非线性大地测量信号小波分析理论与应用研究
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摘要
现代大地测量技术具有大范围、长时间、甚至不间断地对地动态观测能力,其动态观测值中包含丰富的信息,可广泛应用于变形分析、重力测量、地壳形变等领域。由于具有时频域局部分析、多分辨(多尺度)分析等功能,小波分析理论与方法已成为大地测量数据处理中的重要研究方向之一。本文基于小波分析理论与方法,围绕多分辨率分析这条主线,对大地测量时间序列信号中的特征信息分析等问题进行了深入研究,建立了一套较为系统的大地测量信号分析理论与方法。主要包括以下内容:
针对大地测量信号非平稳、随机性特点,分析了信号小波包估计理论与方法,提出了小波包估计的阈值改进算法,研究了大地测量信号以及系统性干扰和突变性干扰下信号的小波包估计方法;结合逼近论,提出了大地测量信号自适应小波包估计方法。分析研究表明:小波包对低频和高频部分同时进行分解与重构,可充分利用信号内涵的信息,可较好地保证重构的精度;利用小波包估计方法,可以有效地消除系统性干扰和突变性干扰;选择良好的小波包基可以提高信号估计质量;不同的阈值选择准则适应不同类型的信号,改进Penalty阈值的信号估计效果明显提高;基于逼近论的Schur凹花费函数小波包估计,可以自适应于噪声的结构,提高信号估计的质量。通过试验,上述方法的信噪比和均方误差得到明显改善。
针对大地测量信号的复杂性,结合小波变换和Fourier变换的谱分析,充分利用小波的局部分析功能,提出了利用小波能量时谱和能量频谱分析大地测量信号特征的方法;研究小波熵,提出了识别大地测量信号主要复杂过程或成分的方法。通过实例,研究分析表明:当特征信号是全局、平稳信号时,功率谱分析是有效的,当信号是非平稳随机过程时,则存在一定的局限性;小波能量谱可在时域中记录信号的突变时间,又可在频域中提取信号突变频段,信号在小波各分解层上的小波能量时谱和能量频谱可以有效地探测大地测量信号内涵的特征信息;小波熵可用于探测大地测量信号中的主要复杂过程(信息)。通过山东基准站数据分析,清楚地探测到微弱的月周期、半年周期和年周期及其复杂性,表明:利用小波谱和小波熵探测大地测量信号内涵的特征信息是有效的。
针对大地测量信号特征信息在小波包分解过程中存在的频率混淆现象,分析产生频率交错和频率折叠等频率混淆现象的机理,研究相应的改进算法,消除或减弱频率混淆的影响,提出了利用小波包单子带重构提取大地测量信号周期性特征信息。通过试验,分析研究表明:小波包各节点都出现不同程度频率混淆,而且随着分解层数的增加,频率混淆更加复杂:采取节点重排序可以消除频带交错现象;单子带重构时选择适当的滤波器,可以消除频率重叠现象;利用FFT和IFFT,在分解和重构时,每一步的高频和低频信号与相应滤波器进行卷积,对卷积后的结果进行一定的变换,可去除各子带多余频率成分;改进的小波包单子带重构可以提取大地测量信号周期性特征信息。通过试验验证了上述方法的有效性。
针对高精度大地测量信号,其变形特征量小,会淹没在噪声之中的情况,在分析二进小波和M带小波的基础上,研究了M带小波包的分解与重构算法;在小波包单子带重构提取特征信息方法的基础上,分析M带小波包分解中的频率混淆现象,提出了利用M带小波包单子带重构特征提取弱大地测量特征信息的方法。试验研究分析表明:与二进小波相比,M带小波包在分解子带数相同的条件下,其对信号进行“多通道”分解,分解的速度更快,且对高频部分有更细的频带划分;M带小波包变换应用于GPS数据序列分解,可有效地减少分解层数,提高分辨率,减弱周期信号频率混淆的传播,从而可以更有效地提取弱信号,提高了提取的质量。
针对两列非平稳大地测量信号,在分析其经典相关性的基础上,研究了小波相关性,提出了在时频两域内分析两列大地测量信号的相似程度的方法;在分析相干函数的基础上,研究了小波相干性,提出了分析两列大地测量信号在不同频率、不同时间分辨率下的相关程度的方法;在分析相位相干性的基础上,研究了小波相位相干性,提出了比较两列大地测量信号间的相位变化关系。研究和试验分析表明:在小波互相关中引入参数α,在小波相干性中引入参数δ,实现了在时频两域内分析两列信号互相关和相干性;小波相关性能够分析大地测量信号在不同频率、不同延迟(相差)时的相似程度,能够反映出信号互相关最大时,在该频率处两个信号的延迟(相差)等信息,为探测两个信号的相似程度提供更丰富的信息;对于给定频率的特征信号,相干性不能区分两个信号的组成成分、幅值和相位,而小波相位相干性能够严格比较两个信号间的相位变化。小波相关性、小波相干性、小波相位相干性为分析两列大地测量信号之间的相互关系提供了精细而有效的工具。
Modern geodetic techniques provide powerful earth observation tools with high coverage, high precision, large scale, high temporal and spatial resolution, and are widely applied to the fields of deformation monitoring, gravimetric survey, crustal deformation, etc. With the abilities of time-frequency analysis and multi-resolution (multi-scale) analysis, the application researches are becoming mature as the wavelet theory research preceded in last decades, and its applications in geodetic data processing and analysis have been made some achievements which are not easily reached by classical parameter estimation theory.
Investigate wavelet analysis theory and technology in the Hilbert space, roduce some conceptions of function approximation theory and information theory for application researches. Focusing on the multi-resolution analysis, a set of relatively systematic theories and technologies of non-linear geodetic signal analysis are established, and the feature information extraction and analysis of geodetic signals are deeply studied. The main contents are summarized as follows:
Investigate wavelet packet estimation theory, improve the wavelet packet threshold de-noising method. Wavelet packet estimation technology of geodetic signal with systematic jamming and abrupt is studied, and adaptive technology is brought forward, combining with approximation theory. The results show that: wavelet packet decomposes and reconstructs both the low-frequency and high-frequency bands, that can exactly give expression to information hidden in signal, and can effectively detect the systematic jamming and abrupt changing; moreover, its estimation quality can be improved with fine wavelet packet basis; different threshold criterias fit for different kind of signals, and the estimation effect is clearly better with improved Penalty threshold put forward in this thesis; wavelet packet estimation based on Schur concave function can adaptively choose best fitting basis to improve the estimation quantity; the SNR and RMSE of results obtained by above-mentioned methods show that the methods are effective.
Study the technology of using wavelet time and frequency energy spectrum to analyze the features of geodetic signal by combining wavelet transform and Fourier transform to make full use of local analysis function of wavelet. By studying wavelet entropy for investigating the complexity character main complexity or component in geodetic signal identified. Research results show that power spectrum analysis is effective only if the feature signal is stationary, and Wavelet energy spectrum can record both the abrupt changing time quantum in time and its frequency band in frequency, so the spectrum can detect the feature information contained in the geodetic signal at different level. Wavelet entropy allows for determining scales that concentrate a maximal amount of information. The analysis results of Shandong monitoring station coordinate series show that combining wavelet spectrum and wavelet entropy analysis can extract all feature signals of weak monthly periodicity, semi-annual periodicity and annual periodicity and their complexity can be respectively detected, but Fourier spectrum analysis. That demonstrates that applying wavelet spectrum and entropy to determine feature information hidden in geodetic signal is applicable.
