【作者】 曲国庆；

【导师】 党亚民； 章传银；

【作者基本信息】 山东科技大学 ， 大地测量学与测量工程， 2008， 博士

【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。更多还原

【Abstract】 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.更多还原