## 7 Validation and Use of the Open-Loop Metrics  
In this section, in order to validate the definition of the the new metrics and demonstrate their use, real datasets collected in low-latitude regions are used. A first dataset is derived from the data collection campaign collected in the frame of the MImOSA project [36] by means of a GNSS SDR data acquisition system [8]. Data are related to GPS L1 C/A signal collected along equatorial regions at \(-22.120\,045^{\circ}\) N, \(-51.408\,671^{\circ}\) E on 25 March 2015. The signal was sampled at \(5\,\mathrm{Msamples}/\mathrm{s}\), with a resolution of 16 bits, and demodulated at baseband. To measure the effects of scintillations, the \(R_{4}\) and \(S_{4}\) parameters are employed and compared. The \(S_{4}\) has been computed by means of a software routine processing the I and Q correlator outputs provided by the closed loop tracking of a GNSS software receiver, and following the methodology explained in Section 3. \(R_{4}\) has been derived following computations of Section 6. In such a data collection, several satellite-receiver links are affected by scintillations. Figure 9 plots the \(S_{4}\) and \(R_{4}\) obtained for PRN1 and PRN3. In particular, \(S_{4}\) values are shown in blue and with a rate of \(0.0167\,\mathrm{Hz}\), whereas, in red, \(R_{4}\) values are reported with a rate of \(0.2\,\mathrm{Hz}\).  
It can be noted that \(R_{4}\) and \(S_{4}\) are somehow correlated. However, \(R_{4}\) is obtained at a higher rate than \(S_{4}\), and, being based on the open-loop architecture, it does not require the tracking to be locked, i.e., it can be obtained also in case of strong scintillation events that threaten the correct operation of a GNSS receiver, as detailed in Section 7.1.  
Figure 8: Change of the distribution in the presence of scintillations. (**a**) best fitting Gaussian distribution in absence of scintillations; (**b**) histogram of the samples for a time window including both samples affected by scintillations and not affected. A Gaussian best fitting would be able to match only the “non-scintillated” part of the histogram.  
In order to demonstrate that \(R_{4}\) is actually carrying the same information of \(S_{4}\), a filtering operation is applied to \(R_{4}\) values to resemble \(S_{4}\) values. A moving average window of width \(\omega\) and with amplitude \(\alpha\) is used. Parameters \(\omega\) and \(\alpha\) were obtained minimizing the root mean square error between the two curves over a large dataset of scintillation events representative of all possible dynamics. Similarity between the curves in Figure 10 shows how \(R_{4}\) follows the same trend of the classical \(S_{4}\) index and thus it carries the same kind of information. This comparison validates the definition of \(R_{4}\) as an alternative to \(S_{4}\) that can be obtained at a higher rate. When, in case of strong events, the estimation of \(S_{4}\) is not available or not reliable, \(R_{4}\) can still be calculated and it extrapolates the same kind of information carried by \(S_{4}\) also in these threatening scenarios.  
Furthermore, many recent works on scintillation are questioning the validity of the classical algorithm for \(S_{4}\) estimation, mainly because of the detrending procedures involved, which, if not properly tuned, might mask or falsify scintillation events. A different index, independent from \(S_{4}\), not requiring detrending operations, and exploiting technological advances such as software defined receivers, might help in this process of redefining the metrics for the characterization of the scintillation events [14; 37].