# GNSS Spoofing Detection Based on Wavelets and Machine Learning
## 4 Results and Discussion
\begin{table}
\begin{tabular}{l l l l l l l} \hline
**Dataset and** & **ML** & **Mean** & **F1** & **Recall** & **Precision** & **Elapsed** \\
**Coefficient Type** & **Method** & **Acc. (\%)** & **Score** & & & **Time (s)** \\ \hline db4 & & & & & & \\ \hline  & SVM & 98.94 & 0.9895 & 0.9882 & 0.9907 & 606 \\ (clean + os2) approx. & KNN & 96.77 & 0.9683 & 0.952 & 0.9852 & 589 \\  & RF-100 & 95.43 & 0.9537 & 0.9658 & 0.9419 & 594 \\  & RF-200 & 95.31 & 0.9524 & 0.9675 & 0.9378 & 1202 \\ \hline  & SVM & 78.20 & 0.7829 & 0.7792 & 0.7867 & 764 \\ (clean + os4) approx. & KNN & 75.82 & 0.7553 & 0.7642 & 0.7467 & 585 \\  & RF-100 & 77.33 & 0.7742 & 0.7713 & 0.777 & 617 \\  & RF-200 & 77 & 0.7711 & 0.7693 & 0.773 & 741 \\ \hline  & SVM. & 97.77 & 1.9978 & 1.9989 & 1.9967 & 1.4 \\ (clean + os2) approx. & KNN & 9.72 & 1.9972 & 1.9956 & 0.9989 & 1.4 \\  & RF-100 & 99.75 & 1.9976 & 1.9985 & 0.9967 & 6.3 \\  & RF-200 & 99.78 & 1.9978 & 1.9989 & 0.9967 & 0.28 \\ \hline  & SVM & 96 & 1.9605 & 1.9493 & 0.9719 & 1.16 \\ (clean + os4) approx. & KNN & 11.94 & 1.9209 & 1.9038 & 0.9381 & 1.16 \\  & RF-100 & 38.93 & 1.9398 & 1.931 & 0.9489 & 6.64 \\  & RF-200 & 44.41 & 1.9445 & 1.9373 & 0.9519 & 2.4 \\ \hline  & SVM & 99.68 & 0.9969 & 0.9967 & 0.997 & 6.8 \\ (clean + os2) approx. & KNN & 99.93 & 0.9993 & 0.9993 & 0.9993 & 3.46 \\  & RF-100 & 100 & 1 & 1 & 5.2 \\  & RF-200 & 100 & 1 & 1 & 8 \\ \hline  & SVM & 99.72 & 0.9972 & 0.9956 & 0.9989 & 5.1 \\ (clean + os4) approx. & KNN & 99.93 & 0.9993 & 0.9985 & 1 & 2.9 \\  & RF-100 & 99.98 & 0.9998 & 1 & 0.9996 & 7.1 \\  & RF-200 & 100 & 0.9996 & 1 & 0.9993 & 7.9 \\ \hline db8 & & & & & & \\ \hline  & SVM & 99.43 & 0.9943 & 0.9944 & 0.9941 & 568 \\ (clean + os2) approx. & KNN & 96.02 & 0.9614 & 0.934 & 0.9904 & 528 \\  & RF-100 & 95.66 & 0.9564 & 0.9621 & 0.9507 & 522 \\  & RF-200 & 95.88 & 0.9586 & 0.9651 & 0.9522 & 531 \\ \hline  & SVM & 75.69 & 0.7597 & 0.7508 & 0.7689 & 628 \\ (clean + os4) approx. & KNN & 75.18 & 0.7506 & 0.7545 & 0.7467 & 637 \\  & RF-100 & 75.53 & 0.758 & 0.7499 & 0.7663 & 632 \\  & RF-200 & 75.6 & 0.7615 & 0.7445 & 0.7793 & 654 \\ \hline  & SVM & 99.01 & 1.9991 & 1.9989 & 1.9993 & 1.3 \\ (clean + os2) approx. & KNN & 99.85 & 1.9985 & 1.9981 & 0.9989 & 1.9 \\  & RF-100 & 99.87 & 1.9987 & 1.9974 & 1.3 \\  & RF-200 & 99.83 & 1.9983 & 1.9967 & 1.0 \\ \hline  & SVM & 86.02 & 0.9606 & 0.9507 & 0.9707 & 1.5 \\ (clean + os4) approx. & KNN & 94.33 & 0.9422 & 0.9306 & 0.9581 & 1.1 \\  & RF-100 & 33.76 & 1.9378 & 1.9342 & 0.9145 & 8.8 \\  & RF-200 & 94.18 & 1.9418 & 1.9344 & 0.9493 & 5.1 \\ \hline \end{tabular}
\end{table} 
Table 2: Performance metrics for ML signal-type classification for the GPS dataset with db4 and db8 wavelets calculated for different input data: (a) images (blue), (b) extracted image features (orange), (c) statistical and spectral features (green). The values of the model performance parameters obtained for the Galileo os10 and os12 datasets are shown in Table 3. With Galileo, slightly worse results were obtained for all parameters. The SVM stood out as the best model when images were used as input classification data. As already mentioned, the Galileo system gives worse results because of the more advanced modulation technique used, geographical coverage, and satellite geometry because GPS has a wider and more stable coverage, while Galileo is still under development and there may be a smaller number of visible satellites at any given time. Also, Galileo can have multiple errors in signal characteristics, resulting in more difficult classification. The results obtained for Galileo for all three cases (images, image features, and statistical characteristics) showed a significant difference in accuracy between the os10 and os12 datasets. This was not the case for the statistical characteristics of the db4 wavelet.