006.
[6]宁津生,汪海洪,罗志才.小波分析在大地测量中的应用及其进展[J].武汉大学学报(自然科学版),2004,29(8)：659-663.
[7]冷建华.傅里叶变换[M].北京：清华大学出版社,2004.
[8]S. Mallat,. A Theory for Multiresolution Signal Decomposition:The Wavelet Representation[J]. IEEE Transactions on pattern Analysis and Machine Intelligence,1989,11(7):674-693.
[9]朱长青,杨启和,王鸿飞.小波分析若干应用模型及在测绘中的应用和展望[J].测绘工程,1998,7(1)：19-24.
[10]曲国庆.非线性大地测量信号小波分析理论与应用研究[D].博士论文.山东科技大学,2008.
[11]袁兴明.GPS坐标时间序列分析[D].硕士论文.山东理工大学,2011.
[12]夏林元.GPS观测值中的多路径效应理论及数值结果[D].硕士论文.测绘科技情报,2001,3-4.
[13]岳建平,席广永.丛于小波变换的GPS周跳探测[J].测绘工程,2003,12(4)：33-35.
[14]肖本林,李纬,陈开利.丛于小波变换的GPS变形监测数据处理方法研究[J].价值工程,2010.
[15]卢鑫.丛于M带小波大地测量信号特征信息提取[D].硕士论文.山东理工大学,2011.
[16]苏晓庆,曲国庆,仇环.变形信号中突变点的检测[J].山东理工大学学报,2008,22(2)：49-52.
[17]曲国庆,党亚民,章传银,苏晓庆.基于M带小波包的GPS数据序列误差分析与特征信息提取[J].煤炭学报,2008,(11).
[18]王坚,高井祥,曹德欣等.动态变形信号二进小波提取模型研究[J].中国矿业大学学报,2007,36(1)：116-120.
[19]王坚,高井祥,苗李莉.强污染单历元GPS形变信号的提取和粗差识别[J].武汉大学学报(信息科学版),2004,29(5)：416-419.
[20]石莹莹.基于离散小波变换的数字图像水印的研究[D].硕士论文.合肥：安徽理工大学,2009.
[21]宋化镜.丛于小波分析和虚拟仪器技术的滚动轴承测试分析系统的研究[D].硕士论文.上海大学,2007.
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