Study On Wavelet Analysis Theory And Its Application In Non-Linear Geodetic Signal

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.