## 4 Results and Discussions
### Comparison of 3D Position Estimation Results  
The purpose of the proposed framework is to estimate the 3D inventory position in a storage yard for management automation. Therefore, we conducted an experiment by filming the inventory and QR code as the video in an environment without shelves and grids, such as a storage yard. The ablation study of the proposed framework was performed for module performance evaluation. First, we compared the position estimation performance of the proposed framework with the base framework removing the DBSCAN module and angle-based correction module. Table 2 shows that the proposed framework has smaller errors and deviations in estimating the inventory 3D position than the base framework. When each of the proposed error correction methods was applied one by one, the performance was similar to or decreased compared to the baseline. If the drone's 3D position estimation result is noise, the angle between the epipolar line of noise and the other epipolar lines increases, so the angle-based error correction method gives a greater weight to the noise frame. Therefore, our proposed error correction methods must be used together to have an effect. In addition, we compared the results of the 3D position estimation of the inventory using the quadrangle, and the results of the 3D position estimation of the inventory using the data zone. The quadrangle is the QR code area detected by the segmentation model. The data zone is the detected area by decoding the QR code, as shown in Figure 4. It was confirmed that the error and deviation of the 3D position estimation of the inventory decreased, compared to the case of using the quadrangle when using the data zone. As a result of the experiment, the proposed framework estimated the inventory 3D position in small errors in the video taken in the real-world environment. Thus, we confirmed that the proposed framework is capable of estimating inventory 3D position in the storage yard. Furthermore, we verified the effectiveness of the error correction method. This means that the performance of the object 3D position estimation can be improved by using the outlier frame removal and the angle between epipolar lines. Therefore, if the outlier frame removal method is improved or a better correction method using the angle  
Figure 10: Results of the QR code segmentation and decoding. between epipolar lines is applied, the performance of the object 3D position estimation can also be improved. Additionally, for comparison with the deep learning model, we performed object 3D position estimation based on the monocular depth estimation deep learning model [59]. The epipolar line for the object was estimated using the segmentation model, and the distance between the drone and object was estimated using the depth estimation deep learning model. Three-dimensional position estimation of the object was performed through the epipolar line and the distance between the drone and the object estimated from deep learning models. However, the deep-learning-based depth estimation model had a distance error of several meters as shown in Figure 11. As a result, the error in the distance between the object and the drone increased, and the error in the object 3D position was very large. Furthermore, we performed a comparison of the added the computational running time due to the added outlier frame removal and the error correction method. The experiment on the running time for outlier frame removal confirmed that it took very little time, i.e., within 0.01 s from 50 to 250 frames. Furthermore, we confirmed that the error correction method took less time than outlier frame removal. The most important contribution of this study is to propose a novel framework for the 3D position estimation of inventory with a drone-mounted monocular camera for inventory management automation. Unlike the need for four ground QR codes in our previous work, the proposed framework estimates the 3D position of object with one ground QR code by using the alignment pattern of the QR code.