Study the mechanism of frequency alias while using fast algorithm of wavelet packet transform in the decomposition and reconstruction of signals, and improve the algorithm to weaken or even avoid affects of aliasing. The elementary operations, convolving with nonideal wavelet filters, keeping one sample out of two and putting one zero between each sample, all arise aliasing, so each wavelet packet node exists different degree of frequency aliasing, the aliasing, which becomes more complex while the decomposition level increases, Reordering the nodes can avoid frequency interleaving; single-band reconstruction algorithm can weaken frequency folding to some extent; use FFT and IFFT to improve the single-band reconstruction algorithm, and the redundant frequencies in each sub-band can be eliminated.
Study the decomposition and reconstruction of M-band wavelet packet for extracting the weak feature geodetic signals. In some case, the feature information is too small to be covered by noise in high precision geodetic signal, and the decomposition and reconstruction algorithms of M-band wavelet packet are studied for extracting those weak geodetic features. Frequency aliasing appearing in M-band wavelet packet is discussed as well, and the method to extract weak feature information of geodetic signal by M-band single sub-band reconstruction algorithm is given. Comparing with dyadic wavelet packet, M-band wavelet packet decomposes much faster and divides high-frequency band more elaborate with the same amount of sub-bands for its multi-channel decomposition. Applying M-band wavelet packet for GPS coordinates time series can effectively decrease the number of levels, increase the time and frequency resolution and weaken transmitting of the frequency aliasing, so that it is superior to extracting the weak feature information, and the quality of extracting is finer as well.
Investigate the correlation of two non-stationary geodetic signals based on classical correlation, and study the wavelet correlation technology to analyze the similarity degree between two geodetic signals in time-frequency domain; wavelet coherence is studied according to the coherence function analysis, and is applied to discriminate linear relation between two signals at different frequencies and different temporal resolutions; wavelet phase coherence is also studied, and is brought to compare the phase changing relation between the two signals. The simulations show that wavelet correlation and coherence realize time-frequency analysis of correlation and coherence by introducing parameter a and 8 to classical correlation and coherence respectively. That makes wavelet correlation and coherence fit for analyzing non-stationary signal, and wavelet correlation can detect the similarity degree between two geodetic signals at different frequency and different delay (phase difference), and reflect the delay (phase difference) information when the correlation is maximum. Wavelet coherence embodies the amplitude and phase shift while wavelet phase coherence gives strict expression to the phase shift between the two signals. Wavelet correlation, wavelet coherence and wavelet phase coherence are exquisite and effective tools to analyze the relationship between two non-stationary geodetic signals.
针对大地测量信号非平稳、随机性特点,分析了信号小波包估计理论与方法,提出了小波包估计的阈值改进算法,研究了大地测量信号以及系统性干扰和突变性干扰下信号的小波包估计方法;结合逼近论,提出了大地测量信号自适应小波包估计方法。分析研究表明:小波包对低频和高频部分同时进行分解与重构,可充分利用信号内涵的信息,可较好地保证重构的精度;利用小波包估计方法,可以有效地消除系统性干扰和突变性干扰;选择良好的小波包基可以提高信号估计质量;不同的阈值选择准则适应不同类型的信号,改进Penalty阈值的信号估计效果明显提高;基于逼近论的Schur凹花费函数小波包估计,可以自适应于噪声的结构,提高信号估计的质量。通过试验,上述方法的信噪比和均方误差得到明显改善。
针对大地测量信号的复杂性,结合小波变换和Fourier变换的谱分析,充分利用小波的局部分析功能,提出了利用小波能量时谱和能量频谱分析大地测量信号特征的方法;研究小波熵,提出了识别大地测量信号主要复杂过程或成分的方法。通过实例,研究分析表明:当特征信号是全局、平稳信号时,功率谱分析是有效的,当信号是非平稳随机过程时,则存在一定的局限性;小波能量谱可在时域中记录信号的突变时间,又可在频域中提取信号突变频段,信号在小波各分解层上的小波能量时谱和能量频谱可以有效地探测大地测量信号内涵的特征信息;小波熵可用于探测大地测量信号中的主要复杂过程(信息)。通过山东基准站数据分析,清楚地探测到微弱的月周期、半年周期和年周期及其复杂性,表明:利用小波谱和小波熵探测大地测量信号内涵的特征信息是有效的。
针对大地测量信号特征信息在小波包分解过程中存在的频率混淆现象,分析产生频率交错和频率折叠等频率混淆现象的机理,研究相应的改进算法,消除或减弱频率混淆的影响,提出了利用小波包单子带重构提取大地测量信号周期性特征信息。通过试验,分析研究表明:小波包各节点都出现不同程度频率混淆,而且随着分解层数的增加,频率混淆更加复杂:采取节点重排序可以消除频带交错现象;单子带重构时选择适当的滤波器,可以消除频率重叠现象;利用FFT和IFFT,在分解和重构时,每一步的高频和低频信号与相应滤波器进行卷积,对卷积后的结果进行一定的变换,可去除各子带多余频率成分;改进的小波包单子带重构可以提取大地测量信号周期性特征信息。通过试验验证了上述方法的有效性。
针对高精度大地测量信号,其变形特征量小,会淹没在噪声之中的情况,在分析二进小波和M带小波的基础上,研究了M带小波包的分解与重构算法;在小波包单子带重构提取特征信息方法的基础上,分析M带小波包分解中的频率混淆现象,提出了利用M带小波包单子带重构特征提取弱大地测量特征信息的方法。试验研究分析表明:与二进小波相比,M带小波包在分解子带数相同的条件下,其对信号进行“多通道”分解,分解的速度更快,且对高频部分有更细的频带划分;M带小波包变换应用于GPS数据序列分解,可有效地减少分解层数,提高分辨率,减弱周期信号频率混淆的传播,从而可以更有效地提取弱信号,提高了提取的质量。
针对两列非平稳大地测量信号,在分析其经典相关性的基础上,研究了小波相关性,提出了在时频两域内分析两列大地测量信号的相似程度的方法;在分析相干函数的基础上,研究了小波相干性,提出了分析两列大地测量信号在不同频率、不同时间分辨率下的相关程度的方法;在分析相位相干性的基础上,研究了小波相位相干性,提出了比较两列大地测量信号间的相位变化关系。研究和试验分析表明:在小波互相关中引入参数α,在小波相干性中引入参数δ,实现了在时频两域内分析两列信号互相关和相干性;小波相关性能够分析大地测量信号在不同频率、不同延迟(相差)时的相似程度,能够反映出信号互相关最大时,在该频率处两个信号的延迟(相差)等信息,为探测两个信号的相似程度提供更丰富的信息;对于给定频率的特征信号,相干性不能区分两个信号的组成成分、幅值和相位,而小波相位相干性能够严格比较两个信号间的相位变化。小波相关性、小波相干性、小波相位相干性为分析两列大地测量信号之间的相互关系提供了精细而有效的工具。
Modern geodetic techniques provide powerful earth observation tools with high coverage, high precision, large scale, high temporal and spatial resolution, and are widely applied to the fields of deformation monitoring, gravimetric survey, crustal deformation, etc. With the abilities of time-frequency analysis and multi-resolution (multi-scale) analysis, the application researches are becoming mature as the wavelet theory research preceded in last decades, and its applications in geodetic data processing and analysis have been made some achievements which are not easily reached by classical parameter estimation theory.
Investigate wavelet analysis theory and technology in the Hilbert space, roduce some conceptions of function approximation theory and information theory for application researches. Focusing on the multi-resolution analysis, a set of relatively systematic theories and technologies of non-linear geodetic signal analysis are established, and the feature information extraction and analysis of geodetic signals are deeply studied. The main contents are summarized as follows:
Investigate wavelet packet estimation theory, improve the wavelet packet threshold de-noising method. Wavelet packet estimation technology of geodetic signal with systematic jamming and abrupt is studied, and adaptive technology is brought forward, combining with approximation theory. The results show that: wavelet packet decomposes and reconstructs both the low-frequency and high-frequency bands, that can exactly give expression to information hidden in signal, and can effectively detect the systematic jamming and abrupt changing; moreover, its estimation quality can be improved with fine wavelet packet basis; different threshold criterias fit for different kind of signals, and the estimation effect is clearly better with improved Penalty threshold put forward in this thesis; wavelet packet estimation based on Schur concave function can adaptively choose best fitting basis to improve the estimation quantity; the SNR and RMSE of results obtained by above-mentioned methods show that the methods are effective.
