# Design and Validation of a Cascading Vector Tracking Loop in High Dynamic Environments
## 3 Results
### Results Analysis
#### 3.2.1 Simulation and Analysis of High Dynamic Signal  
The simulation conditions are summarized as follows: the sampling frequency is set as 40 MHz, the IF frequency is set to 4 MHz, and the sampling bit width is set to 8 bits. The signal is unblocked, and the carrier to noise density of each tracking channel is above 40 dB-Hz. The selected satellite PRN is 05. Without navigation data, the acquired carrier Doppler frequency (f) is approximately 26,572 Hz (The relative velocity between the receiver and the satellite is 5060 m/s). First, to illustrate the difference in dynamic performance of the FLL-PLL and the vector tracking loop, we designed 15 scenarios, ranging from 0 g/s to 140 g/s, in the unit of 10 g/s. In Figure 4, the X coordinate is the acceleration jerk (g/s) in different dynamic conditions, and the Y coordinate represents the tracking standard deviation (STD) of the code phase. The blue and red curves represent the code phase errors of the FLL-PLL and the vector loop, respectively. The dotted curves are the corresponding results without the carrier loop assistance. Although the high dynamic signal will deteriorate the tracking accuracy of the independent code loop, the lock loss in the high dynamic signal is mainly caused by the carrier loop. Furthermore, the code loop is not very sensitive to the change in receiver dynamics. This result also shows that we need not to modify the code loop, but rather use the carrier frequency to assist the normal code tracking for high dynamic signals. The carrier-assisted method will also be adopted later and will not be described again. Figure 5a shows the estimated and real carrier frequencies based on the IF. When the acceleration jerk is 30 g/s, the blue curve oscillates around the truth value with the motion. In Figure 5b, the Doppler frequency error is calculated by subtracting the true Doppler value from the filter output. Frequency tracking can be stabilized around the real value  
Figure 4: Stable tracking results of carrier frequency in the acceleration jerks 30 g/s. (for tracking highly dynamic signals, the frequency bandwidth is 20 Hz, and the phase bandwidth is 40 Hz). The red curves represent the results of the vector structure, and the blue curves represent the results of the FLL-PLL. In Figure 5(a), the STD of the carrier frequency error of FLL-PLL increases slowly with the acceleration jerk. The original STD of FLL-PLL is much larger than that of the vector loop because of the amplification of the noise bandwidth. In Figure 5(b), the steady-state phase tracking error of FLL-PLL is constant in the acceleration jerk scene, which is consistent with the theoretical trend of the steady-state tracking error of the FLL-PLL structure. However, in the pre-filter of this vector structure, we estimate the second derivative of carrier frequency as a parameter, so the vector loop can still track the signal with jerk acceleration accurately. Figure 5: Stable tracking results of carrier frequency in the acceleration jerks 30 g/s. Figure 6: Stable tracking results of carrier frequency under different acceleration jerks. In Figure 7, the meanings of different colors are the same as those in Figure 6. The Y coordinates represent the mean error of the carrier phase and the STD of the carrier phase, respectively. All the blue ones are approximately 80 g/s because the judgment threshold selected is not the theoretical steady-state tracking error threshold but the energy distribution of the IQ value. When the energy of the Q branch reaches half that of the I branch, considering the ephemeris calculation, we regard the subsequent results as having poor tracking accuracy and discard them. According to Figures 6 and 7, we prove that the vector tracking structure based on the UKF has better tracking accuracy and wider tracking range than the FLL-PLL. Then, we designed a special scene to verify the tracking capability of the vector loop.