# A Joint Dual-Frequency GNSS/SINS Deep-Coupled Navigation System for Polar Navigation
## 4 Experimental Results and Discussion
### Experimental Results and Discussion  
#### 4.2.1 Static Test  
The set of static data was used to assess the performance of the proposed system under ionospheric scintillation interference and in a low C/N\({}_{0}\) signal environment. The parameters of the static data were set as shown in Table 4.  
The sky plot of GPS satellites for the static test is shown in Figure 5.  
It can be seen that most of the elevations of satellites are lower than 45\({}^{\circ}\), which may suffer lower C/N\({}_{0}\) signals and ionospheric scintillation interference easier. This is similar to the parameters of the static data. In the following section, we chose SV #3, 12, and 25 to analyze the scintillation statistics and their tracking performance. It is noted that the scintillation of carrier phase fluctuation often occurs with less amplitude fading in polar areas, so we focus on the carrier phase fluctuation. In general, \(\delta\varphi\) > 0.3 cycles indicates strong scintillation with strong carrier phase fluctuation. The \(\delta\varphi\) indicators for SV #3, 12, and 25 during the simulation are shown in Figure 6. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Value** & \\ \hline Visible satellites & SV \# 3 & 12, 17, 32 & 1, 6, 25, 31 \\ \hline Maximum C/N\({}_{0}\) & 47 dB-Hz & 42 dB-Hz & 36 dB-Hz \\ \hline \multirow{3}{*}{Ionospheric scintillation interference} & Strong (SV \#25, 32) & \\  & Moderate (SV \#12) & \\  & Weak (SV \# 3) & \\ \hline Simulation location & (85\({}^{\circ}\) N, 40\({}^{\circ}\) E, 0 m) & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The parameters of the set of static data. Figure 5: Sky plot of GPS satellites in polar areas. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Value** & **Parameter** & **Value** \\ \hline GNSS sampling frequency & 53 MHz & integrated filter period & 100 ms \\ L1 IF frequency & 14.58 MHz & gyro bias & \textless{}0.005 \({}^{\circ}\)/h \\ L2 IF frequency & 7.4 MHz & accelerometer bias & \textless{}7 \(\times\) 10\({}^{-5}\) g \\ coherent integration time & 10 ms & gyro noise density & \textless{}0.005 \({}^{\circ}\)/h \\ pre-filter period & 10 ms & accelerometer noise density & \textless{}5 \(\times\) 10\({}^{-5}\) g \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Parameters defined in the system. From Figure 6a we can see that nearly all \(\delta\varphi\) indices for SV #3 are smaller than 0.1 during the simulation time, which can be considered as weak scintillation. Meanwhile, Figure 6b shows that most of the \(\delta\varphi\) indices for SV #12 fluctuate between 0.13 and 0.15, which can be regarded as moderate scintillation. Several \(\delta\varphi\) values approach and even exceed 0.3 for SV #25 in Figure 6c, which represents strong scintillation. Then, the carrier phase lock indicator (PLI) was used as the criterion of carrier phase tracking performance; it can be expressed as  
\[\text{PLI}\approx abs(I_{\text{P}})/\sqrt{\big{(}I_{\text{P}}^{2}+Q_{\text{P} }^{2}\big{)}}. \tag{34}\]  
The PLI is equal to 1 when the phase is perfectly locked, while it is equal to 0 when the phase lock is lost. In this paper, we use 0.9 and 0.5 as the thresholds of good carrier phase lock and poor carrier phase lock, respectively. The carrier tracking performances of the three satellite signals using a traditional GNSS tracking loop (a third-order tracking loop with 15 Hz fixed bandwidth, denoted T-GNSS) and the proposed ionosphere-free dual-frequency GNSS/SINS deep-coupled navigation system (denoted IF-DDC) are shown in Figure 7. A summary of the carrier phase tracking performance under scintillation is shown in Table 5.  
Figure 6: \(\delta\varphi\) indices: (**a**) weak scintillation for SV #3; (**b**) moderate scintillation for SV #12; (**c**) strong scintillation for SV #25. It can be seen from Figure 7 and Table 5 that both the T-GNSS and IF-DDC have good carrier phase tracking performance under weak scintillation (i.e., SV #3) during the tracking. The tracking does not have losses during the tracking time.