Study the technology of using wavelet time and frequency energy spectrum to analyze the features of geodetic signal by combining wavelet transform and Fourier transform to make full use of local analysis function of wavelet. By studying wavelet entropy for investigating the complexity character main complexity or component in geodetic signal identified. Research results show that power spectrum analysis is effective only if the feature signal is stationary, and Wavelet energy spectrum can record both the abrupt changing time quantum in time and its frequency band in frequency, so the spectrum can detect the feature information contained in the geodetic signal at different level. Wavelet entropy allows for determining scales that concentrate a maximal amount of information. The analysis results of Shandong monitoring station coordinate series show that combining wavelet spectrum and wavelet entropy analysis can extract all feature signals of weak monthly periodicity, semi-annual periodicity and annual periodicity and their complexity can be respectively detected, but Fourier spectrum analysis. That demonstrates that applying wavelet spectrum and entropy to determine feature information hidden in geodetic signal is applicable.
Study the mechanism of frequency alias while using fast algorithm of wavelet packet transform in the decomposition and reconstruction of signals, and improve the algorithm to weaken or even avoid affects of aliasing. The elementary operations, convolving with nonideal wavelet filters, keeping one sample out of two and putting one zero between each sample, all arise aliasing, so each wavelet packet node exists different degree of frequency aliasing, the aliasing, which becomes more complex while the decomposition level increases, Reordering the nodes can avoid frequency interleaving; single-band reconstruction algorithm can weaken frequency folding to some extent; use FFT and IFFT to improve the single-band reconstruction algorithm, and the redundant frequencies in each sub-band can be eliminated.
Study the decomposition and reconstruction of M-band wavelet packet for extracting the weak feature geodetic signals. In some case, the feature information is too small to be covered by noise in high precision geodetic signal, and the decomposition and reconstruction algorithms of M-band wavelet packet are studied for extracting those weak geodetic features. Frequency aliasing appearing in M-band wavelet packet is discussed as well, and the method to extract weak feature information of geodetic signal by M-band single sub-band reconstruction algorithm is given. Comparing with dyadic wavelet packet, M-band wavelet packet decomposes much faster and divides high-frequency band more elaborate with the same amount of sub-bands for its multi-channel decomposition. Applying M-band wavelet packet for GPS coordinates time series can effectively decrease the number of levels, increase the time and frequency resolution and weaken transmitting of the frequency aliasing, so that it is superior to extracting the weak feature information, and the quality of extracting is finer as well.
Investigate the correlation of two non-stationary geodetic signals based on classical correlation, and study the wavelet correlation technology to analyze the similarity degree between two geodetic signals in time-frequency domain; wavelet coherence is studied according to the coherence function analysis, and is applied to discriminate linear relation between two signals at different frequencies and different temporal resolutions; wavelet phase coherence is also studied, and is brought to compare the phase changing relation between the two signals. The simulations show that wavelet correlation and coherence realize time-frequency analysis of correlation and coherence by introducing parameter a and 8 to classical correlation and coherence respectively. That makes wavelet correlation and coherence fit for analyzing non-stationary signal, and wavelet correlation can detect the similarity degree between two geodetic signals at different frequency and different delay (phase difference), and reflect the delay (phase difference) information when the correlation is maximum. Wavelet coherence embodies the amplitude and phase shift while wavelet phase coherence gives strict expression to the phase shift between the two signals. Wavelet correlation, wavelet coherence and wavelet phase coherence are exquisite and effective tools to analyze the relationship between two non-stationary geodetic signals.
引文
1.国家自然科学基金委员会.大地测量学[M].北京:科学出版社,1994
2.潘雄.参数模型的估计理论及其应用[D].武汉:武汉大学,2004,1-2
3.中国测绘学会.测绘学科发展白皮书[M].武汉:武汉大学出版社,2003
4.潘雄.半参数模型的估计理论及其应用[D].武汉:武汉大学,2003.
5.王新州.非线性模型参数估计理论与应用[M].武汉:武汉大学出版社,2002.
6.张松林.非线性半参数模型最小二乘估计理论及应用研究[D].武汉:武汉大学,2003.
7.胡宏昌.半参数模型的估计方法及其应用[D].武汉:武汉大学,2004.
8.丁士俊.测量数据的建模与半参数估计[D].武汉:武汉大学,2005.
9.党亚民.GPS和地球动力学进展[J].测绘科学,2004,29(2):77-80.
10.宁津生,汪海洪,罗志才.小波分析在大地测量中的应用及进展[J].武汉大学学报(自然科学版),2004,29(8):659-663.
11.Gabor D.Theory of communication[M].J.Inst.Wlect.Wngng,1946,93:429-457
12.Albert B,Francis J N.A first cowse in wavelets with Fourier analysis[M].北京:电子工业出版社,2002.
13.Morlet.J,Arens.q,Foruteau.E,et al.Wave propagation and sampling theory and complex waves[J].Geophysics,1982,47(2):222-236.
14.Meyer Y.Ondeletes et Functions splines.Seminaire EDP Ecole Polytechnique,Paris,1986.
15.S.Mallet.A theory for multiresolution signal decomposition:the wavelet representation[J].IEEE Traps on PAMI,1989,11(7):674-693.
16.S.Mallet.Multifrequency channel decomposition of images and wavelet models[J].IEEE Traps on Acoustics,Speech and Signal Processing[J],1989,37(12):2091-2109.
17.Herman O.On the approximation problem in nortrecursive digital filter design[J].IEEE Trans.on Circuit Theory,1971,411-413
18.Daubechies I.The wavelet transform,time-frequency localization and signal analysis[J].IEEE Trans on Information Theory,1990,36(S):961-1005.
19.郑军.小波理论在系统建模与控制中的若干应用研究[D].杭州:浙江大学,2005.6:1-13
20.任哲,陈明华.NA样本半参数回归模型估计的强相合性[J].高校应用数学学报(A辑),2000,15(4):467-474.
21.Antoniads A,Greogoire,G.Mckeague I.W..Wavelet methods for curve estimation,J.A.S.A.,1994,89:1340-1353.
22.柴根象,徐克军.半参数回归的线性小波光滑[J],应用概率统计,1999,15(1):97-105.
23.刘元金,柴根象.半参数模型误差分布小波估计的渐近理论[J].同济大学学报(自然科学版),1999,27(4):463-467.
24.陈敬雨,钱伟民.半参数回归模型小波估计的弱相合速度[J],同济大学学报(自然科学版),1999,27(6):708-712.
25.钱伟民,柴根象,将凤英.半参数回归模型误差方差的小波估计[J].数学年刊,2000,21A(3):341-350.
26.薛留根.半参数回归模型小波估计的随机加权逼近速度[J].应用数学学报,2003,26(1):11-25.
27.徐初斌,钱伟民.不等方差情形下非参数回归模型小波估计[J].同济大学学报(自然科学版),2000,28(5):616-620.
28.施云驰,柴根象.半参数回归模型局部多项式估计的渐近性质[J].同济大学学报(自然科学版),2001,29(3):330-333.
29.潘雄,孙海燕.半参数模型误差为NA序列时的阶矩相合性[J].武汉工业学院学报,2004,23(4):104-111.
30.潘雄.随机删失半参数回归模型小波估计的渐近性质[J].应用数学学报,2006,29(1):68-80.
