## 5 Tracking Performance Verification
### Simulator-Based Testing and Verification
As seen in Figure 16b, the phase tracking error of MEMS INS-aided second-order PLL with an integration time of 20 ms and a bandwidth of 3 Hz slightly increased because of the large dynamics. Figure 15: GNSS carrier phase tracking error in the lower dynamic scenario testing based on the simulator. (**a**) Normal PLL (20 ms, 10 Hz); (**b**) normal PLL (20 ms, 3 Hz); (**c**) MEMS INS-aided PLL (20 ms, 3 Hz); (**d**) medium-grade INS-aided PLL (20 ms, 3 Hz). The test results in Figures 15 and 16 are summarized in Table 3, which clearly shows the performance differences of various types of PLLs. Comparing Line 2 and Line 3 in the table, the statistical results of the normal PLL and the INS-aided PLL with a bandwidth of 3 Hz under a CNR of 45 dB-Hz and an acceleration of 5 m/s\({}^{2}\) show that the static tracking error of the normal PLL is slightly lower than that of the INS-aided PLL, which is because the INS bias-type errors are transferred to the PLL. However, the dynamic tracking error of the normal PLL is much larger than that of the INS-aided PLL, which is consistent with the model analysis result in Figure 8. Hence, the bandwidth of the PLL can be set narrow enough only when the PLL is aided by INS to respond to the vehicle dynamics, which verifies the model analysis conclusion in Section 3.3. Comparing the statistical results of the normal PLL with a bandwidth of 10 Hz (Line 1) with the INS-aided PLL with a bandwidth of 3 Hz (Line 3) under a CNR of 45 dB-Hz and an \begin{table}
\begin{tabular}{c c c c c c} \hline
**1** & **PLL Type** & **Testing Conditions** & **Static Portions** & **Motion Portions** & **All Portions** \\ \hline \multirow{2}{*}{**2**} & Normal PLL & Acc = 5 m/s\({}^{2}\) & & & \\  & 20 ms, 10 Hz & CNR = 45 dB-Hz & & & \\ \hline \multirow{2}{*}{**3**} & Normal PLL & Acc = 5 m/s\({}^{2}\) & & & \\  & 20 ms, 3 Hz & CNR = 45 dB-Hz & & & \\ \hline \multirow{2}{*}{**4**} & MEMS-aided PLL & Acc = 5 m/s\({}^{2}\) & & & \\  & 20 ms, 3 Hz & CNR = 45 dB-Hz & & & \\ \hline \multirow{2}{*}{**5**} & IXSEA-aided PLL & Acc = 25 m/s\({}^{2}\) & & & \\  & 20 ms, 3 Hz & CNR = 45 dB-Hz & & & \\ \hline \multirow{2}{*}{**6**} & Normal PLL & Acc = 25 m/s\({}^{2}\) & & & \\  & 20 ms, 10 Hz & CNR = 50 dB-Hz & & & \\ \hline \multirow{2}{*}{**7**} & Normal PLL & Acc = 25 m/s\({}^{2}\) & & & \\  & 20 ms, 3 Hz & CNR = 50 dB-Hz & & & \\ \hline \multirow{2}{*}{**8**} & MEMS-aided PLL & Acc = 25 m/s\({}^{2}\) & & & \\  & 20 ms, 3 Hz & CNR = 50 dB-Hz & & & \\ \hline \end{tabular}
\end{table} 
Table 3: Standard deviations of carrier phase tracking errors (in degrees) for PLLs. Figure 16: GNSS carrier phase tracking error in the higher dynamic scenario testing based on the simulator. (**a**) Normal PLL (20 ms, 10 Hz); (**b**) MEMS INS-aided PLL (20 ms, 3 Hz). acceleration of 5 m/s\({}^{2}\), the static and dynamic tracking errors of the INS-aided PLL are both lower than that of the normal PLL, which is consistent with the model analysis result shown in Figure 8. The advantage of the PLL with INS aiding would be more apparent with the GNSS signal attenuation, as shown in Figure 9. When the maximum acceleration is up to 25 m/s\({}^{2}\), the dynamic tracking error of the normal PLL with a bandwidth of 10 Hz has significant increases. Therefore, the bandwidth of the normal PLL needs to be wider to reduce the dynamic error. On the contrary, the INS-aided PLL's dynamic tracking error only has a small increase, compared to its static tracking error. Therefore, the INS-aided PLL could reduce the carrier phase tracking error by compressing the bandwidth under motion conditions, which agrees with the analysis conclusion in Section 3.