# Opportunistic In-Flight INS Alignment Using LEO Satellites and a Rotatory IMU Platform
## 5 Experimental Evaluation and Results
### Experimental Results and Discussion
#### 5.3.2 Flight Experiment  
The obtained pseudorange rate measurement from the five overhead satellites led at least two and a maximum of three measurements during the entire trajectory. In the first seconds of the experiment, the aircraft took off from the Joliette airport, and it followed a challengeable trajectory. The GNSS receiver recorded the true reference position of the flight vehicle; however, the algorithm did not utilize the measurements of the GNSS receiver after 5 min. The last 5 min of the trajectory were estimated using multi-satellite LEO-SOP pseudorange rate measurements. Figure 15 demonstrates the true and estimated position of the aircraft, highlighting the GNSS-blocked point and visualizing the experiment's region on a 3-D geographical map. The figure was plotted using the mapping toolbox of the MATLAB.  
Figure 16 shows the North and East errors of the proposed alignment method along with \(\pm 3\sigma\) bounds. The red dash line illustrates the GNSS cut-off point. The flight experiment was able to measure the stability of the system in medium-term durations. It can be seen that by the variation of the aircraft's attitude, the position error increased gradually. Overall, the method bounded the error of the INS by the SOP-aided alignment system. Table 2 shows the root mean square error (RMSE) of the proposed method in different time slots. The goal was to measure the stability and the resiliency of the system in longer terms. As mentioned before, the GNSS was blocked after 5 min and 30 s from the start point of the experiment. The RMSE in the first 1.5 min of the experiment was 35.6654 m, and after 1 min it reached 56.1978 m. Then, it culminated at 372.1078 m in the next minutes. The RMSE of the entire trajectory for 4.5 min of the experiment was 196.7429 m. Figure 17 illustrates the estimated bias of the IMU, and Figure 18 shows the estimated orientation of the aircraft.  
Figure 14: The estimated trajectory of the vehicle compared to the stand-alone INS and the true reference position.  
Figure 13: (**a**) The estimated receiver’s clock bias. (**b**) The estimated receiver’s clock drift.  
Figure 16: The North (**a**) and East (**b**) position errors of the aircraft before and after blocking the GNSS compared with the error of the Doppler positioning method.  
\begin{table}
\begin{tabular}{c c c c c c} \hline  & \(\mathbf{5^{\prime}}\):\(\mathbf{30^{\prime\prime}}\)-\(\mathbf{6^{\prime}}\):\(\mathbf{00^{\prime\prime}}\) & \(\mathbf{5^{\prime}}\):\(\mathbf{30^{\prime\prime}}\)-\(\mathbf{7^{\prime}}\):\(\mathbf{00^{\prime\prime}}\) & \(\mathbf{5^{\prime}}\):\(\mathbf{30^{\prime\prime}}\)-\(\mathbf{8^{\prime}}\):\(\mathbf{00^{\prime\prime}}\) & \(\mathbf{5^{\prime}}\):\(\mathbf{30^{\prime\prime}}\)-\(\mathbf{9^{\prime}}\):\(\mathbf{00^{\prime\prime}}\) & \(\mathbf{5^{\prime}}\):\(\mathbf{30^{\prime\prime}}\)-\(\mathbf{10^{\prime}}\):\(\mathbf{00^{\prime\prime}}\) \\ \hline Duration from start point & 30 s & 1.5 min & 2.5 min & 3.5 min & 4.5 min \\ \hline RMSE (m) & 80.9458 & 110.9693 & 151.5803 & 224.4044 & 550.2049 \\ Doppler positioning & & & & & \\ \hline RMSE (m) & 16.1054 & 35.6654 & 56.1978 & 282.1078 & 196.7429 \\ SOP-aided alignment & & & & & \\ \hline \end{tabular}
\end{table}
Table 2: RMSE of the alignment method for different time slots from the start point compared with the error of the Doppler positioning method.  
Figure 15: Experimental results include the geographical view of the airport and a comparison of the true and estimated trajectory.