31.Hardle W,Kerkyacharian G,,Pcard D,et al.Wavelets,approximation and statistical application[M].Lecture Notes in Statistics,129.New York:springer-verlag,1998.
32.Donoho D L,Johnstone I M.Minimax estimation via wavelet shrinkage[J].AnnStatistist,1998,26:879-921.
33.Donoho D L,Johnstone I M,Kerkyacharian G,et al.Wavelet shrinkage:asymptopia[J].J Roy Statist Soc.Ser B,1995,53:301-369.
34.Donoho D L,Johnstone I M,Kerkyacharian G,et al.Density estimation by wavelet thresholding[J].Ann Statist,1996,24:508-539.
35.Hall P,Patil P.Formulae for mean integated squared error of non-linear waveletbased density estimation[J].Ann Statist,1995,23:905-928.
36.Hall P,Patil P.On the choice of smoothing parameter,threshold and truncation in nonparametric regression by nonlinear wavelet methods[J].J Roy Statist Soc,Ser B,1996,58:361-377.
37.Hall P,Patil P.Effect of threshold rules on performance of wavelet-based curve estimators[J].Statistic Sinica,1996,6:331-345.
38.Johnstone I M.Wavelet threshold estimators for correlated data and inverse problems:Adaptivity results[J].Statistica Sinica,1999,9:51-83.
39.Johnstone I M,Silverman B W.Wavelet threshold estimators for data with correlated noise[J].J Roy Statist Soc,Ser B,1997,59:319-351.
40.柳林涛.小波基本理论及其在大地测量等领域中的应用[D].北京:中国科学院,1999.
41.章传银.小波分析及其在测绘科技中的应用前景[J].测绘科学,1997,(1):16-21.
42.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.
43.郭际明.GPS与GLONAS5组合测量及变形监测数据处理研究[D].武汉:武汉大学,2001.
44.黄声享,刘经南.GPS变形监测系统中消除噪声的一种有效方法[J].测绘学报,2002,31(2):104-107.
45.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.
46.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(1).
47.伍法权,王尚庆.卡尔曼滤波方法在链子崖危岩体变形实时预报中的应用[J],中国地质灾害与防治学报,1996,7(增刊):56-60.
48.黄全义,大坝变形预报神经网络专家系统方法研究[D].武汉:武汉大学,2001.
49.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.
50.Chalermchon Satirapod,Jinling Wang,Chris Rizos.Comparing different Global Positioning System Data Processing Techniques for Modeling Residual Systematic Errors[J],Journal of Surveying Engineerin Gasce/November,2003,129-135.
51.J.Duan,I.S.Oweisb.Dyadic wavelet analysis of PDA signals[J].Soil Dynamics and Earthquake Engineering,2005,25:661-677.
52.邱建丁,邹小勇,梁汝萍,莫金垣,蔡沛祥.复合信号的小波分形特征[J].科学通报,2002,47(23):1787-1792.
53.黄丁发,卓健成.GPS相位观测值周跳检测的小波分析法[J].测绘学报,1997,26(4):352-357.
54.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],北京:中国科学院,2005.
55.C.Satirapod,C.Ogajia,J.Wang.基于小波的GPS双差残差分析[J].2001.
56.杨晓艺,汪远征,文成林.信号序列经小波变换后的相关性分析[J].河南大学学报(自然科学版),2000,30(4):30-34.
57.欧阳森,宋政湘,王建华,陈德桂,耿英三.基于信号相关性和小波方法的电能质量去噪算法[J].电工技术学报,2003,18(3):111-116.
58.Yang H T,Liao C C.A de-noising scheme for enhancing wavelet-based power quality monitoring system[J].IEEE Trans.on Power Delivery,2001,16(3):353-359.
59.Stanley W D,Dougherty G R,Dougherty R.Digital signal processing[J],Va.:Reston Pub.Co.,1984.
60.段晨东,姜洪开,何正嘉.一种基于信号相关性检测的自适应小波变换及应用[J],西安交通大学学报,2004,38(7):674-770.
61.Sweldens W.The lifting scheme:a construction of secondgeneration wavelets[J].Siamj Math Anal,1997,29(2):511-546..
62.荆晓远,杨静宇.基于相关性和有效互补性分析的多分类器组合方法[J],自动化学报,2000,26(6):741-747.
63.孙才新,李新,杨永明.从白噪声中提取局部放电信号的小波变换方法研究[J],电工技术学报,1999,14(3):47-50.
64.李建平.小波分析信息传输基础[M].北京:国防工业出版社,2004,54-91.
65.李强.大震过程中地壳变形的混沌和多重分形特征及其预报意义[J].地球物理学进展,1999,14(1):84-92.
66.郑兆苾,张军.小镇空间分布奇异性谱f(a)[J].中国地震,1994,10(4):371-377.
67.谢平等.多重分形熵及其在非平稳信号分析中的应用研究[J].仪器仪表学报,2005,26(8):610-612.
68.李水根,吴纪桃.分形与小波[M].北京:科学出版社,2002,259-263.
69.符养.中国大陆现今地壳形变与GPS坐标时间序列分析[D],上海:中科院上海天文台,2002.
70.Wong Kon.Wavelet packet division multiplexing and wavelet packet design under timing error efforts[J].IEEE transaction on signal processing,1997,1877-2889.
71.Assaleh Khaled,Al-assaf Yousef.Features extraction and analysis for classifying causable patterns in control charts[J].Computer&Industrial Engineering,2005(49):168-181.
72.张正禄.工程的变形分析与预报方法研究进展[J].测绘信息工程,2001,27(5):37-39.
73.Daubechies I.Ten Lectures on Wavelets[M].Philadelphia,PA:SIAM Press,1992,21-54.
74.刘根友.高精度GPS定位及地壳形变分析的若干问题的研究[D],武汉:中科院测量与地球物理研究所.2004.
75.崔锦泰.小波分析导论[M].西安:西安交通大学出版社,1995
76.Philip Collier.Kinemativ GPS for deformation monitoring[J].Geomatica,1997,51(2):167-168
77.樊计昌,李松林,刘明军.利用小波包变换提取地震波高频信息[J].石油地球物理勘探,2006,41(2):144-149.
78.Johnstone I M.,Silverman.B.W.Wavelet threshold estimators for data with correlation noise[J].Technical report,Stanford University,1992.
79.Law S.S,Li X.Y,Zhu X Q,et al.Structural damage detection from wavelet packet sensitivity[J].Engineering Structures,2005(27):1339-1348.
80.成礼智,王红霞,罗永.小波的理论与应用[M].北京:科学出版社.2004,75-131.
81.赵玉宝.小波变换在地震信号去噪中的应用[D],湖南:中南大学信息物理工程学院,2005.
82.唐晓初.小波分析及其应用[M].重庆:重庆大学出版社.2006,97-108.
83.夏林元.GPS观测值中的多路径效应理论研究及其数值结果[D],武汉:武汉大学测绘学院,2001.
84.郑建国,石智,权豫西.非平稳信号的小波包阈值去噪方法[J].信息技术,2007,3:16-19.
85.Donoho D L,Johnstone I M.Ideal spatial adaptation by wavelet shrinkage[J].Biometrika,1994,81(3):425-455.
86.Donoho D L.De-noising by soft-thresholding[J].IEEE Trans.Information Theory.1995,613-627.
87.Bruce A G,Gao H Y.Understanding waveshrink:variance and bias estimation[J].Biometrika,1996,83(4):727-745.
88.李延兴.首都圈GPS地形变监测网的布设与观测[J].地壳形变与地震,1996,16(20):90-93.
89.文洪雁.基于小波理论的变形分析模型研究[D],武汉:武汉大学测绘学院,2004.
90.薛永安.GPS变形监测数据处理方法研究与软件研制[D],山西:太原理工大学矿业工程学院,2006.
