## 5 Results and Discussion  
For the two experiments above, the changes of weights (Q\({}_{1}\), Q\({}_{2}\), Q\({}_{3}\)) and coordinates (\(X_{G}\), \(Y_{G}\), \(Z_{G}\)) of each spatial line in the iterative process are shown in Table 11 and 12. In the first experiment, the spatial coordinates of the center of the circle are known, so the measured results of the two algorithms can be compared with the true coordinates of the center of the circle. The comparison results are shown in Table 13. It can be seen from the table that the precision of the WFA is obviously higher than that of the EWFA. Since the second experiment is an engineering experiment, the center of the circle cannot be measured directly, and its true coordinates are unknown. Therefore, the accuracy of center fitting is evaluated by the error of multiple radii. RA, RB, RC and RD represent the radii between points \(A\), \(B\), \(C\) and \(D\) and the center of the circle, respectively. The radii calculated in the two experiments are shown in Tables 14 and 15. The true radius of the first experiment is 150 mm, The true radius of the second experiment is 545 mm. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Iteration** & **1** & **...** & **9** & **10** \\ \hline \(Q_{1}\) & 0.2307 &... & 0.3440 & 0.3440 \\ \(Q_{2}\) & 0.1919 &... & 0.3122 & 0.3122 \\ \(Q_{3}\) & 0.5774 &... & 0.3438 & 0.3438 \\ \(X_{G^{\prime}}\) (mm) & 50.2157 &... & 50.1357 & 50.1357 \\ \(Y_{G^{\prime}}\) (mm) & 181.4355 &... & 181.2654 & 181.2654 \\ \(Z_{G^{\prime}}\) (mm) & 17.0186 &... & 17.0200 & 17.0200 \\ \hline \hline \end{tabular}
\end{table} 
Table 11: The iteration of first experiment. \begin{table}
\begin{tabular}{c c c} \hline \hline  & **First Image** & **Second Image** \\ \hline \(X_{S}\) (mm) & \(-\)3904.4757 & \(-\)4225.2792 \\ \(Y_{S}\) (mm) & 2611.1973 & 1679.2832 \\ \(Z_{S}\) (mm) & \(-\)686.9809 & \(-\)695.0026 \\ \(\varphi\) (rad) & \(-\)1.3931 & \(-\)1.4217 \\ \(\omega\) (rad) & 0.5313 & 0.3714 \\ \(\kappa\) (rad) & 1.4773 & 1.5399 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: The elements of exterior orientation of the two images in second experiment. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Results** & \(X\) **(mm)** & \(Y\) **(mm)** & \(Z\) **(mm)** \\ \hline \(A\) & 119.54 & \(-\)27.75 & 579.79 \\ \(B\) & 97.19 & \(-\)153.39 & 579.34 \\ \(C\) & 99.90 & \(-\)266.98 & 579.05 \\ \(D\) & 136.87 & \(-\)401.06 & 578.15 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Calculation results of space points of second experiment. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Results (mm)** & **EWFA** & **WFA** \\ \hline \(\Delta X\) & 0.2157 & 0.1357 \\ \(\Delta Y\) & 1.4355 & 1.2654 \\ \(\Delta Z\) & \(-\)0.9814 & \(-\)0.9800 \\ \hline \hline \end{tabular}
\end{table} 
Table 13: Error comparison of the first experiment. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{2}{c}{**EWFA**} & \multicolumn{2}{c}{**WFA**} \\ \hline
**Results (mm)** & **Measured Values** & **Relative Error** & **Measured Values** & **Relative Error** \\ \hline RA & 151.1412 & 0.76\% & 151.0331 & 0.69\% \\ RB & 150.5402 & 0.36\% & 150.5229 & 0.35\% \\ RC & 149.7944 & 0.14\% & 149.8729 & 0.08\% \\ RD & 148.6531 & 0.90\% & 148.8404 & 0.77\% \\ \hline \hline \end{tabular}
\end{table} 
Table 15: The calculated radii of the second experiment. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **EWFA** & **WFA** \\ \hline
**Results (mm)** & **Measured Values** & **Relative Error** & **Measured Values** & **Relative Error** \\ \hline RA & 556.0752 & 2.03\% & 548.3661 & 0.62\% \\ RB & 555.0094 & 1.84\% & 546.9021 & 0.35\% \\ RC & 555.1416 & 1.86\% & 547.0460 & 0.38\% \\ RD & 555.2869 & 1.89\% & 547.6702 & 0.49\% \\ \hline \hline \end{tabular}
\end{table} 
Table 15: The calculated radii of the second experiment. Figure 9: The error of radii in the first experiment. It can be seen from Tables 10 and 11 that the convergence speed of the algorithms is fast, and it can basically converge within 10 iterations and obtain the optimal value.