- Open Access
Robust detection of ionospheric scintillations using MF-DFA technique
© Miriyala et al. 2015
- Received: 22 April 2015
- Accepted: 9 June 2015
- Published: 24 June 2015
The performance of Global Navigation Satellite System (GNSS) receivers is limited by the ionospheric scintillation effects that cause signal degradation due to refraction, reflection and scattering of the signals. Hence, there is a need to develop an ionospheric scintillation detection technique for robust GNSS receivers. In this paper, a new algorithm based on multifractal detrended fluctuation analysis (MF-DFA) is proposed for detecting the ionospheric irregularities. The ionospheric and scintillation GNSS data recorded at Koneru Lakshmaiah (KL) University, Guntur, India, was considered for the analysis. The carrier to noise ratio (C/N 0) time series data of GNSS satellite vehicles that are affected due to scintillations was decomposed using adaptive time–frequency methods like empirical mode decomposition (EMD), ensemble empirical mode decomposition (EEMD) and complementary ensemble empirical mode decomposition (CEEMD). It was observed that the CEEMD method combined with MF-DFA provides better results as compared to the EMD and EEMD techniques.
- Global positioning system
- Radio wave propagation
- Complementary ensemble empirical mode decomposition
- Multifractal detrended fluctuation analysis
- Hurst exponent
Ionospheric scintillation is one of the predominant propagation impairments at L-band frequencies that persist because of the existence of irregularities in the ionosphere due to refraction, reflection and scattering of the radio signals (e.g. De Paula et al. 2003; Iyer et al. 2006; Cherniak et al. 2014). When a radio wave passes through the ionosphere, the irregularities distort the wavefront and as the wave moves towards the ground, phase mixing occurs creating a diffraction pattern on the ground. This diffraction phenomenon was determined by the size and strength of the ionospheric irregularities (Yeh and Liu 1982). The diffraction mechanism gives rise to amplitude scintillations which occur mainly due to small-scale irregularities when phase variations are small. However, due to large scale irregularities, the phase fluctuations are dominant and the wave becomes non-coherent thereby focusing and defocusing of the rays is not possible (Wernik et al. 2004). As the interference mechanism is not valid under such conditions, amplitude scintillations do not increase further and phase scintillations become significant (Wernik et al. 2004). Amplitude and phase scintillations degrade the Global Navigation Satellite System (GNSS) receiver’s tracking performance (e.g. Kintner et al. 2007; Aquino and Sreeja 2013). In order to improve the positional accuracy and availability of GNSS receivers, several methods have been proposed to detect the ionospheric scintillations (e.g. Suman et al. 2004; Pullen et al. 2009). A real-time ionospheric scintillation model, which determines the automatic threshold for different scintillation signals using the Neyman–Pearson detector, has been implemented (Venkata Ratnam et al. 2015). Mushini et al. (2012) proposed a wavelet-based detrending technique for detrending GPS signals. Wavelet detrending technique reveals local features of the signals as compared to Butterworth detrended filter (Mushini et al. 2012). Empirical mode decomposition (EMD) and ensemble empirical mode decomposition (EEMD) methods have been found to be suitable for analysing non-stationary signals (Wang et al. 2012). Multifractal detrended fluctuation analysis (MF-DFA) has been successfully implemented in medical and geophysics applications to investigate the self similarities and long-range correlations in the signals (e.g. Kantelhardt et al. 2002; Tanna and Pathak 2014).
The multifractality nature of the ionospheric time series data due to long-range correlations can be analysed using the MF-DFA technique. With this technique, the non-linear properties and complexity of random ionospheric irregularities are determined. In this letter, a novel algorithm, complementary ensemble empirical mode decomposition (CEEMD)–MF-DFA, was proposed and implemented to extract the noise components of the GPS signal. The results obtained using the CEEMD–MF-DFA technique was compared and validated with the wavelet, EMD–MF-DFA and EEMD–MF-DFA techniques.
