International Journal of Navigation and Observation

Volume 2016, Article ID 3582176, 18 pages

http://dx.doi.org/10.1155/2016/3582176

## Estimation of Scintillation Indices: A Novel Approach Based on Local Kernel Regression Methods

^{1}Norwegian Mapping Authority, Geodetic Institute, 3511 Hønefoss, Norway^{2}Department of Mathematical Sciences and Technology, NMBU, 1432 Akershus, Norway^{3}Department of Electronics and Telecommunications, NTNU, 7491 Trondheim, Norway

Received 25 January 2016; Revised 25 April 2016; Accepted 9 May 2016

Academic Editor: Sandro M. Radicella

Copyright © 2016 Mohammed Ouassou et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

We present a comparative study of computational methods for estimation of ionospheric scintillation indices. First, we review the conventional approaches based on Fourier transformation and low-pass/high-pass frequency filtration. Next, we introduce a novel method based on nonparametric local regression with bias Corrected Akaike Information Criteria (AICC). All methods are then applied to data from the Norwegian Regional Ionospheric Scintillation Network (NRISN), which is shown to be dominated by phase scintillation and not amplitude scintillation. We find that all methods provide highly correlated results, demonstrating the validity of the new approach to this problem. All methods are shown to be very sensitive to filter characteristics and the averaging interval. Finally, we find that the new method is more robust to discontinuous phase observations than conventional methods.

#### 1. Introduction

Global Navigation Satellite Systems (GNSS) are based on satellite signals being transmitted to receivers on the ground. These signals must pass through the ionosphere on the way, where the variation in electron density causes undesirable fluctuations in the observed signal. This distortion, known as* scintillation*, can affect both the amplitude and phase of GNSS signals. The relevant electron density variations range from decameters to kilometers in size [1–3].

In the auroral zones, it is much more common for phase scintillation than amplitude scintillation to be the dominant effect (e.g., [4–6]). Scintillation is a large challenge for navigational systems, as it can disturb not only single-receiver systems but also networked systems [3, 4, 7–9]. In a worst-case scenario, the user receiver can end up with a loss of signal lock, which causes discontinuities in the phase measurements. This is known as a* cycle-slip*.

A good understanding of the ionosphere morphology can aid the development of suitable mitigation algorithms, that is, algorithms that assign weights to observations based on the scintillation distortion of each satellite link.

To be more specific, a more realistic stochastic model for GNSS observables would have to take into account the variance caused by scintillation. This would avoid biased solutions. Today, the stochastic model includes the following: correlation among observations [10]; satellite elevation dependency modeled by exponential function [11]; temporal and cross-correlations [12]; and multipath detection and monitoring [13]. That is, a suitable robust weighting algorithm that reduces the influence of the satellite exposed by scintillation will look similar to the one proposed by Eueler and will enhance the ability to resolve the carrier-phase ambiguity and to improve the stochastic model for GNSS processes.

This is most commonly gauged by the* phase scintillation index *, which is simply defined as the standard deviation of the detrended carrier phase over some period of time. A critical step in the calculation of is a frequency filter, which is used to separate the high-frequency ionospheric distortions from the low-frequency distortions due to, for example, multipath interference. The scintillation indices are usually calculated for one-minute intervals and then processed with a Butterworth sixth-order high-pass filter [14–23]. However, the estimated value of can be highly sensitive to the cutoff frequency of the filter. While the most common cutoff frequency is 0.1 Hz, it has been shown that this is suboptimal at high latitudes and that higher values like 0.3 Hz might yield better results [24]. The variation in the carrier phase of GNSS signals is also commonly quantified using the rate of total electron content index (ROTI) [25–27]. Several other indices for quantifying phase variations have also been proposed [24, 28–32]. It is worth noting that all of these indices are directly related to the scintillation signal variance.

Some scintillation indices use methods based on wavelet transforms for the filtration. A major advantage of wavelet filters is that they manage to preserve local features in the signal, thus avoiding misinterpretation that can occur when using standard filter approaches [24, 33–36]. While such wavelet filters may yield better results than conventional filters, the computational load can become very high, especially when processing data with high sampling rates (50+ Hz). The improvement that can be achieved by substituting a wavelet filter for the conventional filters must therefore be weighed against the computational load required, especially if the algorithm is intended for real-time applications.

The primary focus of this paper is on nonparametric local regression with bias Corrected Akaike Information Criteria as a viable alternative for the computation of reliable scintillation indices. In addition, we perform a statistical analysis of the scintillation indices and show that they can be well described by the Nakagami and Frechet distributions. The paper is organized as follows.

Section 2: it includes detailed description of the data sets used in this paper; Section 3: it deals with digital filter construction of low-pass filter algorithms for amplitude scintillation index computation and high-pass filter algorithms for phase scintillation computation. Filter types discussed are the Chebyshev, Butterworth, and Elliptic filters. These algorithms are used to validate the new approach; Section 4: it tackles nonparametric regression with kernel smoothing; Section 5: this section presents how the scintillation indices are computed by the conventional methods and the new approach; Section 6: it shows statistical analysis of scintillation indices, including distributions, sensitivity, and correlation analysis of implemented algorithms; Section 7: it presents generalization of the preceding sections; Section 8: it includes conclusion and applications of the results.

#### 2. Test Data

The data used for the investigation herein was obtained from three different NRISN observation sites in the northernmost parts of Norway. These sites are highlighted with an italic typeface in Table 1 and encircled in Figure 1. The observational data is taken from day 50 of year 2014, which according to the I95 index corresponds to relatively high ionospheric activity. (The* I95 index* [37] is used for the classification of ionospheric activity by CPOS software.) For more information about the ionospheric activity levels, see Figures 15 and 16. The NRISN sites are equipped by dual-frequency Septentrio PolaRxS receivers tracking GPS and GLONASS L1 and L2 frequencies with sampling rate of 100 Hz and are capable of tracking up to 12 satellites for each system. The baselines vary between 176 and 1988 km, and the height difference between sites is around m. To give a full picture of the baseline lengths and the height difference between sites above the ellipsoid WGS84, Tables 2 and 3 are provided.