# Visual-Inertial Method for Localizing Aerial Vehicles in GNSS-Denied Environments
## 3 Results  
The method to retrieve the localization of aerial vehicles, described in the previous paragraph, was tested using real data. The world coordinates of 11 points to be used as reference were defined using a LiDAR model of the Colegio Almada Negreiros building (University NOVA Information Management School in Lisbon, Portugal, see Figure 4). The LiDAR data was acquired with the YellowScan Surveyor LiDAR system, which has a density of approximately 80 pts/m\({}^{2}\) and a nominal accuracy of 5 cm. In addition to the on-board UAS differential GPS, a Septentrio Altus NR3 GNSS base station was operated to record precise GPS and GLONASS data. These underwent post-processed kinematic (PPK). The world coordinates of 11 reference points, expressed in UTM WGS84 29 zone number North, are provided in Table 1.  
The reference points mentioned above were used to retrieve the position of 11 still images acquired with a DJI Inspire 1 Pro equipped with an optical camera FC550. Two reference points were used in each image, in accordance with what has been discussed in the previous paragraph. The focal length and pixel Pitch of the camera, which are required parameters for the calculation, are 15 mm and 3.76 \(\upmu\)m [23]. The aerial assets used in this study are also capable of generating ancillary tags in Exchangeable Image File Format (EXIF) containing, among other information, the orientation and position of the camera when each image was acquired. As previously mentioned, only Pitch and Roll (Euler) angles were used in the calculation. The GNSS position provided in the EXIF data was used as a comparison with the results of the calculation. The horizontal GNSS accuracy of the DJI Inspire 1 is \(\pm\)2.5 m [24]. On the other hand, the elevation data acquired by the system during the survey exhibited errors exceeding 20 m, which are easily detectable and appear to be a common issue with consumer-level drones [25]. Unfortunately, we were unable to access other sources of information, such as autopilot data, where the elevation may be corrected by additional sensors, like barometers. The comparison with the GPS was therefore performed only on the X and Y coordinates. The evaluation of the results was also conducted against the camera pose estimation, which was performed using RealityCapture 1.4. This photogrammetry software extracts feature points from images and matches extracted features for the alignment of images in 3D coordinate space. After the alignment of images, pixels from images are projected into 3D space through trilateration as a sparse/dense point cloud. Although georeferencing information contained in images' EXIF is used in this photogrammetry workflow, it is inaccurate as the source of geolocation information is the built-in GNSS receiver of the UAV. Additionally, the image alignment \begin{table}
\begin{tabular}{c c c c} \hline  & **X (m)** & **Y (m)** & **Z (m)** \\ \hline Point 1 & 486,122.57 & 4,287,155.23 & 124.00 \\ Point 2 & 486,130.63 & 4,287,172.75 & 112.96 \\ Point 3 & 486,113.11 & 4,287,192.46 & 102.72 \\ Point 4 & 486,102.19 & 4,287,203.52 & 101.76 \\ Point 5 & 486,019.27 & 4,287,129.58 & 103.81 \\ Point 6 & 486,041.72 & 4,287,136.00 & 103.40 \\ Point 7 & 486,046.09 & 4,287,137.73 & 104.93 \\ Point 8 & 485,991.41 & 4,287,112.81 & 119.48 \\ Point 9 & 486,000.96 & 4,287,116.35 & 112.79 \\ Point 10 & 486,071.86 & 4,287,147.96 & 105.92 \\ Point 11 & 486,057.19 & 4,287,141.66 & 106.02 \\ \hline \end{tabular}
\end{table} 
Table 1: Coordinates of the reference points (UTM WGS84 29 zone number North). Figure 4: LiDAR model of the Colegio Almada Negreiros in Lisbon. This model was used to obtain the coordinates of 13 reference points used as reference for the calculations. The position in the 3D model and the localization of the points are shown in chips. The coordinates of the points are provided in Table 1.  
and subsequent trilateration are also inaccurate.