# Design and Validation of a Cascading Vector Tracking Loop in High Dynamic Environments
## 3 Results
### Results Analysis
#### 3.2.2 Signal Analysis Based on the Simulator
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Acceleration (g)** & \(-\mathbf{20}\) & \(-\mathbf{40}\) & \(-\mathbf{60}\) & \(-\mathbf{80}\) & \(-\mathbf{100}\) \\ \hline Carrier phase tracking error of vector tracking structure (STD, unit: mm) & 0.57 & 0.55 & 0.52 & 0.51 & 0.52 \\ Carrier phase tracking error of second-order frequency locked loop assisted third-order phase locked loop loop (STD, unit: mm) & 3.50 & 3.56 & 3.71 & The lock has been lost in the variable acceleration section & The lock has been lost in the variable acceleration section \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Tracking result between FLL-PLL loop and vector loop. locked loop assisted phase locked loop increases with the dynamic increase of the carrier until signal loss (Table 3). Testing for the vector tracking structure, when the acceleration of the carrier is \(-100\) g, the corresponding results of the cascading vector tracking loop are shown in Figure 10. The black vertical line similarly shows the moment when the IQ values converge steadily. Figure 11 provides the energy distribution of the I branch when the code shifts are leading, real time, and lagging. The red curve represents the energy of the instant code, and the blue and green discrete points are the energies of the leading and lagging codes, respectively. When the energy of a real-time code branch exceeds those of the other two branches stably, the correctness of navigation message demodulation of the vector tracking mode is proven. The results of the two branches in Figure 11 indicate that the I and Q values can be completely separated after nearly \(100\) ms of convergence. Compared with Figures 10 and 11 shows that the vector tracking mode  
The results in Table 3, Figure 10a,b, and Figure 11b are used to compare FLL-PLL and the vector loop. In view of vector tracking, the dynamic range is larger, the convergence time from traction to locking is shorter during loop switching, and the influence of the carrier's dynamic change on the loop is smaller. Again, taking the highly dynamic environment of \(-100\) g for example, Figure 12a shows the feedback input from the code loop assisted by the vector tracking structure to the code NCO (dL2, red scatter) and that from the independent code loop to the code NCO (dL1, blue scatter). The x-coordinate is the time, and the y-coordinate is the frequency of the ranging code in the current tracking loop. The blue scatters stabilize after a period of convergence, which, compared with Figure 10 and Table 3, indicates that the independent code loop is robust during carrier loop switching and insensitive to dynamic changes when the carrier loop can be stably tracked. The comparison between the red and blue scatters indicates that the period of code loop stabilization can be greatly reduced with the help of the vector carrier tracking loop, and the tracking performance can be improved. In Figure 12b, the abscissa is time, and the ordinate represents acceleration existing only on the Y-axis. As a supplement to the dynamic scene, the red, blue, yellow, black, and green curves represent the resolving results of the carrier under different dynamic circumstances (initial velocity is 5000 m/s in the Y-axis direction, with different acceleration, from top to bottom, namely, \(-20\), \(-40\), \(-60\), \(-80\), and \(-100\) g). Clearly, the current dynamic environment is far from reaching the dynamic limit of this loop. Finally, we provide the velocity and acceleration results of the vector loop at the static state and the \(-100\) g scenario. In Figure 13 (the static state), the red, green, and blue curves represent the velocities of the three axes, which are near zero and conform to the static positioning scene. The thumbnail represents the entire picture of the convergence process. Figure 12: (**a**) Code frequencies of the feedback input, (**b**) Y axis acceleration under different dynamics.