## 4 Results and Discussion
### Application Experiment of Multi-Object Positioning for Monocular Image  
Object positioning is commonly used in digital twin applications. This study designed a multi-object spatial positioning application experiment based on a monocular image to verify the effectiveness of this method in object positioning. Once the pose of the camera is computed, the object target can be located. This experiment was conducted using the digital twin city model data. The error between the result of object geolocation and that obtained from the model data was analyzed. Three different points in each image were selected as target points in the image; the position of each point in the image is shown in Figure 10. The coordinates of the points were calculated based on Trials 1, 4, and 5 and the coordinates of the target points corresponding to the model data as true values. Figure 9: Experimental results of time performance test: (**a**) time performance comparison of image matching algorithm; (**b**) time performance comparison of feature extraction. Table 4 lists the basic information for each target point, and Table 5 lists the different experimental results obtained. In the target point information, target distance (TD) refers to the distance between the target point and the camera in meters, and radial distance (RD) refers to the radial distance of the target point on the image from the principal point in pixels. Base coordinates (BC) refer to the coordinates of the target point in the base geographic data, which are used to evaluate the errors of the coordinates of the target point calculated in different trials. The evaluation index includes the position error (PE), absolute position error (APE), and relative position error (RPE). The PE refers to the error of the target point in the ECEF system. The APE is the L2 distance of the PE. The RPE is the relative error calculated using RPE \(=\) APE/TD. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **T1** & **T2** & **T3** & **T4** & **T5** & **T6** \\ \hline TD(m) & 225.08 & 172.25 & 119 & 103 & 82 & 64 \\ RD & (728,435) & (111,655) & (423,755) & (696,534) & (138,433) & (751,863) \\  & \(-2093175.39\) & \(-2093268.12\) & \(-2093291.67\) & \(-2093828.59\) & \(-2093861.08\) & \(-2093831.16\) \\ BC & 4806240.40 & 4806242.66 & 4806203.83 & 4806463.96 & 4806437.85 & 4806415.05 \\  & 3621093.20 & 3621000.58 & 3621049.34 & 3620461.02 & 3620453.39 & 3620457.80 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Basic Information for Each Target Point. Figure 10: Target object points in P1 and P2. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Target** & **Index** & **Trial 1** & **Trial 4** & **Trial 5** \\ \hline \multirow{3}{*}{T1} & PE(m) & \(-0.31/-0.36/0.13\) & \(-0.27/0.64/-0.41\) & \(0.18/-0.38/0.5\) \\  & APE(m) & 0.50 & 0.80 & 0.65 \\  & RPE & 0.25\% & 0.39\% & 0.32\% \\ \hline \multirow{3}{*}{T2} & PE(m) & \(-0.25/-0.32/0.31\) & \(-0.98/0.88/-1.68\) & \(-2.88/0.21/-2.06\) \\  & APE(m) & 0.68 & 2.13 & 3.54 \\  & RPE & 0.4\% & 1.2\% & 2.0\% \\ \hline \multirow{3}{*}{T3} & PE(m) & \(-1.52/0.19/-0.66\) & \(-0.72/0.72/1.97\) & \(-1.31/-1.64/1.56\) \\  & APE(m) & 1.66 & 2.21 & 2.61 \\  & RPE & 1.5\% & 1.90\% & 2.37\% \\ \hline \multirow{3}{*}{T  
Experiments show that this method can alleviate the uneven distribution of target position errors. In Trials 4 and 5, targets T1, T4, and T5 are located near the image center with an average relative error of 0.3%, while T3 and T6 are located near the edge of the image with an average relative error of 3.84%. This is because the camera pose error is larger in the vertical direction, resulting in a target position error in the image, which also presents the problem of uneven distribution in the vertical direction.