## 3 Leica Pegasus Backpack Survey
### Precision Assessment  
Assessment of the system precision is done by comparing the point clouds obtained when entering/exiting in/from the bastion. First, Figure 3 shows average point-to-point distances between the two georeferenced point clouds (i.e., absolute positioning error case): averages have been computed on slices orthogonal to the \(u\) line shown in Figure 2(red line). The width of each slice is 10 cm. Figure 2(b) shows the bastion silhouette evaluated by projecting bastion model points on the vertical plane passing through the \(u\) line: coordinates on the horizontal axis correspond to those along the \(u\) line in Figure 2(a). Figure 2(c) shows the point-to-point average distances varying the slice coordinate along the \(u\) line.  
It is worth noticing that two peaks are clearly visible in correspondence with ceiling openings (at \(u\approx 6\) m and \(u\approx 16\) m, approximately). These peaks are clearly due to the point missing in the two point clouds: the right parts of these openings were well reconstructed in the point cloud shown in Figure 2(b), whereas the left parts were better reconstructed in the other point cloud, depending on the walking direction (and hence the sensor orientation with respect to the openings).  
As reported in Table 1, the average point-to-point distance between the two point clouds of the corridor is 4.7 cm; the root mean square (RMS) point-to-point distance is 5.8 cm; and the maximum distance is 110.3 m. The motivation of the large maximum distance value is that points are missing in the ceiling openings, as described above.  
Then, Figure 3d shows the average point-to-point distances along line \(u\) after refining the registration between the two point clouds with the ICP algorithm (relative error case). The ICP algorithm was applied to the two point clouds after centering them with respect to the center of the first one. This registration led to a translation of 19.7 cm, \(-14.4\) cm, \(-1.4\) cm in the three axes  
\begin{table}
\begin{tabular}{c c c c} \hline  & **Average Error (cm)** & **RMS (cm)** & **Maximum Error (cm)** \\ \hline absolute error & 4.7 & 5.8 & 110.3 \\ relative error & 2.2 & 3.1 & 60.5 \\ \hline \end{tabular}
\end{table}
Table 1: Leica Pegasus 3D model precision assessment.  
Figure 3: Leica Pegasus precision assessment: comparison of two 3D models generated in successive surveys. (**a**) Top view of the Pegasus backpack 3D model and line \(u\) (in red) corresponding to the corridor direction. (**b**) Profile view of the corridor of the Pegasus backpack 3D model. (**c**) Average error between the two 3D models evaluated on slices distributed along the line \(u\). (**d**) Average error between the two 3D models after registration with ICP.  
(east, north, vertical respectively) and a 0.8 degree rotation. Average and RMS distances are 2.2 cm and 3.1 cm, respectively.  
The above-mentioned translation and rotation between the two point clouds cause the numerical result difference between the absolute and relative error case. Such a difference is clearly mostly due to the absence of the GNSS signal and hence to errors of the INS and SLAM algorithm. The obtained absolute positioning error is within the nominal value of the Pegasus backpack error in absence of the GNSS signal (50 cm).