## 3 Results  
For each trajectory estimated by the four proposed systems during the 12 trials, the root mean square point to point distance (D. RMS) and the multivariate \(R^{2}\) (see Equation (6)) between the measured and estimated trajectory were computed.  
The results obtained for the stationary, slow-motion and fast-motion conditions are reported in Tables 1, 2 and 3, respectively.  
\begin{table}
\begin{tabular}{c c c c c c} \hline
**Traj. \#** & **ArUco** & **AKBT** & **OpenPose** & **YOLO** \\ \hline
1 & 2.8 (0.4) & 6.1 (1.0) & 6.1 (0.4) & 13.1 (0.5) \\
2 & 2.7 (0.4) & 8.9 (0.9) & 5.3 (0.2) & 14.5 (0.4) \\
3 & 3.0 (0.4) & 6.9 (2.3) & 5.6 (0.2) & 24.4 (0.5) \\
4 & 2.5 (0.5) & 5.4 (1.2) & 5.9 (0.2) & 25.1 (0.4) \\
5 & 4.7 (0.1) & 2.1 (1.5) & 10.1 (0.7) & 13.4 (0.1) \\
6 & 4.6 (0.8) & 11.2 (1.6) & 5.1 (0.8) & 8.7 (0.4) \\
7 & 4.6 (0.9) & 10.3 (1.0) & 4.1 (0.4) & 8.5 (0.3) \\
8 & 3.1 (1.3) & 7.3 (0.4) & 7.6 (0.2) & 7.9 (0.1) \\
9 & 3.0 (1.0) & 9.2 (0.7) & 7.4 (0.2) & 7.9 (0.1) \\
10 & 2.6 (0.4) & 8.7 (0.2) & 7.2 (0.1) & 7.9 (0.1) \\
11 & 3.1 (0.3) & 8.9 (0.3) & 7.1 (0.1) & 8.0 (0.1) \\
12 & 1.5 (0.1) & 15.3 (0.4) & 8.1 (0.2) & 7.9 (0.1) \\ \hline  & 3.1 (1.0) & 8.9 (3.8) & 6.7 (1.6) & 11.9 (6.1) \\ \hline \end{tabular}
\end{table}
Table 1: Mean and standard deviation of root mean square point to point distance (D. RMS) expressed in cm calculated on each trajectory for all methods (stationary condition).  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline
**Traj. \#** & **ArUco** & **AKBT** & **OpenPose** & **YOLO** \\ \hline
1 & 7.0 (1.1) & 0.99 & 20.6 (5.3) & 0.98 & 11.2 (1.3) & 0.99 & 14.7 (1.8) & 0.99 \\
2 & 9.0 (3.3) & 0.99 & 23.1 (2.7) & 0.97 & 12.4 (1.3) & 0.99 & 11.6 (1.9) & 0.99 \\
3 & 8.2 (3.5) & 0.99 & 20.0 (1.7) & 0.98 & 11.1 (0.7) & 0.99 & 12.1 (1.2) & 0.99 \\
4 & 9.8 (4.6) & 0.99 & 22.4 (1.5) & 0.97 & 12.6 (0.9) & 0.99 & 13.4 (1.2) & 0.99 \\
5 & 5.0 (2.7) & 0.99 & 18.3 (0.9) & 0.92 & 9.1 (1.9) & 0.98 & 13.4 (3.4) & 0.96 \\
6 & 6.2 (1.9) & 0.99 & 27.5 (15.6) & 0.84 & 10.0 (2.2) & 0.98 & 15.7 (4.9) & 0.95 \\
7 & 9.0 (2.3) & 0.98 & 13.1 (1.4) & 0.97 & 10.7 (1.3) & 0.98 & 12.5 (0.9) & 0.97 \\
8 & 9.7 (4.5) & 0.98 & 15.0 (2.9) & 0.97 & 6.8 (1.5) & 0.99 & 14.9 (6.4) & 0.96 \\
9 & 11.0 (4.7) & 0.98 & 14.1 (3.6) & 0.97 & 6.6  
The results show that, in all of the conditions, the ArUco method has a great performance. Indeed, it shows a significantly lower root mean square point to point distance (D.RMS) than AKBT and YOLO (stationary ArUco vs. YOLO: \(t\)-stat = \(-2.154\), \(p<0.001\); stationary ArUco vs. AKBT: \(t\)-stat = \(-2.308\), \(p<0.001\); slow-motion ArUco vs. YOLO: \(t\)-stat  
ArUco vs. YOLO: \(t\)-stat = \(-1.917\), \(p\) = 0.002; fast-motion ArUco vs. AKBT: \(t\)-stat = \(-2.833\), \(p\) < 0.001), but not OpenPose; the ArUco variability increases in dynamic conditions. In addition, OpenPose obtained notable results, showing a significantly lower D.RMS than AKBT and YOLO in the slow-motion condition (OpenPose vs. AKBT: \(t\)-stat = \(2.077\), \(p\) < 0.001; OpenPose vs. YOLO: \(t\)-stat = \(-1.308\), \(p\) = 0.05) and only AKBT in the fast-motion condition (\(t\)-stat = 1.917, \(p\) = 0.002). It appears to be the most reliable in terms of variability compared to all of the methods. On the other hand, the multivariate \(R^{2}\) results (Figure 12, Table 5) show that the ArUco performance is significantly better than YOLO and AKBT (slow-motion ArUco vs. YOLO: \(t\)-stat = 1.846, \(p\) = 0.002; slow-motion ArUco vs. AKBT: \(t\)-stat = 2.462, \(p\) < 0.001; fast-motion ArUco vs. YOLO: \(t\)-stat = 1.667, \(p\) = 0.009; fast-motion ArUco vs. AKBT: \(t\)-stat = 2.583, \(p\) < 0.001) but is comparable with OpenPose in dynamic conditions, and also confirm the difference between OpenPose and Kinect (slow-motion OpenPose vs. YOLO: \(t\)-stat = 1.385, \(p\) = 0.037; slow-motion OpenPose vs. AKBT: \(t\)-stat = \(-2.0\), \(p\) < 0.001; fast-motion OpenPose vs. AKBT: \(t\)-stat = \(-2.167\), \(p\) < 0.001).