# An Adaptive INS-Aided PLL Tracking Method for GNSS Receivers in Harsh Environments
## 5 Software Simulation
### Simulation Result Analysis  
To evaluate the performance of the adaptive tracking method, it is compared with other four INS-aided PLL tracking methods with different loop parameter selections under the simulated harsh environment. The total five loop parameter selections are \(B_{n}=10\) Hz, T = 1 ms, \(B_{n}=10\) Hz, T = 20 ms, adapt-\(B_{n}\), T = 1 ms, adapt-\(B_{n}\), T = 20 ms and adapt-\(B_{n}\), adapt-T. The performance evaluation method used in here is based on the phase discriminator output and the phase lock indicator (PLI) which can be calculated as [23]. \[PLI_{n}=\frac{I_{n}^{2}-Q_{n}^{2}}{I_{n}^{2}+Q_{n}^{2}} \tag{35}\]  
Figure 9: The PD tracking error for different \(C/N_{0}\). where \(PLI_{n}\) presents the PLI value computed from correlation values \(I_{n}^{2}\) and \(Q_{n}^{2}\) corresponding to the \(n\)th tracking loop update, \(PLI_{n}\) is averaged over 1 second to obtain more reliable estimate of the PLI. During the simulation, noise is added into the lower dynamic data with a rate of 1.5 dB/s, and a 3 dB/s noise is added into the higher one after 14 s. Figures 10 and 11 show the variation of tracking performance under the two environments stated above, respectively. The adaptive tracking method achieves the best performance in both harsh environments with a 4-9 dB sensitivity improvement. The tracking methods with the 20 ms integration time show better performance than those with the 1 ms integration time when the dynamics are relatively lower, while their performance degrades more quickly when the dynamics increase. Both figures also demonstrate that the improvement by adapt-T is more significant than that by adapt-\(B_{n}\). The choices of noise bandwidth and integration time under the two harsh environments are shown in Figures 12 and 13 respectively. Using the adaptive tracking method, the integration time will increase with the attenuation of \(C/N_{0}\), while just the opposite occurs with the noise bandwidth. From the comparison of the two figures, it can be seen that in the higher dynamic environment, the noise bandwidth cannot be chosen too small and the choice of the integration time should be relatively short. The choices of the two parameters are in accord with the theoretical analysis results in Section 4. Figure 11: The output of PD (**left**) and the corresponding PLI (**right**) when \(p=200\) m/s\({}^{3}\). Figure 10: The output of PD (**left**) and the corresponding PLI (**right**) when \(p=50\) m/s\({}^{3}\). Furthermore, a comparison is also made with other methods to evaluate the performance of the adaptive method. For the harsh environment with high dynamics and signal attenuation, the improvement methods for INS-aided PLL mainly focus on adjusting the noise bandwidth as in [8,15]. The main ideas of the adaptive method proposed in this paper and the methods presented in [8,15] are listed in Table 1 as follows. The tracking performance of these three methods under the two environments stated above are illustrated in Figures 14 and 15. It can be seen that the adaptive method by choosing the optimal noise bandwidth and integration time can achieve a better performance over the other two methods that only choose the adaptive bandwidth with a 3-6 dB sensitivity improvement. \begin{table}
\begin{tabular}{c c} \hline \hline
**Method** & **Main Idea** \\ \hline Adaptive Method & Choose the optimal integration time and bandwidth for a given application under the minimum tracking error criterion. \\ \hline Method 1 ([15]) & The Doppler aiding error resulting from the navigation uncertainty is derived and used to design the adaptive loop filter, so as to adjust the noise bandwidth. \\ \hline Method 2 ([8]) & Using the fuzzy logic controller (FLC) to adjust the PLL noise bandwidth on-line. \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The comparison of three improvement tracking methods for INS-aided PLL. Figure 12: The choices of \(T\) (**left**) and \(B_{n}\) (**right**) when \(p=50\) m/s\({}^{3}\).