## 4 Results and Discussion
### Simulation Experiments and Analysis  
Due to differences in modeling methods and data sources, the accuracy of 3D models used in digital twin applications is often different, and different devices and environments have an impact on 2D-3D registration. To further analyze the impact of 2D-3D registration accuracy, simulation experiments were carried out in this study. The error factors affecting the registration algorithm are divided into systematic and random errors. The systematic error can be compensated for in the algorithm by measuring the camera calibration in the laboratory; therefore, the random error from various sensor measurements was the main factor causing the localization error. Table 6 lists the commonly used error terms and their distributions. The impact of the parameters in Table 5 on registration accuracy requires in-depth analysis. The literature [35; 36; 37] has analyzed and performed experiments on parameters \begin{table}
\begin{tabular}{c c c} \hline \hline
**Data** & **Error Model** & **Unit** \\ \hline Camera Position Error & Normal Distribution & \(\varphi_{A}/(^{\circ})\) \\ Camera Orientation Error & Normal Distribution & \(\psi/(^{\circ})\) \\ Pixel Measurement Error & Normal Distribution & \(u/(pixel)\) \\ Feature Matching Error & Normal Distribution & / \\ Image Distortion Error & / \\ Virtual Scene RMS Error & Normal Distribution & \(m\) \\ Feature Count & / & / \\ Field of View & / & / \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Parameters affecting target localization accuracy. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Target** & **Index** & **Trial 1** & **Trial 4** & **Trial 5** \\ \hline \multirow{3}{*}{T5} & PE(m) & 0.27/0.12/0.11 & 0.21/0.14/0.05 & \(-\)0.32/0.22/0.02 \\  & APE(m) & 0.32 & 0.25 & 0.40 \\  & RPE & 0.4\% & 0.49\% & 0.35\% \\ \hline \multirow{3}{*}{T6} & PE(m) & \(-\)0.05/1.54/\(-\)1.71 & \(-\)0.1/2.32/\(-\)2.39 & 1.01/2.27/\(-\)2.86 \\  & APE(m) & 2.30 & 3.33 & 3.79 \\ \cline{1-1}  & RPE & 3.5\% & 5.2\% & 5.9\% \\ \hline \hline \end{tabular}
\end{table} 
Table 5: _Cont._such as image distortion and camera pose. Hence, we adopted the Monte Carlo [38] method to analyze the impact of virtual scene errors on camera positioning and object positioning accuracy. The Monte Carlo method, also known as the stochastic simulation method, uses computers to generate qualified random data that can replace data that are difficult to obtain in experiments. Figure 11a shows the relationship between virtual scene data errors and calculated camera position root mean square (RMS) errors when the camera distance D is from 100 m to 500 m. Taking the center point of the image as the object position, Figure 11b describes the relationship between the RMS object position error and the virtual scene data error. The results show that the camera position error increases with the increase in virtual scene errors, but at different distances D, the RMS camera position errors remain approximately the same. When analyzing the object position error, the virtual scene data error increases when the RMS target position error increases. Additionally, when D increases, the incremental proportion of the RMS object position error is smaller than the incremental proportion of the distance D.  
These experimental results show that: (1) The camera position can be used as a constraint condition for image matching. If only the virtual scene data error needed to be considered, when the virtual scene data error was 10 m and the object distance was 500 m, the calculated RMS camera position error was only 5 m. (2) The result of object localization was better than the calculated result for the camera position. When D = 100 m, the calculated RMS object position error was only half of the camera position error. This is because when the camera direction was aimed at the target, a more accurate target localization result could be obtained. Figure 12 illustrates the impact of the field of view and feature count on the calculation accuracy of the camera pose and target position.