## 5 Experimental Results and Analysis
### Anti-Spoofing Effect of the Multi-Correlator Structure  
In order to facilitate the discussion, in addition to the above spoofing, spoofing with fixed short delays is applied to PRN18, PRN15, and PRN26, and spoofing with fixed long delays is applied to PRN9 and PRN6. The setups of time delays are shown in Table 1. The counterfeit signal and its corresponding authentic signal from each satellite are set to have the same carrier phase. Figure 11 shows the estimation result of PRN22's carrier phase when the carrier phases of the counterfeit signal and its corresponding authentic signal are different. Hence, the carrier phases of the counterfeit signal and its corresponding authentic signal from each satellite are set to be the same in order to focus on the estimation of time delay and amplitude. In addition, we let \(A=0.2A_{0}\) empirically. \begin{table}
\begin{tabular}{c c} \hline \hline
**Counterfeit Signal** & **Fixed Delay** \\ \hline PRN18 & 0.11 chips \\ PRN15 & 1.05 chips \\ PRN26 & 1.5 chips \\ PRN9 & 1.69 chips \\ PRN6 & 2.49 chips \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Time delays of counterfeit signals. Figure 10: The \(\delta_{\text{cp}}\) of the code phase discriminator of PRN21. Figure 9: Outputs of the prompt correlators of PRN21 I and Q branches. Figure 11 shows \(\hat{x}\) and \(\hat{y}\) of the counterfeit signal of PRN22. It can be seen that the carrier phase of the counterfeit signal is different from that of the authentic signal, which is consistent with the results in Figures 7 and 8. If the effect of the data bit flipping is disregarded, the carrier phase of the counterfeit signal is approximately \(-\pi/2\). Since the results of ML estimation at different instants are independent, and its effects at different instants are similar, the estimation results at a certain instant are visualized in order to demonstrate the effect of the multi-correlator structure and to verify the estimation method described conveniently in Section 4. Figure 12 shows all correlators' outputs of I branches of PRN22, PRN18, PRN15, and PRN26, and corresponding estimated time delays and amplitudes of the counterfeit signals. It is observed that the estimates are consistent with the true values, which means the proposed multi-correlator structure is accurate in estimating the time delays and amplitudes of the counterfeit signals. Figure 12: _Cont._  
Figure 13 shows all correlators' outputs of I branches of PRN9 and PRN6. Since the time delay of the counterfeit signal of PRN9 is close to 1.6 chips, the stimulating effect on the last correlator in  
Figure 12: Estimated time delays and amplitudes of the counterfeit signals with short delays  
subfigure (a) is significant. The receiver can easily determine that the counterfeit signal has a long delay and directly starts discriminating the phase of the authentic signal. Note that the sizes of \(\hat{x}_{7}\) and \(\hat{x}_{8}\) in subfigure (b) are close. However, if the time delay of the counterfeit signal is within the effective estimation interval of the multi-correlator structure from 0 to 1.6 chips, it is impossible that \(\hat{x}_{n}\) and \(\hat{x}_{n+1}\) of two adjacent correlators are close in size but are opposite in direction. Therefore, this can help the receiver to recognize the counterfeit signal with a long delay, and then perform phase discrimination directly on the authentic signal. Figure 14 shows the positioning results after applying all the spoofing and the positioning results after employing the proposed anti-spoofing method in an east-north-up geographic coordinate system. The period of data update is 20 ms. In subfigure (a), the positioning of the target receiver is normal at 0-300 ms. Then, all the spoofing is executed at 300 ms. As a result, the positioning results of the target receiver gradually deviate from the real position and finally arrive at the steady state.