# An Optimized Vector Tracking Architecture for Pseudo-Random Pulsing CDMA Signals
## 5 Simulation and Results
### Simulation Results  
This paper pays more attention to the influence of the PLPS on tracking and position accuracy, weakening the impact of factors, such as the received signal power fluctuation, with the distance variation. Thus, the received signal power is set as fixed. The carrier-to-noise ratio (\(C/N_{0}\)) of IF PRPS is set to 50 dB \(\cdot\) Hz in this simulation scenario. Next, three different VTL structures are applied to track the preset IF PRPS. Finally, the tracking and navigation results are analyzed and compared.  
The tracking errors of VTL mainly refer to doppler error and code phase error, which are obtained by the difference between the local replica signal and the received signal. Figures 9 and 10 shows the tracking errors of the 10 th-Pseudilite. The blue, yellow, and red lines represent the position errors of VTL, IUP-VTL, and IUPPM-VTL algorithms, respectively. The dashed box shown in Figure 9 describes the peak caused by sudden changes in acceleration. From the enlarged view, it can be seen that the IUPPM-VTL can respond to acceleration changes faster. The root mean square errors (RMSE) of doppler and code phase are calculated and recorded in Table 2. It is illustrated that the IUPPM-VTL has the best tracking accuracy throughout the tracking process. The tracking results of all pseudolites are demonstrated in Figure 11a,b.  
Figure 8: Reference dynamic. (**a**) Reference velocity. (**b**) Reference acceleration.  
Figure 10: Code phase error of the 10 th-Pseudilite.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**RMSE** & **VTL** & **IUP-VTL** & **IUPPM-VTL** \\ \hline Doppler [Hz] & 0.7001 & 0.5218 & 0.5073 \\ Code Phase [m] & 0.2097 & 0.1124 & 0.0505 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Comparision of doppler and code phase errors of the 10 th-Pseudilite.  
Figure 9: Doppler error of the 10 th-Pseudilite.  
The position error is the difference between the position result and the reference trajectory shown in Figure 7. Figure 12 shows the position errors in XYZ directions. Because the IUPPM-VTL adopts a more accurate model, it performs a slighter jitter in position errors than VTL and IUP-VTL. The RMSEs of the position errors of VTL, IUP-VTL, and IUPPM-VTL are 0.63 m, 0.30 m, and 0.12 m, respectively. Hence, the proposed IUPPM-VTL performs best in position precision.  
The velocity error is the difference between the velocity result and the reference velocity shown in Figure 8. Figure 13 shows the velocity errors in XYZ directions. The enlarged views of the solid line boxes demonstrate the velocity errors at the steady-state. The velocity errors at the abrupt acceleration in the X and Y directions are shown in the dotted box (details are shown in the enlarged version). When adopting the IUPPM-VTL, the sudden change in acceleration has a shorter disturbance time to the speed estimation than VTL and IUP-VTL because the proposed IUPPM-VTL has higher doppler tracking accuracy and more robust acceleration response capability. The RMSEs of the velocity errors of VTL, IUP-VTL, and IUPPM-VTL are 0.50 m/s, 0.40 m/s, and 0.24 m/s, respectively. Thus, the proposed IUPPM-VTL significantly improves velocity accuracy.