## Improving Placement Accuracy
### Validation of the Improved Placement Accuracy  
Placement accuracy improvements were validated by comparing the differences in the amount of projection errors occurring between AROS_\(\alpha\) versus AROS_\(\beta\). As discussed in Section 5.2, the mean error needed to be under 0.1 m, the criterion specified by the inspectors as the maximum allowable tolerance.  
Table 6 shows the results of the longitudinal and transverse measurements. The mean errors along the longitudinal (x-z plane) and transverse (x-y plane) axes were 0.066 and 0.013 m, respectively; thus, both axes were under the target threshold.  
For the transverse axis, the mean values at all intervals satisfied the requirement of being under 0.1 m. In the longitudinal axis, mean values under 9 m also satisfied the threshold. However, projections at 12 and 15 m exceeded the requirement, showing mean errors of 0.134 and 0.137 m, respectively.  
The minimum error was observed at 9 m in both axes (longitudinal and transverse). The causal analysis revealed that this was due to the correlation between the projection distance and the number of point clouds collected by LiDAR. The number of point clouds proportionally increased as the distance increased from 3 to 9 m. With more point cloud data points, ARWorldMap was able to recognize more topographical features and provide more legitimate anchor points. However, at projection distances of more than 9 m, the extracted point clouds were too far, and thus ARWorldMap was not as effective in identifying the useful features.  
The differences in the amount of error between the longitudinal and transverse axes also resulted from the quality of the point clouds. As the x-y plane of the transverse axes used the point clouds of the ground surface as an anchor, it was possible to recognize a continuous and consistent number of anchors, thereby maintaining high accuracy. Conversely, the point clouds used in the longitudinal axes (x-z plane) were segmented, and thus the number of legitimate anchors was smaller.  
In summary, the results revealed that the anchors extracted from the bridge's x-z plane were most effective at a projection distance of up to 9 m. At distances over 9 m, projection errors rapidly increased as the anchors were lost. Accordingly, inspections conducted at around 9 m would provide the most optimal placement accuracy in using AROS_\(\beta\).  
Table 7 and Figure 10 show the quantitative improvement in the placement accuracy of AROS_\(\beta\) compared to AROS_\(\alpha\). The introduction of additional anchors using ARWorldMap decreased the placement error of AROS_\(\alpha\) by a mean of \(-\)0.083 m. The improvement in the longitudinal and transverse axes were \(-\)0.070 and \(-\)0.096 m, respectively, revealing better performance in the transverse axis. The highest rate of improvement was observed at 3 and 6 m distances, where the use of QR codes is most effective. The results reinforce the validity of using a hybrid target method to improve projection placement accuracy.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline
**Distance** & **3 m** & **6 m** & **9 m** & **12 m** & **15 m** & **Mean (Total)** \\ \hline
**Standard Plane** & **x-z** & **x-y** & **x-z** & **x-y** & **x-z** & **x-y** & **x-z** & **x-y** & **x-z** & **x-y** & **x-z** & **x-y** \\ \hline
1 & 0.030 & 0.040 & 0.030 & 0.020 & 0.010 & 0.000 & 0.170 & 0.020 & 0.120 & 0.000 & 0.072 & 0.016 \\
2