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

Authors

  • Gabriela de Oliveira Nascimento Brassarote UNESP - São Paulo State University
  • Eniuce Menezes de Souza UEM - Maringá State University
  • João Francisco Galera Monico UNESP - São Paulo State University

DOI:

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

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.

Author Biographies

Eniuce Menezes de Souza, UEM - Maringá State University

Department of Statistics

João Francisco Galera Monico, UNESP - São Paulo State University

Department of Cartography

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.

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Published

2015-09-07

How to Cite

Brassarote, G. de O. N., Souza, E. M. de, & Monico, J. F. G. (2015). Multiscale Analysis of GPS Time Series from Non-decimated Wavelet to Investigate the Effects of Ionospheric Scintillation. Trends in Computational and Applied Mathematics, 16(2), 119. https://doi.org/10.5540/tema.2015.016.02.0119

Issue

Vol. 16 No. 2 (2015)

Section

Original Article

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