Browsing by Author "Savolainen, Outi"

Today, Global Navigation Satellite Systems (GNSS) provide services that many critical systems [1] as well as normal users, need in everyday life. These signals are threatened by unintentional and intentional interference. The received satellite signals are complex-valued by nature, however, state-of-the-art anomaly detection approaches operate in the real domain. Changing the anomaly detection into the complex domain allows for preserving the phase component of the signal data. In this thesis, I developed and tested a fully complex-valued Long Short-Term Memory (LSTM) based autoencoder for anomaly detection. I also developed a method for scaling of complex-numbers that forces both real and imaginary units into the range [-1,1] and does not change the direction of a complex vector. The model is trained and tested both in the time and frequency domains, and the frequency domain is divided into two parts: real and complex domain. The developed model’s training data consists only of clean sample data, and the output of the model is the reconstruction of the model’s input. In testing, it can be determined whether the output is clean or anomalous based on the reconstruction error and the computed threshold value. The results show that the autoencoder model in the real domain outperforms the model trained in the complex domain. This does not indicate that the anomaly detection in the complex domain does not work; rather, the model’s architecture needs improvements, and the amount of training data must be increased to reduce the overfitting of the complex domain and thus improve the anomaly detection capability. It was also investigated that some anomalous sample sequences contain a few large valued spikes while other values in the same data snapshot are smaller. After scaling, the values other than in the spikes get closer to zero. This phenomenon causes small reconstruction errors in the model and yields false predictions in the complex domain.