## 2 GNSS Scintillation Measurement  
As previously recalled, ionospheric scintillations are rapid and hard-to-predict fluctuations of the amplitude and phase of radio signals propagating through the atmosphere. The propagation through ionosphere is one of the main error sources affecting the GNSS signal processing stages of the receiver. In fact, the signal is potentially affected by strong degradation, introducing significant problems in any GNSS application requiring high accuracy, precision, reliability and continuity. On the other hand, scintillation mitigation is still an open issue in most of the commercial devices, mainly due to the inherently random nature of such events, which makes modelling impossible [13]. Scintillations are then, at the moment, one of the main limiting factors for high accuracy applications.  
Scintillation events are traditionally characterized by means of two indices evaluated over an 60 s observation interval.  
* The amplitude scintillation index, named \(S_{4}\), estimates the amount of amplitude fluctuations. Such an index is computed as the normalized standard deviation of the detrended Signal Intensity (SI), derived from in-phase (I) and quadrature (Q) prompt correlation outputs, normalized by its mean value.
* The phase scintillation index denoted \(\sigma_{\phi}\) measuring the impact on the phase of the signal; it is equivalent to the standard deviation of the detrended carrier phase measure.  
The majority of the works related to scintillation detection and monitoring are based on the analysis of the value of these two indices, often comparing them with predefined thresholds. However, the estimation of \(S_{4}\) and \(\sigma_{\phi}\) requires the GNSS receiver to be in lock conditions, i.e., the values of I and Q correlators must be available. In the case of strong scintillation events, receivers designed according to the classical closed-loop architecture might not be robust enough to keep the correct tracking of the signals, incurring in a LoL event. If this happens, the receiver is not able to provide the values needed to characterize the the scintillation event, which is, in a generic way, classified as \"strong\". At the same time, the computation of \(S_{4}\) and \(\sigma_{\phi}\) requires a detrending operation, which envisages the use non-trivial mathematical operations. Although this process has been standardized and is largely used, several authors pointed out that it can introduce artifacts in the signal processing chain falsifying the scintillation estimation [14; 15]. This opens the way to the definition of alternative measures of scintillation [14; 16; 17; 18].  
Some of these methods start from the observation that, in the presence of scintillations, the statistics of the samples of the amplitudes change over time and it is correlated to the values taken by the \(S_{4}\) index. In statistical terms, according to [4], scintillation-derived amplitude fluctuations follow a Nakagami-m distribution, the shape of which depends on the severity of the fluctuations. This is depicted in Figure 1, where the histograms of the samples for different \(S_{4}\) values are displayed. The method introduced in this paper aims at estimating the statistic of the amplitude samples in the presence of scintillations, building on top of that a new metric for the characterisation of the scintillation event, as will be explained in the following sections.