## 4 Experimental Tests
### Test Results  
The proposed cross-modal image matching approach (CMM) is compared with HOP [11], which combines histograms of oriented gradients (HOG), optical flow (OF), and particle filter (PF). HOP uses a matching method based on HOG for positioning, and, to accelerate the matching process, OF and PF are employed to decrease the searching area. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Type of Sensor** & **Infrared** & **Visible Light** \\ \hline Image Resolution & 640 \(\times\) 480 Pixels & 2048 \(\times\) 2048 Pixels \\ \hline Field of View & 73 \(\times\) 58 deg & 78 \(\times\) 78 deg \\ \hline Wave Length & 1.0–1.6 um & - \\ \hline Maximum Frames per Second & 60 fps & 60 fps \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Camera parameters. Figure 8: The flying tests platform. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Sensor** & **Parameters** & **Values** \\ \hline \multirow{4}{*}{Gyroscope} & Range & 400 deg/s \\ \cline{2-3}  & Bias Repeatability & \textless{}0.1 deg/h \\ \cline{2-3}  & Bias Instability (at 25 \({}^{\circ}\)C) & \textless{}0.5 deg/h \\ \cline{2-3}  & Scale Factor Repeatability & \textless{}15 ppm \\ \cline{2-3}  & Scale Factor Nonlinearity & \textless{}100 ppm \\ \hline \multirow{4}{*}{Accelerometer} & Range & 8 g \\ \cline{2-3}  & Bias Repeatability & \textless{}3.5 mg \\ \cline{2-3}  & Noise Density & \textless{}25 ug/sqrt (Hz) \\ \cline{2-3}  & Scale Factor Nonlinearity & \textless{}1000 ppm \\ \hline \hline \end{tabular}
\end{table} 
Table 3: MEMS inertial sensor parameters. The positioning accuracy of CMM and HOP is evaluated by comparing their positioning results with the GPS RTK, which generally has an accuracy of 0.02 m under benign environments. The correct positioning ratio (CPR) is selected for evaluating the positioning reliability of CMM and HOP. Herein, the CPR is defined as \(\text{CPR}=\text{CP}/\text{P}\), where P is the total number of positioning, and CP is the correct number of positioning. According to the positioning requirement of the UAV, herein, we define that a positioning result is correct if its error is less than 30 m compared with the GPS RTK. The root-mean-squares error (RMSE) of the correct positioning is selected for evaluating the positioning accuracy. Eight UAV flights are carried out to evaluate the aforementioned approaches, namely, CMM and HOP. The flight parameters are provided in Table 4. The flight trajectories are shown in Figure 9. The correct positioning ratio and the positioning RMS error of CMM and HOP are compared in Table 5.  
It can be noted from Table 5 that both the CPR and positioning accuracy of HOP are significantly lower than those of CMM for all the flights. There are mainly two reasons for the low performances of HOP. First, the image matching algorithm of HOP is developed for visible light images, which is unreliable for matching cross-modal images; therefore, its CPRs are very low in the flights with infrared camera. Second, the searching area of HOP is small (about 30 m \(\times\) 30 m) due to the high computation complexity of the matching; therefore, the true position could be out of the searching area when a false prediction is introduced by a false matching. Furthermore, the contribution of the coarse matching of CMM can be observed by comparing the CPR of HOP with that of CMM. The feature descriptor of the proposed coarse matching is enhanced by PCA, which is more reliable for matching cross-modal images. In addition, the searching process of the coarse matching of CMM is significantly accelerated, which means we can afford a significantly larger searching area (\(\geq\) 150 m \(\times\) 150 m). Therefore, the CMM can re-track the flight path even when the true position is far from the predict position, which also helps in improving the reliability of CMM. Table 6 shows the time-consuming statistics of CMM, where the visible light real-time image is resized from 2048 \(\times\) 2048 pixels to 512 \(\times\) 512 pixels.