## 4 Experimental Methods and Results
### Experimental Results  
The performance comparison between single- and multiple-marker approaches was conducted by analyzing the mean and standard deviation of pose estimation errors. The image processing of the graphical markers was executed using an Intel Core i3-8145U CPU with integrated UHD Graphics 620 and 12 GB of RAM. Pose estimation with a single marker achieved a processing speed of 30 frames per second (FPS), while using multiple markers resulted in a speed of 25 FPS. Both cases demonstrated processing speeds suitable for real-time application on mobile robots. Figure 5 presents error bar graphs showing these statistics across all six relative poses between the fixed camera and the representative marker. The bars represent mean errors, while the lines indicate standard deviations. Figure 5a shows position errors along the x-, y-, and z-axes, as well as Euclidean distance errors. Table 1 provides detailed numerical values for the mean and standard  
Figure 4: Experimental setup for pose estimation. (**a**) Experiment using fixed camera, (**b**) Experiment using drone mounted camera. Figure 5: Mean and standard deviation of pose error measured with fixed camera. Red and blue represent experimental results using single marker and multiple markers. (**a**) Position error, (**b**) Orientation error. deviation of position errors. The \(t\)-test analysis demonstrated statistically significant differences (\(p<0.05\)) between single-marker and multiple-marker estimation methods for all relative camera-marker configurations in Table 1, except for the x-direction error where the camera center was 10 cm away from the marker origin and tilted by 0 degrees. The results demonstrate that the pose estimation using multiple markers achieved lower mean errors across all directional components and Euclidean distances compared with the single-marker method. Additionally, the standard deviations were consistently smaller when using multiple markers, indicating improved precision. Figure 5b presents orientation errors in roll, pitch, and yaw angles, where \(\varphi\), \(\theta\), and \(\psi\) represent errors in roll, pitch, and yaw angles, respectively. The detailed values are provided in Table 2. Statistical analysis using \(t\)-tests revealed significant differences (\(p<0.05\)) between single-marker and multiple-marker estimation approaches for all configurations listed in Table 2, except for the \(\theta\) where the camera center was only displaced along the z-axis with a 45-degree tilt from the marker. The pose estimation using multiple markers showed superior performance in both accuracy (mean error) and precision (standard deviation) compared with the single-marker method. This improvement was particularly pronounced when the camera was tilted at 60\({}^{\circ}\) relative to the marker plane, where the pose estimation using a single marker showed significantly larger errors and variations in \(\varphi\) direction. The most significant performance difference between single- and multiple-marker approaches was observed when the camera was located at its initial position and tilted 60\({}^{\circ}\) around the x-axis. Figure 6 illustrates the temporal evolution of pose errors under this fixed-camera setup. In Figure 6, red lines represent pose estimation results using a single marker, and blue lines show pose estimation results using multiple markers. Three graphs in the first row, from Figure 6a-c, show position errors along the x-, y-, and z-axes, respectively. Other graphs in the second row, from Figure 6d-f, present roll, pitch, and yaw errors, respectively. The pose estimation results using a single marker exhibited notable error spikes, highlighted by the red boxes, and temporal fluctuations. The pose estimation results using multiple markers demonstrated more stable and accurate measurements.