# Weak and Dynamic GNSS Signal Tracking Strategies for Flight Missions in the Space Service Volume
## 5 Simulation and Experiment Results
### Result Comparison  
Seen from Figure 8, during the second phase, the loop measurement error obtained by an adaptive KF-based structure is roughly the same as that obtained by the conventional structure, namely SSV RRAM. However, in the third and fourth phases, the adaptive KF makes some improvement to reduce the measurement error, compared to SSV RRAM. It is clearly shown that the measurement errors of both the two structures exceed the tracking threshold of 15\({}^{\circ}\) after the 300 th s. The result reveals several conclusions. First, the two schemes of CL form can work properly in non-maneuvering status when the C/N\({}_{0}\) is over 16.85 dB-Hz. Second, adaptive KF performs better than SSV RRAM due to its flexibility of regulating LNBW in harsh environment. Third, both the two structures lose their locks in orbital maneuvering status and they are incapable of accomplishing navigation in the orbital transfer period of the lunar upper stage. Figure 9a shows a comparison of the Doppler frequency estimations of different tracking schemes in the same experiment scenario. The results are obtained through repeated trials for each scheme. In Figure 9b, no maneuver is made, all of the six schemes keep track of the target signal but the estimation accuracies diverge from each other. In Figure 9c, the probe makes an orbital maneuver, then the two CL schemes, SSV RRAM, as well as the adaptive KF-based method, are unavailable because the loop is out of lock. To demonstrate the performances of all these schemes clearly, we zoom in the plot around the 300 th s with higher resolution in Figure 9d, and it is obvious that the estimation accuracy of INS-assisted strategy is determined by the quality of the IMUs. The IMU of the navigation grade is the best one, the tactical grade is secondary, the civil grade is tertiary, and the MEMS grade is the worst. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**IMU Parameters** & **MEMS IMU** & **Civil IMU** & **Tactical IMU** & **Navigation IMU** \\ \hline gyro errors & constant bias, \({}^{\circ}\)/h & 300 & 50 & 1 & 0.01 \\ accelerometer errors & constant bias, mg & 10 & 1 & 0.1 & 0.01 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Input IMU parameters [27] for local frequency prediction in SDR. Figure 8: PLL lock status of two CL form tracking strategies, SSV RRAM and the adaptive KF-based method. Figure 10 provides the comparison of the estimation error of the six schemes. Through statistical computing of the estimation errors in the second phase, the root mean square (RMS) is 2.3188 Hz for SSV RRAM and 0.4324 Hz for the adaptive KF-based method. This leads to the conclusion that the adaptive KF-based method can get more precise estimates of the Doppler frequency than the conventional SSV RRAM when the space vehicle operates under normal or non-maneuvering condition. For the INS-assisted schemes of OL form, the frequency errors accumulate continuously. The maximum frequency errors are shown in Table 5 after a drift time of 270 s. It is obvious that the cumulative errors of the schemes aided by MEMS IMU and civil IMU grow quickly, which does not meet the performance requirements of SSV navigation. If the drift time without IMU calibration is short enough, e.g., within 77 s, the scheme aided by tactical IMU performs a little better than the adaptive KF-based method. However, once the drift time is over 78 s, the estimation error using the tactical IMU is above 0.4324 Hz which is inferior to the adaptive KF-based method. Although the scheme aided by navigation IMU is more accurate, the estimation error would exceed 0.4324 Hz after a cumulative time of 775 s. Therefore, if the drift time is too long or the dynamic is not too great, the adaptive KF-based method has its specific advantage compared to INS-assisted schemes. Therefore, what the OL tracking strategy actually improves is the loop robustness of GNSS signals tracking function, owing to the fact that OL tracking with high-quality IMU can work properly under orbital maneuvering conditions.