# Detection of Induced GNSS Spoofing Using S-Curve-Bias
## 4 Experiments
### Comparison of Two Methods  
When the false alarm probability is set as 0.1, the thresholds of two algorithms are selected as those in Tables 1 and 2. It is reminded that the detection probability is calculated every 10 s. Figure 9 shows detection probabilities with time for the proposed method and the ratio method, respectively. The red solid and blue dashed curves are separately corresponding to the proposed algorithm and the ratio method. It is noted that the solid and dashed curves are separately corresponding to the proposed algorithm and the ratio method. At about the 110-th s, the proposed method can detect spoofing and the detection probability is almost unity. However, until about the 294-th s, the ratio method reaches the maximal detection probability which is about 0.7. But it is still slightly lower than the proposed method. Therefore, compared with the ratio method, the proposed algorithm can detect induced spoofing at a much earlier stage, which is because the proposed method utilizes the dynamic feature of induced spoofing.  
\begin{table}
\begin{tabular}{c c c} \hline \hline \multicolumn{2}{c}{**False Alarm Probability (\%)**} & \multicolumn{1}{c}{**Detection Threshold**} \\ \hline
1 & 10 & 0.455 \\
2 & 1 & 0.413 \\
3 & 0.1 & 0.379 \\
4 & 0.01 & 0.342 \\
5 & 0 & 0.315 \\ \hline \hline \end{tabular}
\end{table}
Table 2: The relationship between false alarm probability and detection threshold for the ratio method.  
Figure 8: The ratio method curve for PRN 23. The solid curve is the ratio method metric. The dashed curves are detection thresholds according to different false alarm probabilities.  
In order to obtain more details, the detection probabilities of the two algorithms are compared for different lengths of the received signal. When the length of the data are separately 200 s and 294 s, Figures 10 and 11 show the relationship between detection probability and false alarm probability.  
Figure 10 shows the detection probabilities for the first 200 s data. As expected, \(P_{d}\) tends to 1 for increasing \(P_{fa}\) values. However, the curves corresponding to the proposed algorithm attain \(P_{d}\to 1\) faster than the ratio method. Therefore, when the data length is 200 s, the proposed algorithm outperforms the ratio method.  
Figure 10: The relationship between detection probability and false alarm probability for the first 200 s data. The red solid and blue dashed curves are separately corresponding to the proposed algorithm and the ratio method.  
Figure 9: The relationship between detection probability and time length. The red solid and blue dashed curves are separately corresponding to the proposed algorithm and the ratio method. The false alarm probability was set to 0.1.  
When the data length is 294 s, the relationship between the detection probability and false alarm probability is shown in Figure 11. With much longer data length, the performance of the ratio method is significantly improved. It means that, for a given satisfied detection performance, the ratio method needs longer data. At the same time, the performance of the proposed algorithm is also improved. Moreover, the proposed algorithm performs still better than the ratio method.