# GNSS Spoofing Detection Based on Wavelets and Machine Learning
## 5 Conclusions  
This paper proposed an integrated approach which combined the discrete wavelet transform and machine learning for spoofing attack detection and signal-type classification in the pre-correlation phase. The paper aimed to investigate radio frequency fingerprinting methods with emphasis on the discrete wavelet transform, which is in its infancy in the GNSS field. The motivation for the research presented in this paper was to show how the DWT and machine learning methods could be used for the successful detection of spoofing attacks and signal-type classification. The motivation was also to try to reduce computational complexity by using some other data type than an image. For the first time, in this research, radio frequency fingerprinting methods were applied on OAKBAT's static scenarios and different satellite constellations (GPS and Galileo). Models performance metrics showed that all machine learning models achieved very good classification results, but generally, the SVM with a Gaussian kernel exhibited the best behavior for the different types of input data, both GPS and Galileo constellations, and both types of the used Daubechies wavelets, db4 and db8. For example, for images as the input data, the SVM for the GPS os2 dataset (where authentic signals have a 10 dB power advantage compared to fake signals) achieved 98.94% accuracy for the db4 and 99.43% for the db8 wavelet. On the other hand, the SVM method for the GPS os4 dataset in which authentic signals have a 0.4 dB power advantage to fake signals, had worse results with an accuracy of 78.20% for the db4 and 75.69% for the db8 wavelet. The same behavior of the models applied to the Galileo os10 and os12 datasets, which are equivalent to the GPS os2 and os4 datasets in terms of power level. Generally, in comparison with GPS, Galileo had slightly worse results for all parameters. The reason was the geographical coverage and satellite geometry, because GPS has a wider and more stable coverage, while Galileo is still under development. When comparing the os2 with the os10 dataset for images as the input data and the SVM method for the db4 wavelet, os2 had an accuracy of 98.94% and os10 had an accuracy of 93.94%. The same was true when comparing os4 with os12. For images as the input data and SVM as the classification method, the accuracy for os4 was 78.20% and the accuracy for os12 was 75%. Regarding the wavelet type, the application of both db4 and db8 gave good results. Regarding the computational complexity, the highest was for the KNN method which used images as input classification data due to the dominant quadratic complexity \(N^{2}\). The lowest computational complexity was obtained by the SVM method which used pre-extracted features for classification. It can be concluded that the input data type significantly affects the computational complexity and choosing pre-extracted features for classification reduces the computational complexity. The evaluation results showed that the proposed integrated approach gave very good results in spoofing attack detection and signal-type classification. Based on the results in this paper, it can be concluded that the SVM model with a Gaussian kernel in combination with Daubechies db4 and db8 wavelets represents a robust and powerful approach in weak- and high-spoofing scenarios. Furthermore, it is the most suitable for use in terms of computational complexity and with the different types of input classification data. Using pre-extracted features as input classification data reduces the computational complexity. To confirm the robustness of the proposed approach, future work will include the application of the integrated approach on different GPS and Galileo datasets by combining approximation and detail DWT coefficients and several decomposition levels. Furthermore, experiments with some other types of wavelets will be performed.