## 5 Tracking Performance Verification
### Simulator-Based Testing and Verification  
A GNSS/INS hardware signal simulator can generate typical scenarios with strict repeatability, well controlled motion states, less external disturbance and, most importantly, with perfect true values for error analysis. The simulation testing setup is shown in Figure 14. GPS L1 and IMU signals from the simulator are connected to the deeply-coupled hardware prototype through the RF module and the IMU module, respectively. Additionally, Table 2 shows the two typical IMU configuration parameters used in the simulation, one for low-grade MEMS IMU, the other for medium-grade IMU. To test the PLL's dynamic tracking performance, two sets of motion scenarios are designed, including the static,  
Figure 13: Time delay of the INS aiding data. acceleration/deceleration, constant speed, turning, _etc._, while the maximum acceleration is less than 5 m/s\({}^{2}\) in the first set of motion scenarios, and the maximum acceleration is about 25 m/s\({}^{2}\) in the second set of motion scenarios. In the lower dynamic scenario (the maximum acceleration is less than 5 m/s\({}^{2}\)), the tracking error of pseudorandom noise (PRN) 22 as an example is analyzed with a CNR of 45 dB-Hz and an elevation of 20 degrees. Figure 15 shows the tracking errors of normal PLLs and INS-aided PLLs. While the upper part in each subfigure is the Doppler between the vehicle and satellite, which could reflect the vehicle movement toward the satellite, the lower part is the discriminator output, which could reflect the phase tracking error [27]. Figure 15a shows the tracking performance of the normal second-order PLL with an integration time of 20 ms and a bandwidth of 10 Hz. Since the vehicle acceleration is small and the bandwidth of the PLL is wide, the tracking error almost has no change when the vehicle movement changes. Figure 15b depicts the tracking error of the normal second-order PLL with an integration time of 20 ms and a bandwidth of 3 Hz. The overall magnitude of the tracking error does not significantly reduce compared with that in Figure 15a. That is because compressing the bandwidth cannot remove much thermal noise when the GNSS signal is strong, which can be explained by Equation (4). However, a larger error would appear once the vehicle movement changes due to the narrow bandwidth. The above phenomenon illustrates that a normal PLL is not suitable for a narrow bandwidth to suppress noise \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Parameters**} & **Low-Grade IMU** & **Medium-Grade IMU** \\  & **(MEMS)** & **(IXSEA)** \\ \hline Gyro bias (deg/h) & 36 & 0.05 \\ Gyro white noise (deg/\(\backslash\)h) & 3.0 & 0.003 \\ Gyro scale factor (ppm) & 300 & 30 \\ Accelerometer bias (mGal) & 2000 & 100 \\ Accelerometer white noise (m/s/\(\backslash\)h) & 0.12 & 0.09 \\ Accelerometer scale factor (ppm) & 300 & 40 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: IMU configuration parameters in the simulator. IXSEA is the model of a typical medium-grade INS. Figure 14: Setup of the simulation testing. under dynamic conditions. As is seen in Figure 15c,d, with the MEMS INS or the medium-grade INS aiding, the tracking error of the PLL with an integration time of 20 ms and a bandwidth of 3 Hz does not increase when the vehicle accelerates/decelerates. In the higher dynamic scenarios (the maximum acceleration is about 25 m/s\({}^{2}\)), the tracking error of PRN 24 as an example is analyzed with a CNR of 50 dB-Hz and an elevation of 34 degrees. Figure 16 shows the tracking errors of normal PLLs and INS-aided PLLs. Figure 16a shows the tracking performance of the normal second-order PLL with an integration time of 20 ms and a bandwidth of 10 Hz. Although the bandwidth is wide, the phase tracking error has a significant increase due to large dynamics. The above phenomenon illustrates that a normal PLL is not suitable for long time integration and a narrow bandwidth to suppress noise when the vehicle acceleration is large (more than 9.8 m/s\({}^{2}\)).