## 3 Spoofing Detection Method
### Performance Analysis  
The receiver operator characteristic (ROC) can reflect the detection performance of the detection method when the threshold changes. This section takes the ROC as a reference and analyzes the factors affecting the detection performance through simulation. During the simulation, two navigation signals are set, with their true directions being \((185^{\circ},85^{\circ})\) and \((270^{\circ},65^{\circ})\). The spoofer simulates the transmission of the second set of navigation signals, and the angle at which the spoofing signal deviates from the true signal is represented as \((dq_{2},d\theta_{2})\). Assuming that the receiver is spoofed, the first set of signals it receives is a real signal, and the second set of signals is a spoofing signal with a different direction from the real signal. Unless otherwise specified, the parameter settings for the rotating antenna during the simulation process are shown in Table 1. The entire simulation process is based on Formulas (25)-(29). By inputting the parameters from Table 1 into Formula (29) to calculate the ROC curve, the relationship between relevant factors and detection performance can be further analyzed. During this process, no navigation signal is generated and no navigation solution is calculated. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline \(r(\mathrm{m})\) & 0.2 \\ \(\omega(^{\circ}/\mathrm{s})\) & 30 \\ \(T_{0}(\mathrm{s})\) & 1 \\ \(\beta(^{\circ})\) & 70 \\ \(N\) & 100 \\ \(\sigma^{2}_{\mathrm{CNR}}(\mathrm{dB}^{2}\mathrm{Hz}^{2})\) & 1 \\ \(\sigma^{2}_{\mathrm{Q}}(\mathrm{m}^{2})\) & 0.02 \\ \(d\varphi_{2}(^{\circ})\) & 10 \\ \(d\theta_{2}(^{\circ})\) & 10 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation parameter settings. Figure 4: Architecture of spoofing-detection method. First, we analyzed the impact of the spoofing signal deviation angle on the performance of the spoofing-detection methods. Figure 5 shows the ROC when the spoofing signal's pitch angle direction deviates from the real signal's angle. Figure 6 shows the ROC when the azimuth direction of the spoofing signal deviates from the angle of the real signal. The simulation results show that the more the incident angle of the spoofing signal deviates from the true signal, the better the detection performance. By observing Formula (26), it was found that the parameters \(r\sin(\omega T_{0})\), \(\beta\), and \(N\) also affect the performance of the detection algorithm. Figures 7-9 show the ROC with different values of the above parameters. The simulation results show that the changes in the above parameters will affect the ROC. By analyzing the simulation results, the following conclusions can be drawn: (1) The larger the angle between the axis of the rotating antenna and the horizontal plane, the better the spoofing detection performance. (2) The more sampled data, the better the performance of the spoofing detection. (3) The larger the horizontal projection distance from the antenna center to the rotation center, the better the detection performance. The horizontal projection distance is the product of the cosine value of the antenna inclination angle and the radius. When the inclination angle of the antenna is determined, the larger the antenna radius, the better the detection performance. (4) The  
Figure 5: Relationship between the deviation of the spoofing signal pitch angle from the true signal angle and ROC. Figure 6: Relationship between the deviation of the spoofing signal azimuth angle from the true signal angle and ROC. closer the product of the antenna rotation angular velocity and sampling period is to \(\pi\), the better the detection performance. Figure 10 shows the relationship between the rotation speed and the detection performance. It can be seen that the detection performance is proportional to \(\sin(\omega T_{0})\), which is consistent with the simulation results in Figure 7.  
Figure 8: Relationship between \(\beta\) and ROC. Figure 7: Relationship between \(r\sin(\omega T_{0})\) and ROC.