## 4 Performance Evaluation
### Flight Test Data Analysis  
We successfully obtained the real data of the INS, the GPS and the IRA from the flight test. All the real data were time synchronized using GPS Time. We verified that wind effect actually existed in the data and that the positions of the closest points calculated using each formula are different. First, in order to check whether the wind effect was present in the actual flight test results, the effective pitch and heading angle were compared with the pitch and heading of the flight body (Figure 14). The effective pitch angle did not show a large difference by altitude, but a clear difference between effective pitch angle and pitch angle can be seen in Figure 14a. It cannot be determined whether the heading angle difference depends on the trajectory or on the altitude, but the heading angle difference increases in the order of 1 km, 3 km and 5 km (Figure 14b). The cause for this is not clear, but the results show that the difference between \(\beta\) (effective heading angle) and heading angle was greatest at flight altitude of 5 km, which means the effect of winds blowing from the sides of the aircraft was strongest. In addition, we have argued that there is a difference between the roll angle + \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{\begin{tabular}{c} **Trajectory** \\ **(km)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Average Flight** \\ **Height (m)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Average** \\ **Terrain** \\ **Elevation (m)** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **Flight Time (s)** \\ **Distance (km)** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Flight** \\ **Velocity (m/s)** \\ \end{tabular} } \\ \hline
1 & 1560 & 140 & 318 & 27 & 86 \\
3 & 3640 & 130 & 248 & 21 & 85 \\
5 & 5600 & 220 & 255 & 21 & 83 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Information on flight trajectory. Figure 13: Flight test preparation (**a**) System configuration; (**b**) Trajectory [12]. look angle (\(\angle\)COA + \(\angle\)BOT in Figure 12g) and \(\xi\) (effective roll angle) due to the \(\beta\) value, as described in Section 3.3. Figure 15 shows the difference between roll angle + look angle and \(\xi\). As expected, the maximum difference between the roll angles was largest at a flight altitude of 5 km, when the \(\beta\) value was largest. Second, we checked that the positions of the closest points calculated using each formula were different. The simple method (Equation (3) in Section 3.1) has been shown to be significantly less accurate than the conventional method (Equation (13) in Section 3.2) from the previous paper [12], and its results are excluded from the results analysis in this paper. The proposed method (Equation (36) in Section 3.3) is compared with the conventional method. The horizontal position difference between the closest points found using each method is defined as follows. \[\Delta p_{k,\varepsilon}= p_{k,\varepsilon(proposed\ method)}-p_{k,\varepsilon(conventional\ method)} \tag{37}\] \[\Delta p_{k,n}= p_{k,n(proposed\ method)}-p_{k,n(conventional\ method)}\] (38) \[\Delta p_{k}=\sqrt{\Delta p_{k,\varepsilon}{}^{2}+\ \Delta p_{k,n}{}^{2}} \tag{39}\]  
Figure 14: Comparison between aircraft attitude and effective observation angle: (**a**) Pitch angle difference; (**b**) Heading angle difference. Figure 15: Difference between angles (\(\gamma+\theta\)) and \(\xi\). where \(p_{k,e}\) and \(p_{k,n}\) are the east and north direction relative distance to the closest point, \(p_{k(proposed\ method)}\) and \(p_{k(conventional\ method)}\) are the relative distance to the closest point calculated using the proposed method and the conventional method. Figure 16 shows \(\Delta p_{k}\) obtained using both calculation methods. Figure 16a shows that the maximum value of \(\Delta p_{k}\) was largest at the flight altitude of 5 km and smallest at the flight altitude of 1 km. Figure 16b-d show histograms and cumulative probabilities of \(\Delta p_{k}\) at each altitude.