# Joint Iterative Satellite Pose Estimation and Particle Swarm Optimization
## 4 Results  
### Training Results  
First, the experiment runs for one epoch and 100 batches to evaluate the trend of the PE-PSO method. Figures 2(a), 2(b) and 2(c) express the \(Error_{total}\), \(Error_{position}\), and \(Error_{orientation}\) values produced the first 100 batches of training in the first iteration, respectively. The conventional method and the PE-PSO method are compared with \(\omega=1\) and \(\omega_{damp}=0.9\), and the Common Objects in Context (COCO) weight, where the ResNet50 architecture is used as the backbone. At the beginning, the PE-PSO method yields high values for every aspect of the error. However, these errors gradually decrease when the number of batches increases. Therefore, the hypothesis is that the PSO algorithm can work jointly with the PE process. In the next experiments, five test cases are implemented, which are summarized as shown in Table 1.  
The weight (\(\omega\)) and weight damping ratio (\(\omega_{damp}\)) are deployed to conduct PSO processes, with different values used for each test case. Test case number 1 is the conventional method that implements processes without the joint iterative method including the PSO algorithm. Test cases 2 to 5 are the joint processing methods with the PSO algorithm that apply a \(\omega_{damp}\) of 0.5 and vary the value of the weight (\(\omega\)) to 0.5, 0.3, 0.2, and 0.1, respectively. All the experiments are implemented with 100 epochs, each epoch includes 1000 training batches, the ResNet50 structure is used as the backbone, and the model runs on a desktop computer equipped with an NVIDIA GeForce RTX 4070 GPU possessing 16 GB of VRAM. The experiment is performed with two types of pretrained weights: (1) the COCO weight and (2) the Soyuz_hard weight [11]. \(Error_{position}\), \(Error_{orientation}\), and \(Error_{total}\), which are calculated via Equations (10), (11), and (12), respectively, are presented in Figure 4. The results obtained with different training conditions exhibit different performances. For the COCO pretrained weight, the \(Error_{total}\) of the conventional method is worse than those of the other methods, whereas PE-PSO with \(\omega=0.3\) and \(\omega_{damp}=0.5\) performs best, as shown in Figure 4a. Figure 4c shows the \(Error_{position}\) results. Although the graph does not clearly verify that the PE-PSO method has better performance than the original method does, Table 2 presents a slight improvement. Corresponding to \(Error_{total}\) in Figure 4e, the PE-PSO method with \(\omega=0.3\) and \(\omega_{damp}=0.5\) provides the best \(Error_{orientation}\) results, whereas the conventional method has the highest orientation error. \begin{table}
\begin{tabular}{c c} \hline \hline
**Test Case No.** & **Training Condition** \\ \hline
1 & The conventional method \\
2 & The PE-PSO method with \(\omega=0.5\) and \(\omega_{damp}=0.5\) \\
3 & The PE-PSO method with \(\omega=0.3\) and \(\omega_{damp}=0.5\) \\
4 & The PE-PSO method with \(\omega=0.2\) and \(\omega_{damp}=0.5\) \\
5 & The PE-PSO method with \(\omega=0.1\) and \(\omega_{damp}=0.5\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Summary of test cases and training conditions. Figure 3: (**a**) Total loss, (**b**) position loss, and (**c**) orientation loss produced over 100 batches of training in the first epoch. Figure 4: The different errors induced by the conventional method and the PE-PSO method with various hyperparameters in test cases 2 to 5 are compared in Table 1. The \(Error_{total}\) values obtained with (**a**) the COCO weight and (**b**) the Soyuz_hard weight are shown. The \(Error_{position}\) values induced with (**c**) the COCO weight and (**d**) the Soyuz_hard weight are further presented. The \(Error_{orientation}\) values obtained with (**e**) the (COCO) weight and (**f**) the Soyuz_hard weight are also demonstrated. Tables 2 and 3 present the average accuracies achieved over 100 epochs of the training process with the COCO pretrained weight and the Soyuz_hard pretrained weight, respectively.