91.郑作亚,黄珹,卢秀山,等.采矿区地层移动GPS动态检测数据的小波分析[J].大地测量与地球动力学,2003,23(3):107-111.
92.夏林元.GPS观测值中的多路径效应理论研究及其数值结果[D],武汉:武汉大学测绘学院,2001.
93.Donoho D L,Johnstone I M.Ideal spatial fadaptation by wavelet shrinkage[J],Biornetrika,1994,81(3):425-455.
94.栾元重,班训海.矿区GPS变形监测网的建立与变形值计算方法[J].矿山测量,2000(2):33-34.
95.王军,城市GPS地面变形监测网的精度研究[J].测绘通报,2004(7):6-8.
96.Shimizu N,Mizuta Y,Kondo H,et al.A new GPS real time monitoring system for deformation measurements and its application[C].Proceeding of the 8th Int.Symp.On Deformation Measurements,1996,47-54.
97.增法力.小波包分析在齿轮故障诊断中的应用[D],武汉:武汉科技大学,2005.
98.郑军.小波理论在系统建模与控制中的若干应用研究[D],浙江大学,杭州:2005.
99.Ananga N,Sakurai S,Kawashima I,et al.Cut slop deformation determination with GPS[J].Survey Review,1997,34(265):144-150.
100.徐绍铨,程温鸣,黄学斌等.GPS用于三峡库区滑坡监测的研究[J].水利学报,2003,(1):114-118.
101.Donoho D L.De-noising by soft-thresholding[C].IEEE Trans.Information Theory,1995.613-627.
102.李建平.小波分析信息传输基础[M].北京:国防工业出版社,2004,138-171.
103.葛永,陈建安.基于改进小波包算法的水声信号消噪与重构研究[J].声学与电子工程,2004,(2):5-9.
104.Coifman R R,Wickerhauser M V.Entropy-based algorithms for best basis selection[J].IEEE Trans.Info.Theory,1992,38(2):713-718
105.周宏,任震,黄雯莹,吴国沛,管霖.小波变换在电力设备故障诊断中的应用研究.中国电机工程学报,2000,(10)
106.Hudgins,L.,Friehe,C.A.,Mayer,M.E..Wavelet tmnsformsand atmospheric turbulence[J].Physical Review Letters,1993,71(20),3279-3282
107.Brunet,Y.,Collineau,S..Wavelet analysis of diurnal and nocturnal turbulence above a maize crop [C].In:Foufoula-Georgiou,E.,Kumar,P.(Eds.),Wavelets in Geophysics.Academic Press,New York,1995,129-150
108.Liu,P.C..Wavelet spectrum analysis and ocean wind waves[C].In:Foufoula-Georgiou,E.,Kumar,P.(Eds.),Wavelets in Geophysics.Academic Press,New York,1995,151-166
109.Shannon,C.E..A mathematical theory of communication[J].Bell System Technology Journal,1946,27:379-423,623-656
110.Sello,S..Wavelet entropy and the multi peaked structure ofsolar cycle maximum[J].New Astronomy 1,2003
111.Blanco,S.,Figliola,A.,Quiroga,R.Q.,Rosso,O.A.,Serrano,E..Time-frequency analysis of electroencephalogram series.Ⅲ.Wavelet packets and information cost function.Physical Review E,1998,57(1):932-940
112.李杰,殷海涛等.山东地壳运动GPS观测网的建设与初步结果分析[J].大地测量与地球动力学,2007(27)增刊:9-13.
113.杨建国.基于小波包的滚动轴承故障特征提取[J].中国机械工程,2002,13(11):935-937
114.杨建国.小波分析及其工程应用[M].北京:机械工业出版社,2005.79-97.
115.纪跃波.小波包的频率顺序[J].振动与冲击,2005,(3):96-110.
116.薛蕙,杨仁刚,郭永芳.小波包变换(WPT)频带划分特性的分析[J].电力系统及其自动化学报,2003,15(2):5-8.
117.李征航,黄劲松.GPS测量与数据处理[M].武汉:武汉大学出版社,2005:38-77
118.Hehong Zou,Tewfik Ahmed H.Discrete orthogonal M-band wavelet decompositions[J].IEEE Trans on Signal Processing,1992,4(4):605-608
119.Asim Bhatti and Hnseyin Oakaramanli.M-band multiwavelets from spline super functions with approximation order[J].IEEE ICASSP Orlando,Florida.2002.
120.LI LI,Peng Yuhua,Yang Mingqinag,Xue peiun.A New De-noising Method Based on 3-band Wavelet and Nonparametric and Aptive Estimation[J].Journal of Electronic,2007,24(3):358-361
121.LMT Heil,C.E.,Walnut,D.F..Continuous and discrete wavelet transforms[J].SIAM Review,1989,31(4):628-666
122.David Labat.Recent advances in wavelet analyses:Part 1.A review of concepts[J].Journal of Hydrology.2005,314:275-288
123.Onorato.M.,Salvetti,M.V.,Buresti.G.,Petagna.P..Application of a wavelet cross-correlation analysis to DNS velocity signals[J].European Journal of Mechanics B,1997,16(4):575-597
124.L.T.Liu,H.T.Hsu,E.W.Grafarend.Wavelet coherence analysis of Length-Of-Day variation and El Nino-Southern Oscillation[J].Journal of Geodynamics,2005,(39):267-275
125.Li,H.,Nozaki,T..Application of wavelet cross-correlation analysis to a plane turbulent jet[J].JSME International Journal,Series B,1997,40(1):58-66
126. Sello, S., Bellazzini, J.. Wavelet cross-correlation analysis of turbulent mixing from large-eddy simulations [J]. Eighth European Turbulence Conference, Barcelona, Spain, 2000, 27-30
127. Mizuno-Matsumoto, Y. , Yoshimine, T. , Nii, Y. , Kato, A., Janiguchi, M, Lee, J.K., Ko, T.S., Date, S., Tamura, S.Shimojo, S.Shinosaki, K.Inouye, T.Takeda, M.Landau-Kleffner syndrome: localization of epileptogenic lesion using wavelet cross-correlation analysis[J]. Epilepsy and Beha-viour, 2001, 2: 288-294.
128. Mizuno-Matsumoto,Y. Motamedi, G.K.Webber, W.R.S.Lesser.Wavelet cross-correlation analysis can help predict whether bursts of pulse stimulation willterminate after discharges [J]. Clinical Neurophysiology, 2002, 113: 3342.
129. Liu P. Wavelet spectrum analysis and ocean wind waves [J]. In: Foufoula-Georgiou E, Kumar P, editors. Wavelets in geophysics.New York: Academic Press, 1994, 151-166
130. Van Milligen B, Sanchez E, Estrada T, Hidalgo C, Branas B, Carreras B. Wavelet bicoherence: a new turbulence analysis tool [J]. Phys Plasmas, 1995,2: 3017-3032.
131. Santoso S, Powers E, Bengtson R, Ouroua A. Time-series analysis of nonstationary plasma fluctuations using wavelet trans-forms [J]. Rev Sci Instrum, 1997, 68: 898-901
132. Gardner, W. A.. A unifying view of coherence in signal processing [J]. Signal Processing , 1992, 29: 113-140
133. Jean-Philippe Lachaux, Antoine Lutz, David Rudrauf, Diego Cosmelli, Michel Le Van Quyen, Jacques Martinerie, Francisco Varela. Estimating the time-course of coherence between single-trial brain signals: an introduction to wavelet coherence [J]. Neurophysiol Clin, 2002, 32: 157-174
134. Challis R, Kitney R. Biomedical signal processing, II. The frequency transforms and their inter-relationships [J]. Med Biol Eng Comput, 1991,29: 1-17
135. Auger F, Flandrin P, Gonzalves P, Lemoine O. Time-frequency toolbox. For use with Matlab. Tutorial, 1997
136. Bullock T, McClune M, Achimowicz J, Iragui-Madoz V, Duck-row R, Spencer S. EEG coherence has structure in the millime-ter domain: subdural and hippocampal recordings from epileptic patients [J]. Electroencephalogr Clin Neurophysiol, 1995,95: 161-177.
