# Joint Iterative Satellite Pose Estimation and Particle Swarm Optimization
## 5 Conclusions  
The vision-based navigation field has advanced because of the availability of research and the development of artificial intelligence, which can be applied to develop space technology. For example, vision-based navigation is applied in satellite PE because of the high precision of the close proximity, on-orbit servicing, and active space debris removal operations. Two types of vision-based navigation are available: key point-based estimation and end-to-end estimation. Key point-based satellite PE extracts key points from images via different techniques and then inputs them into a deep learning model to conduct the PE \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**K**} & \multicolumn{3}{c}{_Error\({}_{position}\)_} \\ \cline{2-4}  & **Conventional** & **PE-PSO** & **Improvement (\%)** \\ \hline
1 & 0.2035 & 0.2011 & 1.2\% \\
2 & 0.1839 & 0.1827 & 0.7\% \\
3 & 0.1982 & 0.1971 & 0.6\% \\
4 & 0.1869 & 0.1826 & 2.3\% \\
5 & 0.2016 & 0.1981 & 1.7\% \\
6 & 0.1874 & 0.1889 & \(-\)0.8\% \\
7 & 0.1864 & 0.1818 & 2.5\% \\
8 & 0.1855 & 0.1804 & 2.8\% \\
9 & 0.1826 & 0.1784 & 2.3\% \\
10 & 0.1873 & 0.1842 & 1.7\% \\ \hline Mean & 0.1903 & 0.1875 & 1.5\% \\ \hline \hline \end{tabular}
\end{table} 
Table 7: The mean position error for cross-validation. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**K**} & \multicolumn{3}{c}{_Error\({}_{position}\)_} \\ \cline{2-4}  & **Conventional** & **PE-PSO** & **Improvement (\%)** \\ \hline
1 & 9.5549 & 9.5286 & 0.3\% \\
2 & 9.4215 & 9.4259 & 0.0\% \\
3 & 9.4670 & 9.4544 & 0.1\% \\
4 & 9.4421 & 9.4345 & 0.1\% \\
5 & 9.5356 & 9.5201 & 0.2\% \\
6 & 9.4632 & 9.4113 & 0.6\% \\
7 & 9.4887 & 9.4882 & 0.0\% \\
8 & 9.4406 & 9.4363 & 0.1\% \\
9 & 9.4922 & 9.4835 & 0.1\% \\
10 & 9.4552 & 9.4557 & 0.0\% \\ \hline Mean & 9.4761 & 9.4639 & 0.1\% \\ \hline \hline \end{tabular}
\end{table} 
Table 8: The mean orientation error for cross-validation. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**K**} & \multicolumn{3}{c}{_Error\({}_{total}\)_} \\ \cline{2-4}  & **Conventional** & **PE-PSO** & **Improvement (\%)** \\ \hline
1 & 9.7583 & 9.7298 & 0.3\% \\
2 & 9.6054 & 9.6086 & 0.0\% \\
3 & 9.6652 & 9.6515 & 0.1\% \\
4 & 9.6290 & 9.6171 & 0.1\% \\
5 & 9.7371 & 9.7181 & 0.2\% \\
6 & 9.6506 & 9.6002 & 0.5\% \\
7 & 9.6751 & 9  
process. The drawback of this method also depends on the performance of the implemented key-point extraction technique, while other advantages include a reduction in the required processing time. For end-to-end satellite PE, the given RGB images are directly input into a deep learning model for the PE process, in which the interference of the extraction method is ignored because of the original input source. Although more computational time is required in this method than in the first approach, the overhead of computer equipment is substantial. PE-PSO, the joint iterative deep learning-based PE and PSO method, is proposed as a novel method, where the objective is to improve the accuracy of satellite PE. The PE-PSO method is designed by adding slack variable modifications for the input data contained in every training batch of the PE algorithm. The size of the modified slack variable is adjusted so that it is equal in size to the batch size implemented in the PE algorithm, which is updated on the fly based on the concept of the PSO algorithm. The results are presented in terms of the error reduction achieved in each epoch. In this experiment, three types of errors are analyzed: position estimation error, orientation estimation error, and total estimation error, which include position and orientation errors. PE-PSO performs well by mitigating the mean position estimation error and the mean orientation estimation error by 13.1% and 29.1% on the testing dataset, respectively, based on the COCO pretrained weight.