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

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 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 GPS satellite signals is investigated. Results obtained in this investigation of the time series of the S4 scintillation index indicate the presence of a pattern that is repeated in the series on consecutive days. Through decomposition in multiscale by wavelets, this periodic daily effect could be identified in smoother scales of the wavelet periodogram, estimated and corrected from the original time series. Therefore, this paper presents an innovative methodology for the analysis of the effects of ionospheric scintillation on GPS signals, and take a first step toward separating the effect of scintillation in relations the other effects that may influence its analysis.

Non-decimated wavelets; maximum overlap discrete wavelet transform; multiescale analysis; time series; ionospheric scintillation; GPS