## 4 Discussion  
The proposed algorithm was validated using a mockup point cloud, which introduces several notable differences compared to an actual spacecraft's point cloud data. These differences are essential to consider for the practical application of the algorithm. One significant aspect is the resolution of the point cloud data. The ToF camera used in our laboratory had a resolution of 640 \(\times\) 480 pixels, whereas LiDAR systems typically used for actual spacecraft produce higher-quality data. While this study focused on algorithm validation, future research must explore how variations in imaging resolution impact the algorithm's performance. Another critical difference lies in the noise characteristics. Laboratory-acquired mockup data may include system noise from the camera, ambient light noise, and multipath reflection noise, which are relatively stable and controllable. In contrast, point cloud data from an actual on-orbit spacecraft would be subject to more diverse and complex noise sources, including space radiation, temperature fluctuations, and other environmental factors. Addressing these complex noise characteristics is crucial for ensuring the robustness of the proposed algorithm in real-world conditions. The surface reflectivity properties of the mockup and actual spacecraft also differ significantly. The materials and structures of the satellite model used in our experiments are simplified compared to those of real spacecrafts, which have more complex materials and reflectivity characteristics. These differences can affect the quality and accuracy of the point cloud data, necessitating future studies to investigate how varied reflectivity properties influence the performance of pose estimation algorithms. Additionally, the geometric complexity of the model used in the experiments presents another difference. The 1:35 scale Beidou satellite model lacks the detailed geometric intricacies of an actual spacecraft due to its smaller size. Real spacecrafts would produce point cloud data with richer geometric texture information. Therefore, future work should focus on validating the algorithm using actual spacecraft models to capture these complex details. To enhance the applicability of the proposed algorithm to actual spacecraft, several measures can be considered. These include advanced data preprocessing and filtering techniques, such as Gaussian filtering, median filtering, and neighborhood-based statistical filtering, to reduce sensor noise and improve data reliability. Employing dual cameras to capture point cloud data and applying interpolation or downsampling techniques can help match the resolution of LiDAR scan data. Optimizing algorithm parameters and models based on actual spacecraft data, and validating the algorithm's performance in real-world environments through simulations or practical tests, will ensure its robustness and applicability under various conditions. The results from our experiments indicate that the proposed method significantly improves the accuracy of point cloud alignment and robustness against noise and outliers. However, the computational efficiency of our approach can still be further enhanced. In the context of accelerating algorithmic performance, integrating machine learning methods like PARSAC [30] can provide substantial benefits. PARSAC addresses the computational bottlenecks found in traditional methods such as CONSAC by predicting sample weights for all model instances simultaneously. Adopting a similar strategy, future work could focus on integrating a neural network to predict sample weights for the coarse registration process in point cloud alignment. By predicting both sample and inlier weights, the alignment process could be handled in parallel, significantly accelerating the computation. This would particularly benefit scenarios where rapid and accurate alignment is crucial, such as in dynamic space missions involving non-cooperative targets.