137. Weiss S, Rappelsberger P. EEG coherence within the 13-18 Hz band as a correlate of a distinct lexical organisation of concrete and abstract nouns in humans [J]. Neurosci Lett, 1996, 209: 17-20.
138. Gray C, Engel K, Konig P, Singer W. Synchronization of oscil-latory neuronal responses in cat striate cortex: temporal proper-ties [J]. Vis Neurosci, 1992, 8: 337-347
139. Torrence. C., Webster. P. J.. Interdecadal changes in the ENSO-monsoon system. Journal of Climate [J], 1999,12: 2679-2690
140. J.F. Valdes-Galicia, V.M. Velasco. Variations of mid-term periodicities in solar activity physical phenomena. Advances in Space Research [J], 2008,41: 297-305
141. Lachaux JP, Rodriguez E, Martinerie J, Varela FJ. Measuring phase synchrony in brain signals [J]. Hum Brain Mapp, 1999, 8: 194-208.
142. Goldstein S. Phase coherence of the alpha rhythm during photic blocking [J]. Electroencephalogr Clin Neurophysiol, 1970,29: 127-136.
143. Dobie R, Wilson M. Objective detection of 40 Hz auditory evoked potentials: phase-coherence vs. magnitude-squared co-herence [J]. Electroencephalogr Clin Neurophysiol, 1994, 92: 405-413
144. Rodriguez E, George N, Lachaux JP, Martinerie J, Renault B,Varela FJ. Perception's shadow: long-distance synchronization of human brain activity [J]. Nature, 1999, 397: 430-433
145. Zhang Jiankang, Bao Zheng. Theory of orthonormal M-band wavelet packets. Journal of Electronics, 1998,15(3):193-198
2.潘雄.参数模型的估计理论及其应用[D].武汉:武汉大学,2004,1-2
3.中国测绘学会.测绘学科发展白皮书[M].武汉:武汉大学出版社,2003
4.潘雄.半参数模型的估计理论及其应用[D].武汉:武汉大学,2003.
5.王新州.非线性模型参数估计理论与应用[M].武汉:武汉大学出版社,2002.
6.张松林.非线性半参数模型最小二乘估计理论及应用研究[D].武汉:武汉大学,2003.
7.胡宏昌.半参数模型的估计方法及其应用[D].武汉:武汉大学,2004.
8.丁士俊.测量数据的建模与半参数估计[D].武汉:武汉大学,2005.
9.党亚民.GPS和地球动力学进展[J].测绘科学,2004,29(2):77-80.
10.宁津生,汪海洪,罗志才.小波分析在大地测量中的应用及进展[J].武汉大学学报(自然科学版),2004,29(8):659-663.
11.Gabor D.Theory of communication[M].J.Inst.Wlect.Wngng,1946,93:429-457
12.Albert B,Francis J N.A first cowse in wavelets with Fourier analysis[M].北京:电子工业出版社,2002.
13.Morlet.J,Arens.q,Foruteau.E,et al.Wave propagation and sampling theory and complex waves[J].Geophysics,1982,47(2):222-236.
14.Meyer Y.Ondeletes et Functions splines.Seminaire EDP Ecole Polytechnique,Paris,1986.
15.S.Mallet.A theory for multiresolution signal decomposition:the wavelet representation[J].IEEE Traps on PAMI,1989,11(7):674-693.
16.S.Mallet.Multifrequency channel decomposition of images and wavelet models[J].IEEE Traps on Acoustics,Speech and Signal Processing[J],1989,37(12):2091-2109.
17.Herman O.On the approximation problem in nortrecursive digital filter design[J].IEEE Trans.on Circuit Theory,1971,411-413
18.Daubechies I.The wavelet transform,time-frequency localization and signal analysis[J].IEEE Trans on Information Theory,1990,36(S):961-1005.
19.郑军.小波理论在系统建模与控制中的若干应用研究[D].杭州:浙江大学,2005.6:1-13
20.任哲,陈明华.NA样本半参数回归模型估计的强相合性[J].高校应用数学学报(A辑),2000,15(4):467-474.
21.Antoniads A,Greogoire,G.Mckeague I.W..Wavelet methods for curve estimation,J.A.S.A.,1994,89:1340-1353.
22.柴根象,徐克军.半参数回归的线性小波光滑[J],应用概率统计,1999,15(1):97-105.
23.刘元金,柴根象.半参数模型误差分布小波估计的渐近理论[J].同济大学学报(自然科学版),1999,27(4):463-467.
24.陈敬雨,钱伟民.半参数回归模型小波估计的弱相合速度[J],同济大学学报(自然科学版),1999,27(6):708-712.
25.钱伟民,柴根象,将凤英.半参数回归模型误差方差的小波估计[J].数学年刊,2000,21A(3):341-350.
26.薛留根.半参数回归模型小波估计的随机加权逼近速度[J].应用数学学报,2003,26(1):11-25.
27.徐初斌,钱伟民.不等方差情形下非参数回归模型小波估计[J].同济大学学报(自然科学版),2000,28(5):616-620.
28.施云驰,柴根象.半参数回归模型局部多项式估计的渐近性质[J].同济大学学报(自然科学版),2001,29(3):330-333.
29.潘雄,孙海燕.半参数模型误差为NA序列时的阶矩相合性[J].武汉工业学院学报,2004,23(4):104-111.
30.潘雄.随机删失半参数回归模型小波估计的渐近性质[J].应用数学学报,2006,29(1):68-80.
31.Hardle W,Kerkyacharian G,,Pcard D,et al.Wavelets,approximation and statistical application[M].Lecture Notes in Statistics,129.New York:springer-verlag,1998.
32.Donoho D L,Johnstone I M.Minimax estimation via wavelet shrinkage[J].AnnStatistist,1998,26:879-921.
33.Donoho D L,Johnstone I M,Kerkyacharian G,et al.Wavelet shrinkage:asymptopia[J].J Roy Statist Soc.Ser B,1995,53:301-369.
34.Donoho D L,Johnstone I M,Kerkyacharian G,et al.Density estimation by wavelet thresholding[J].Ann Statist,1996,24:508-539.
35.Hall P,Patil P.Formulae for mean integated squared error of non-linear waveletbased density estimation[J].Ann Statist,1995,23:905-928.
36.Hall P,Patil P.On the choice of smoothing parameter,threshold and truncation in nonparametric regression by nonlinear wavelet methods[J].J Roy Statist Soc,Ser B,1996,58:361-377.
37.Hall P,Patil P.Effect of threshold rules on performance of wavelet-based curve estimators[J].Statistic Sinica,1996,6:331-345.
38.Johnstone I M.Wavelet threshold estimators for correlated data and inverse problems:Adaptivity results[J].Statistica Sinica,1999,9:51-83.
39.Johnstone I M,Silverman B W.Wavelet threshold estimators for data with correlated noise[J].J Roy Statist Soc,Ser B,1997,59:319-351.
40.柳林涛.小波基本理论及其在大地测量等领域中的应用[D].北京:中国科学院,1999.
41.章传银.小波分析及其在测绘科技中的应用前景[J].测绘科学,1997,(1):16-21.
42.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.
43.郭际明.GPS与GLONAS5组合测量及变形监测数据处理研究[D].武汉:武汉大学,2001.
44.黄声享,刘经南.GPS变形监测系统中消除噪声的一种有效方法[J].测绘学报,2002,31(2):104-107.
45.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.
46.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(1).
