## 4 Simulation Experiments
### Effectiveness of the Proposed Technique  
In this subsection, the effectiveness of the proposed technique is verified. First, the performance of the phase bias detection is validated. Then, the carrier tracking performance is focused on. For comparison, the RPC with averaging estimation and the RPC with robust estimation are both considered. They are denoted in the figures by the legends \"RPC, AE\" and \"RPC, RE\", respectively. Note that the results without phase compensation are denoted by the legend \"Original\".  
Figures 4 and 5 show the designed indicators and the corresponding phase bias detection statistics, respectively. From Figure 4, it can be seen that the ICR is close to zero when there is no jammer; otherwise, it becomes extremely large, indicating that the interference is being mitigated. Moreover, when the jamming environment changes, significant changes in the ICR and POW occur immediately, indicating that a new phase bias is induced. It can also be seen from Figure 5 that the designed indicators are suitable for phase bias detection by setting appropriate thresholds. It should also be noted that these two detection statistics are complementary. Taking the complement of the two allows the phase bias appearance time to be fully located. This alerts the phase compensation techniques to start.  
Figure 6 shows the carrier tracking errors with and without phase compensation techniques. From Figure 6a, it is clear that the PI algorithm without phase compensation techniques introduces significant biases into the carrier phase measurement. The carrier phase measurement accuracy is sacrificed for the purpose of interference mitigation. It can also be noted that the SPC can reduce the phase distortions to some extent, but its performance is limited due to poor phase bias estimation. The RPCs compensate for most  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline GNSS signal \(C/N_{0}\) & 40 dB-Hz \\ GNSS elevation angle & 75 deg \\ GNSS azimuth angle & 200 deg \\ BB interference-to-noise ratio & 40 dB \\ BB elevation angle & 15 deg \\ BB azimuth angle & 60 deg \\ CW interference-to-noise ratio & 50 dB \\ CW elevation angle & 10 deg \\ CW azimuth angle & 150 deg \\ \hline \hline \end{tabular}
\end{table}
Table 1: Parameters used in the simulations.  
phase biases and provide the best carrier phase accuracy. Moreover, when there are no outliers in the observation window, the RPC with averaging estimation and the RPC with robust estimation achieve similar phase bias estimation and compensation performance. This result is in agreement with that in Section 4.1. It can also be seen from Figure 6b that when the phase bias appears, the Doppler frequency jumps accordingly and then converges to the unbiased steady state. The use of phase compensation techniques can reduce the Doppler frequency errors during the transient state, thereby improving the Doppler frequency accuracy.  
Figure 4: Designed indicators for phase bias detection. **(a)** ICR. **(b)** POW.  
Figure 5: Phase bias detection statistics. **(a)**\(d_{\text{ICR}}\). **(b)**\(d_{\text{POW}}\).  
Figure 6: Carrier tracking errors with and without phase compensation techniques. **(a)** Carrier phase error. **(b)** Doppler frequency error.