# Joint Iterative Satellite Pose Estimation and Particle Swarm Optimization
## 4 Results
### Training Results
Test cases 2 to 5, which are joint processes with the PSO algorithm, tend to yield better results than the conventional method does for pretrained weights. For the COCO pretrained weight, test case number 3, whose weight (\(\omega\)) = 0.3, performs the best for every error aspect, with a decrease of 3.6% in \(Error_{total}\). Under the Soyuz_hard pretrained weight, test case number 4 attains the optimal performance for \(Error_{total}\) and \(Error_{orientation}\). The proposed method outperforms the conventional method by 0.1% in terms of both types of error, whereas test case number 3 improves \(Error_{position}\) by 3.3% over that of the conventional method. Although Figures 4b, 4d and 4f, which plot the \(Error_{total}\), \(Error_{position}\), and \(Error_{orientation}\) induced with the Soyuz_hard pretrained weight, respectively, clearly present outstanding performance, the improvement is reflected by the numerical values in Table 3 and is clearly described above. In addition, the computational times of the conventional method and the PE-PSO method are not different, as detailed in Tables 2 and 3. Table 2 shows that there is no pattern for setting the optimal number of weights (\(\omega\)) and inertia weight damping ratio \(\left(\omega_{damp}\right)\). Large or small parameter values do not always result in the best performance. The results are dependent on the proper values, which are affected by several factors, such as the dataset and hyperparameters. Moreover, the mean and standard deviation (\(\sigma\)) of each modified element of the slack variable (\(\xi\)) mentioned in Equation (4) are addressed, as presented in Table 4 and Figure 5, by implementing test case number 3. In Figure 5, batch numbers 400, 600, and 800 are chosen for plotting, and the behaviors of these modified slack variables are presented. The Y-axis represents the modifications of the slack variables \(\xi_{1},\xi_{2},\xi_{3},\xi_{4}\) in Figure 5a, Figure 5b, Figure 5c, and Figure 5d, respectively, while the X-axis represents the number of epochs. This figure clearly shows that when time passes, the values of these variables tend to be stable and vary less than they did at the beginning of the interaction process. The graph in Figure 5 corresponds to the standard deviation values (\(\sigma\)) in Table 4. The standard deviation (\(\sigma\)) decreases with time, and the smallest value is obtained when the number of epochs is 100, which is the last epoch of the experiment. This finding supports the fact that higher accuracy is attained in the final case. However, slack variable element number 1 (\(\xi_{1}\)) is modified, where the standard deviation (\(\sigma\)) does not comply with the assumption because  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Test Case No** & \(Error_{total}\) & **Improvement** & \(Error_{position}\) & **Improvement** & \(Error_{orientation}\) & **Improvement** & \begin{tabular}{c} **Computation** \\ **Time (s)** \\ \end{tabular}  \\ \hline
1 & 6.6347 & - & 0.0976 & - & 6.5372 & - & 59,131.9780 \\
2 & 6.6226 & 0.2\% & 0.0994 & \(-\)1.9\% & 6.5232 & 0.2\% & 60,345.0513 \\
3 & 6.3971 & **3.  
the number of iterations is not sufficient. The tradeoff between iteration time and accuracy must be carefully defined to attain appropriate performance.