## 3 Methodology
### Main Flow and Procedures of the Proposed Approach  
The overall methodology is pictorially described in Figure 1. On each of the \(C/N_{0}\) time series generated by the GNSS receiver for each satellite in the constellation, an analysis of the quality of the data is performed. On the overall set of 47 satellites (24 GPS and 23 Galileo satellites), roughly half were in conditions of visibility and not all of them provided significant information for the detection of the interference because the GNSS signal did not have enough strength for the whole measurement duration. The consequence is that the generated \(C/N_{0}\) would not have enough \(C/N_{0}\) points for further processing or its level would be below an acceptable threshold. For this reason, a pre-processing step is performed, where only the satellites with a significant mean value are considered. The application of a threshold-based approach for filtering the appropriate satellites may not be suitable in this context for the following reasons: (1) It is difficult to set a specific threshold level and the consequent steps in the methodology could be biased by a wrong threshold value. On the other hand, an optimization of the threshold would require the repeated execution of the entire set of procedures described in this methodology, which would be quite time consuming. (2) Due to the presence of interference, the \(C/N_{0}\) series are different for each interference condition or level of attenuation or bit-depth in the data set. As a consequence, a filtering step with the threshold may create unbalanced data sets across the different conditions, which may complicate the application of ML/DL more. This approach is based on a sorting of the average \(C/N_{0}\) values for each satellite time series where only the first 8 satellites are considered. The number 8 was chosen as a trade-off between having enough satellites for the application of ML/DL and the need to have \(C/N_{0}\) time series with a significant level of quality (\(C/N_{0}\) over 36 dB-Hz). As a consequence, this first pre-processing step for the GNSS satellite selection is data driven and it does not require hyper-parameters. The subsequent step is to apply a sliding window with an overlapping factor on the \(C/N_{0}\) time series for each of the considered 8 satellites. While both the overlapping factor and the length of the sliding window could be considered hyper-parameters in a generic time series analysis, their values can be defined in this specific context because the GNSS receiver will process the GNSS signal in a limited number of samples and a small value of overlapping factor should be used. The length of the sliding window should also be long enough to support the estimate of statistical features in the ML approach and to support the application of the CNN in the DL approach. In addition, the overlapping factor should be small enough to produce a significant number of samples in the \(C/N_{0}\) time series with a length of 17,448 samples. Based on these considerations, a value of 4 was chosen for the overlapping factor and a value of 32 for the sliding window size to produce a data set of 433 samples for each satellite. In the next phase, two different branches of the methodology are adopted. For the ML approach, a set of features were applied to each sliding window to create a feature space for each satellite. The feature spaces were concatenated on the 8 satellites to create the final feature space on which the shallow Machine Learning algorithms described in Section 3.2 are applied. For the DL approach, the segments based on the sliding window length were used as input to the CNN. However, the size of the data set (433 samples) may be too small for the application of the CNN. To address this aspect, a simple data augmentation based on the application of Additive White Gaussian Noise (AWGN) with values \(\pm 1\) dB was used to increase it to three times the size of the original data set. See [15; 16] for a discussion on the advantages of data augmentation for CNNs.