Multiscale Analysis of GPS Time Series from Non-decimated Wavelet to Investigate the Effects of Ionospheric Scintillation

Gabriela de Oliveira Nascimento Brassarote, Eniuce Menezes de Souza, João Francisco Galera Monico

Abstract


Due to the numerous application possibilities, the theory of wavelets has been applied in several areas of research. The Discrete Wavelet Transform is the most known version. However, the downsampling required for its calculation makes it sensitive to the origin, what is not ideal for some applications,mainly in time series. On the other hand, the Non-Decimated Discrete Wavelet Transform (or Maximum Overlap Discrete Wavelet Transform, Stationary Wavelet Transform, Shift-invariant Discrete Wavelet Transform, Redundant Discrete Wavelet Transform) is shift invariant, because it considers all the elements of the sample, by eliminating the downsampling and, consequently, represents a time series with the same number of coefficients at each scale. In the present paper, the objective is to present the theorical aspects of the a multiscale/multiresolution analysis of non-stationary time series from non-decimated wavelets in terms of its implementation using the same pyramidal algorithm of the decimated wavelet transform. An application with real time series of the effect of the ionospheric scintillation on artificial satellite signals is investigated. With this analysis some information and hidden patterns which can not be detected in the time domain, may therefore be explained in the space-frequency domain.

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References


C. CHATFIELD, The Analysis of Times Series: An Introduction , Chapman and Hall: London, 2003.

I. DAUBECHIES, Ten Lectures on Wavelets, SIAM, Philadelphia, PA, 1992.

P. A. MORETTIN, Ondas e Ondaletas: da análise de Fourier à análise de ondaletas, EDUSP, São Paulo, 1999.

P. A. MORETTIN, C. M. C. TOLOI, Análise de Séries Temporais, Edgar Blucher: São Paulo, 2004.

G. P. NASON, Wavelet Methods in Statistics with R, Springer, New York, 2008.

G. P. NASON, B. W. SILVERMAN, The stationary wavelet transform and some statistical applications,

In Lecture Notes in Statistics, 103, Springer-Verlag (1995), 281--299.

D. B. PERCIVAL, A. T. WALDEN, Wavelets Methods for Time Series Analysis, Cambridge University Press, Cambridge, England, 2000.

J.H. STRANGEWAYS, Determining scintillation effects on GPS receivers, Radio Science, v. 44, 2009, doi:10.1029/2008RS004076.




DOI: https://doi.org/10.5540/tema.2015.016.02.0119

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Trends in Computational and Applied Mathematics

A publication of the Brazilian Society of Applied and Computational Mathematics (SBMAC)

 

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