47.伍法权,王尚庆.卡尔曼滤波方法在链子崖危岩体变形实时预报中的应用[J],中国地质灾害与防治学报,1996,7(增刊):56-60.
48.黄全义,大坝变形预报神经网络专家系统方法研究[D].武汉:武汉大学,2001.
49.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.
50.Chalermchon Satirapod,Jinling Wang,Chris Rizos.Comparing different Global Positioning System Data Processing Techniques for Modeling Residual Systematic Errors[J],Journal of Surveying Engineerin Gasce/November,2003,129-135.
51.J.Duan,I.S.Oweisb.Dyadic wavelet analysis of PDA signals[J].Soil Dynamics and Earthquake Engineering,2005,25:661-677.
52.邱建丁,邹小勇,梁汝萍,莫金垣,蔡沛祥.复合信号的小波分形特征[J].科学通报,2002,47(23):1787-1792.
53.黄丁发,卓健成.GPS相位观测值周跳检测的小波分析法[J].测绘学报,1997,26(4):352-357.
54.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],北京:中国科学院,2005.
55.C.Satirapod,C.Ogajia,J.Wang.基于小波的GPS双差残差分析[J].2001.
56.杨晓艺,汪远征,文成林.信号序列经小波变换后的相关性分析[J].河南大学学报(自然科学版),2000,30(4):30-34.
57.欧阳森,宋政湘,王建华,陈德桂,耿英三.基于信号相关性和小波方法的电能质量去噪算法[J].电工技术学报,2003,18(3):111-116.
58.Yang H T,Liao C C.A de-noising scheme for enhancing wavelet-based power quality monitoring system[J].IEEE Trans.on Power Delivery,2001,16(3):353-359.
59.Stanley W D,Dougherty G R,Dougherty R.Digital signal processing[J],Va.:Reston Pub.Co.,1984.
60.段晨东,姜洪开,何正嘉.一种基于信号相关性检测的自适应小波变换及应用[J],西安交通大学学报,2004,38(7):674-770.
61.Sweldens W.The lifting scheme:a construction of secondgeneration wavelets[J].Siamj Math Anal,1997,29(2):511-546..
62.荆晓远,杨静宇.基于相关性和有效互补性分析的多分类器组合方法[J],自动化学报,2000,26(6):741-747.
63.孙才新,李新,杨永明.从白噪声中提取局部放电信号的小波变换方法研究[J],电工技术学报,1999,14(3):47-50.
64.李建平.小波分析信息传输基础[M].北京:国防工业出版社,2004,54-91.
65.李强.大震过程中地壳变形的混沌和多重分形特征及其预报意义[J].地球物理学进展,1999,14(1):84-92.
66.郑兆苾,张军.小镇空间分布奇异性谱f(a)[J].中国地震,1994,10(4):371-377.
67.谢平等.多重分形熵及其在非平稳信号分析中的应用研究[J].仪器仪表学报,2005,26(8):610-612.
68.李水根,吴纪桃.分形与小波[M].北京:科学出版社,2002,259-263.
69.符养.中国大陆现今地壳形变与GPS坐标时间序列分析[D],上海:中科院上海天文台,2002.
70.Wong Kon.Wavelet packet division multiplexing and wavelet packet design under timing error efforts[J].IEEE transaction on signal processing,1997,1877-2889.
71.Assaleh Khaled,Al-assaf Yousef.Features extraction and analysis for classifying causable patterns in control charts[J].Computer&Industrial Engineering,2005(49):168-181.
72.张正禄.工程的变形分析与预报方法研究进展[J].测绘信息工程,2001,27(5):37-39.
73.Daubechies I.Ten Lectures on Wavelets[M].Philadelphia,PA:SIAM Press,1992,21-54.
74.刘根友.高精度GPS定位及地壳形变分析的若干问题的研究[D],武汉:中科院测量与地球物理研究所.2004.
75.崔锦泰.小波分析导论[M].西安:西安交通大学出版社,1995
76.Philip Collier.Kinemativ GPS for deformation monitoring[J].Geomatica,1997,51(2):167-168
77.樊计昌,李松林,刘明军.利用小波包变换提取地震波高频信息[J].石油地球物理勘探,2006,41(2):144-149.
78.Johnstone I M.,Silverman.B.W.Wavelet threshold estimators for data with correlation noise[J].Technical report,Stanford University,1992.
79.Law S.S,Li X.Y,Zhu X Q,et al.Structural damage detection from wavelet packet sensitivity[J].Engineering Structures,2005(27):1339-1348.
80.成礼智,王红霞,罗永.小波的理论与应用[M].北京:科学出版社.2004,75-131.
81.赵玉宝.小波变换在地震信号去噪中的应用[D],湖南:中南大学信息物理工程学院,2005.
82.唐晓初.小波分析及其应用[M].重庆:重庆大学出版社.2006,97-108.
83.夏林元.GPS观测值中的多路径效应理论研究及其数值结果[D],武汉:武汉大学测绘学院,2001.
84.郑建国,石智,权豫西.非平稳信号的小波包阈值去噪方法[J].信息技术,2007,3:16-19.
85.Donoho D L,Johnstone I M.Ideal spatial adaptation by wavelet shrinkage[J].Biometrika,1994,81(3):425-455.
86.Donoho D L.De-noising by soft-thresholding[J].IEEE Trans.Information Theory.1995,613-627.
87.Bruce A G,Gao H Y.Understanding waveshrink:variance and bias estimation[J].Biometrika,1996,83(4):727-745.
88.李延兴.首都圈GPS地形变监测网的布设与观测[J].地壳形变与地震,1996,16(20):90-93.
89.文洪雁.基于小波理论的变形分析模型研究[D],武汉:武汉大学测绘学院,2004.
90.薛永安.GPS变形监测数据处理方法研究与软件研制[D],山西:太原理工大学矿业工程学院,2006.
91.郑作亚,黄珹,卢秀山,等.采矿区地层移动GPS动态检测数据的小波分析[J].大地测量与地球动力学,2003,23(3):107-111.
92.夏林元.GPS观测值中的多路径效应理论研究及其数值结果[D],武汉:武汉大学测绘学院,2001.
93.Donoho D L,Johnstone I M.Ideal spatial fadaptation by wavelet shrinkage[J],Biornetrika,1994,81(3):425-455.
94.栾元重,班训海.矿区GPS变形监测网的建立与变形值计算方法[J].矿山测量,2000(2):33-34.
95.王军,城市GPS地面变形监测网的精度研究[J].测绘通报,2004(7):6-8.
96.Shimizu N,Mizuta Y,Kondo H,et al.A new GPS real time monitoring system for deformation measurements and its application[C].Proceeding of the 8th Int.Symp.On Deformation Measurements,1996,47-54.
97.增法力.小波包分析在齿轮故障诊断中的应用[D],武汉:武汉科技大学,2005.
98.郑军.小波理论在系统建模与控制中的若干应用研究[D],浙江大学,杭州:2005.
99.Ananga N,Sakurai S,Kawashima I,et al.Cut slop deformation determination with GPS[J].Survey Review,1997,34(265):144-150.
100.徐绍铨,程温鸣,黄学斌等.GPS用于三峡库区滑坡监测的研究[J].水利学报,2003,(1):114-118.
101.Donoho D L.De-noising by soft-thresholding[C].IEEE Trans.Information Theory,1995.613-627.
102.李建平.小波分析信息传输基础[M].北京:国防工业出版社,2004,138-171.
103.葛永,陈建安.基于改进小波包算法的水声信号消噪与重构研究[J].声学与电子工程,2004,(2):5-9.