EMD is an adaptive technique used to analyse non-linear and non-stationary signals. The major advantage of this time–frequency data analysis method lies in deriving the basis functions from the characteristics of the signal, whereas the basis functions in wavelets are predefined based on the mother wavelet used (Mallat 1999). Sifting process is used to generate the intrinsic mode functions (IMF), and a residue which, when added, will give the original signal reconstruction. The residue represents the trend of the signal and cannot be decomposed further. To achieve the effective functioning of EMD, the differences between the frequencies and amplitude must be sufficient for decomposition analysis, which otherwise leads to the limitation known as mode mixing (Huang et al. 1998).
Hence, to avoid the consequences of a mode-mixing problem, an improved EMD algorithm has been proposed known as EEMD. In this method, a Gaussian white noise is added before decomposition to minimise the effects of mode mixing in the EMD process. However, the inclusion of white noise with inappropriate amplitudes will generate a different number of modes that contains the components not related to the signal. Also, it introduces the residual of noise in the reconstructed signal (Wu and Huang 2009).
To overcome the problems of the EEMD method, CEEMD has been proposed in which positive and negative white noises are added to the data. Hence, two sets of ensemble IMFs are produced, and the reconstructed signal can be obtained by finding the mean of these IMFs. In CEEMD, residual of the added white noise contained in the IMFs is eliminated completely (Yeh et al. 2010). IMFs of EMD, EEMD and CEEMD have been derived for preparing inputs of the MF-DFA techniques.
where M is the length of the time series.
where h(q) is the scaling exponent known as generalised Hurst exponent (Hurst 1951). For a multifractal time series data, there exist a number of Hurst exponents for different q orders of fluctuation. For positive values of q, Hurst exponent characterises the scaling nature of the segments with large variations, and for negative q values, h(q) indicates the scaling performance of the segments with small variations exhibiting the multiscaling features of the signal considered (Kantelhardt et al. 2002).
The Hurst exponent value is a key parameter in estimating the threshold, and the IMFs with h(q) greater than the threshold are considered for reconstruction of the signal; the remaining IMFs constitute the scintillation components. As the scintillation noise was assumed as white noise, Hurst exponent of 0.5 was considered for analysis. In the case of EMD–MF-DFA, to reduce mode-mixing effects, a threshold φ = H + 0.2 = 0.7 was used for identifying the noisy IMFs. For the EEMD–MF-DFA and CEEMD–MF-DFA techniques, a threshold φ = H = 0.5 was considered as a mode-mixing problem does not exist in these methods (Mert and Akan 2014).
Koneru Lakshmaiah (KL) University, Guntur (16.31°N, 80.37°E), falls under the transition zone of equatorial ionisation anomaly crest and trough of low latitude regions. Pseudo random noise (PRN) code 15 satellite signal (29 June 2013) was applied with the CEEMD–MF-DFA technique. To avoid multipath effects, the signal with elevation angles greater than 30° was considered. The maximum amplitude scintillation index (S 4 index) value observed was 0.85 at 23.28 h (IST). The corresponding decrease in carrier to noise ratio (C/N 0) to 31 dB-Hz indicates the presence of non-linear irregularities in the ionosphere.
A new algorithm based on CEEMD–MF-DFA was implemented for mitigating the noise components due to ionospheric scintillations in GNSS signals. The performance of the proposed method was compared with the results of the wavelet, EMD–MF-DFA and EEMD–MF-DFA methods. The IMFs obtained using EMD, EEMD and CEEMD for C/N 0 signal were applied to the MF-DFA method to calculate the Hurst exponent, which is essential for estimating the threshold for detecting the noise due to scintillation. 8.20 dB-Hz of noise was detected and reduced using CEEMD–MF-DFA. It is evident from the results that more than 1.1 dB-Hz noise was filtered out by the proposed method as compared to other techniques. The results will be useful for understanding the morphology of non-linear ionospheric irregularities.
The above work has been carried out under the project titled “Development of Ionospheric Forecasting models for Satellite based Navigation Systems over low latitude stations” sponsored by the Department of Science and Technology, New Delhi, India, vide sanction letter No: SR/FTP/ETA-0029/2012, dated: 08.05.12. The authors are very much thankful to Dr. D. Venkata Ratnam, Professor, KL University, for his outstanding guidance in the work and cooperation.
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