# A Joint Dual-Frequency GNSS/SINS Deep-Coupled Navigation System for Polar Navigation
## 4 Experimental Results and Discussion
### Experimental Results and Discussion
#### 4.2.2 Dynamic Test  
In the dynamic test, a flight test was set to assess the dynamic performance of the proposed system in polar areas. The parameters of the set of dynamic data are shown in Table 6.  
Figure 7: Carrier phase error and phase lock indicator (PLI): (**a**) Traditional GNSS tracking loop (T-GNSS); (**b**) Ionosphere-free dual-frequency GNSS/SINS deep-coupled navigation system (IF-DDC). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Satellite Pseudo Random**} & \multirow{2}{*}{**Method**} & \multicolumn{2}{c}{**PLI \textless{0.9**}} & \multicolumn{2}{c}{**PLI \textless{0.5**}} \\  & & \multicolumn{2}{c}{**(Total No. = 11,000)**} & \multicolumn{2}{c}{**(Total No. = 11,000)**} \\ \cline{3-6}  & & **L1 CA** & **L2 CM** & **L1 CA** & **L2 CM** \\ \hline \multirow{2}{*}{SV \#3} & T-GNSS & 0 & 5 & 0 & 0 \\  & IF-DDC & 0 & 2 & 0 & 0 \\ \hline \multirow{2}{*}{SV \#12} & T-GNSS & 112 & 399 & 3 & 12 \\  & IF-DDC & 26 & 119 & 0 & 0 \\ \hline \multirow{2}{*}{SV \#25} & T-GNSS & 950 & 1766 & 128 & 280 \\  & IF-DDC & 247 & 532 & 0 & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Summary of tracking performance under scintillation. It is noted that the parameters of the visible satellites, C/N\({}_{0}\), and ionospheric scintillation interference in the dynamic test are the same as the parameters in the static test. The flight trajectory for the dynamic test in polar areas is shown in Figure 8.  
It can be seen that the flight motions include climb, level off, straight flight, turn, and come-down. Meanwhile, the flight velocity and the flight acceleration and jerk are shown in Figures 9 and 10, respectively. \begin{table}
\begin{tabular}{c c c} \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 Start point & (85\({}^{\circ}\) N, 40\({}^{\circ}\) E, 0 m) & \\ \hline Maximum velocity & 91 m/s & \\ \hline Maximum acceleration & 5 g & \\ \hline Maximum jerk & 50 g/s & \\ \hline \end{tabular}
\end{table} 
Table 6: The parameters of the set of dynamic data. Figure 8: The flight trajectory for the dynamic test in polar areas. Figure 9: The flight velocity of the dynamic test in polar areas. It can be seen that there are several periods of acceleration and jerk with maximum acceleration and jerk of \(5g\) and \(50\)\(g\)/s, respectively. It is noted that the time axis of Figures 9 and 10 starts from 432,018 s which is the start epoch of the system outputting the navigation results after about 34 s of tracking. Figures 11 and 12 illustrate the carrier frequency tracking performance using different methods. In this section, the moderate scintillation (i.e., SV #12) and strong scintillation (i.e., SV #25) were focused upon to assess their performance. It can be seen in Figure 11 that the IF-DDC method allows a reduction in the noise presented in the carrier Doppler compared with the T-GNSS method. The IF-DDC achieves the best performance in terms of noise and scintillation reduction. This is even more evident from Figure 12 where the signal suffers lower C/N\({}_{0}\) and stronger scintillation. Besides this, when compared with Figure 10, some trends related to flight dynamics can be seen in Figure 11b. The transient errors as well as the effects of jerk still remain when the T-GNSS method is used. However, these trends are all removed by the IF-DDC method due to the aid of the grid SINS information. Figure 11: Carrier frequency tracking performance of SV #12: (**a**) carrier Doppler; (**b**) Doppler error. Figure 10: The flight acceleration and jerk of the dynamic test in polar areas: (**a**) acceleration; (**b**) jerk.