104.Coifman R R,Wickerhauser M V.Entropy-based algorithms for best basis selection[J].IEEE Trans.Info.Theory,1992,38(2):713-718
105.周宏,任震,黄雯莹,吴国沛,管霖.小波变换在电力设备故障诊断中的应用研究.中国电机工程学报,2000,(10)
106.Hudgins,L.,Friehe,C.A.,Mayer,M.E..Wavelet tmnsformsand atmospheric turbulence[J].Physical Review Letters,1993,71(20),3279-3282
107.Brunet,Y.,Collineau,S..Wavelet analysis of diurnal and nocturnal turbulence above a maize crop [C].In:Foufoula-Georgiou,E.,Kumar,P.(Eds.),Wavelets in Geophysics.Academic Press,New York,1995,129-150
108.Liu,P.C..Wavelet spectrum analysis and ocean wind waves[C].In:Foufoula-Georgiou,E.,Kumar,P.(Eds.),Wavelets in Geophysics.Academic Press,New York,1995,151-166
109.Shannon,C.E..A mathematical theory of communication[J].Bell System Technology Journal,1946,27:379-423,623-656
110.Sello,S..Wavelet entropy and the multi peaked structure ofsolar cycle maximum[J].New Astronomy 1,2003
111.Blanco,S.,Figliola,A.,Quiroga,R.Q.,Rosso,O.A.,Serrano,E..Time-frequency analysis of electroencephalogram series.Ⅲ.Wavelet packets and information cost function.Physical Review E,1998,57(1):932-940
112.李杰,殷海涛等.山东地壳运动GPS观测网的建设与初步结果分析[J].大地测量与地球动力学,2007(27)增刊:9-13.
113.杨建国.基于小波包的滚动轴承故障特征提取[J].中国机械工程,2002,13(11):935-937
114.杨建国.小波分析及其工程应用[M].北京:机械工业出版社,2005.79-97.
115.纪跃波.小波包的频率顺序[J].振动与冲击,2005,(3):96-110.
116.薛蕙,杨仁刚,郭永芳.小波包变换(WPT)频带划分特性的分析[J].电力系统及其自动化学报,2003,15(2):5-8.
117.李征航,黄劲松.GPS测量与数据处理[M].武汉:武汉大学出版社,2005:38-77
118.Hehong Zou,Tewfik Ahmed H.Discrete orthogonal M-band wavelet decompositions[J].IEEE Trans on Signal Processing,1992,4(4):605-608
119.Asim Bhatti and Hnseyin Oakaramanli.M-band multiwavelets from spline super functions with approximation order[J].IEEE ICASSP Orlando,Florida.2002.
120.LI LI,Peng Yuhua,Yang Mingqinag,Xue peiun.A New De-noising Method Based on 3-band Wavelet and Nonparametric and Aptive Estimation[J].Journal of Electronic,2007,24(3):358-361
121.LMT Heil,C.E.,Walnut,D.F..Continuous and discrete wavelet transforms[J].SIAM Review,1989,31(4):628-666
122.David Labat.Recent advances in wavelet analyses:Part 1.A review of concepts[J].Journal of Hydrology.2005,314:275-288
123.Onorato.M.,Salvetti,M.V.,Buresti.G.,Petagna.P..Application of a wavelet cross-correlation analysis to DNS velocity signals[J].European Journal of Mechanics B,1997,16(4):575-597
124.L.T.Liu,H.T.Hsu,E.W.Grafarend.Wavelet coherence analysis of Length-Of-Day variation and El Nino-Southern Oscillation[J].Journal of Geodynamics,2005,(39):267-275
125.Li,H.,Nozaki,T..Application of wavelet cross-correlation analysis to a plane turbulent jet[J].JSME International Journal,Series B,1997,40(1):58-66
126. Sello, S., Bellazzini, J.. Wavelet cross-correlation analysis of turbulent mixing from large-eddy simulations [J]. Eighth European Turbulence Conference, Barcelona, Spain, 2000, 27-30
127. Mizuno-Matsumoto, Y. , Yoshimine, T. , Nii, Y. , Kato, A., Janiguchi, M, Lee, J.K., Ko, T.S., Date, S., Tamura, S.Shimojo, S.Shinosaki, K.Inouye, T.Takeda, M.Landau-Kleffner syndrome: localization of epileptogenic lesion using wavelet cross-correlation analysis[J]. Epilepsy and Beha-viour, 2001, 2: 288-294.
128. Mizuno-Matsumoto,Y. Motamedi, G.K.Webber, W.R.S.Lesser.Wavelet cross-correlation analysis can help predict whether bursts of pulse stimulation willterminate after discharges [J]. Clinical Neurophysiology, 2002, 113: 3342.
129. Liu P. Wavelet spectrum analysis and ocean wind waves [J]. In: Foufoula-Georgiou E, Kumar P, editors. Wavelets in geophysics.New York: Academic Press, 1994, 151-166
130. Van Milligen B, Sanchez E, Estrada T, Hidalgo C, Branas B, Carreras B. Wavelet bicoherence: a new turbulence analysis tool [J]. Phys Plasmas, 1995,2: 3017-3032.
131. Santoso S, Powers E, Bengtson R, Ouroua A. Time-series analysis of nonstationary plasma fluctuations using wavelet trans-forms [J]. Rev Sci Instrum, 1997, 68: 898-901
132. Gardner, W. A.. A unifying view of coherence in signal processing [J]. Signal Processing , 1992, 29: 113-140
133. Jean-Philippe Lachaux, Antoine Lutz, David Rudrauf, Diego Cosmelli, Michel Le Van Quyen, Jacques Martinerie, Francisco Varela. Estimating the time-course of coherence between single-trial brain signals: an introduction to wavelet coherence [J]. Neurophysiol Clin, 2002, 32: 157-174
134. Challis R, Kitney R. Biomedical signal processing, II. The frequency transforms and their inter-relationships [J]. Med Biol Eng Comput, 1991,29: 1-17
135. Auger F, Flandrin P, Gonzalves P, Lemoine O. Time-frequency toolbox. For use with Matlab. Tutorial, 1997
136. Bullock T, McClune M, Achimowicz J, Iragui-Madoz V, Duck-row R, Spencer S. EEG coherence has structure in the millime-ter domain: subdural and hippocampal recordings from epileptic patients [J]. Electroencephalogr Clin Neurophysiol, 1995,95: 161-177.
137. Weiss S, Rappelsberger P. EEG coherence within the 13-18 Hz band as a correlate of a distinct lexical organisation of concrete and abstract nouns in humans [J]. Neurosci Lett, 1996, 209: 17-20.
138. Gray C, Engel K, Konig P, Singer W. Synchronization of oscil-latory neuronal responses in cat striate cortex: temporal proper-ties [J]. Vis Neurosci, 1992, 8: 337-347
139. Torrence. C., Webster. P. J.. Interdecadal changes in the ENSO-monsoon system. Journal of Climate [J], 1999,12: 2679-2690
140. J.F. Valdes-Galicia, V.M. Velasco. Variations of mid-term periodicities in solar activity physical phenomena. Advances in Space Research [J], 2008,41: 297-305
141. Lachaux JP, Rodriguez E, Martinerie J, Varela FJ. Measuring phase synchrony in brain signals [J]. Hum Brain Mapp, 1999, 8: 194-208.
142. Goldstein S. Phase coherence of the alpha rhythm during photic blocking [J]. Electroencephalogr Clin Neurophysiol, 1970,29: 127-136.
143. Dobie R, Wilson M. Objective detection of 40 Hz auditory evoked potentials: phase-coherence vs. magnitude-squared co-herence [J]. Electroencephalogr Clin Neurophysiol, 1994, 92: 405-413
144. Rodriguez E, George N, Lachaux JP, Martinerie J, Renault B,Varela FJ. Perception's shadow: long-distance synchronization of human brain activity [J]. Nature, 1999, 397: 430-433
145. Zhang Jiankang, Bao Zheng. Theory of orthonormal M-band wavelet packets. Journal of Electronics, 1998,15(3):193-198
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