# Star Identification Algorithm Based on Dynamic Distance Ratio Matching
## 5 Experiment and Analysis
### Image Distortion  
By simulating the identification accuracy of various algorithms under radial distortion, we can evaluate their robustness to distortion. We test several values of the distortion coefficient \(K\) ranging from \(-5\times 10^{-7}\) to \(+5\times 10^{-7}\) in Equation (14). When the \(K\) value is less than zero, it indicates the presence of barrel distortion, while a positive \(K\) value signifies the presence of pincushion distortion.  
\[\left\{\begin{array}{l}x_{0}=x(1+Kr^{2})\\ y_{0}=y(1+Kr^{2})\end{array}\right. \tag{14}\]  
As the distortion coefficient increases, the degree of distortion in the star image becomes more pronounced, and the positional deviation of each pixel increases with the distance from the center of the image. When the distortion coefficient is set to 5\(\times 10^{  
It can be observed that the proposed algorithm does not demonstrate a significant advantage in computational efficiency compared to other algorithms, particularly when compared to some existing highly efficient algorithms, as there is a gap in computation time. Specifically, we employ a two-dimensional lookup table structure during algorithm execution to optimize search efficiency. The algorithm primarily relies on distance ratios and angular features for matching. Accordingly, the navigation star database is utilized to construct a two-dimensional lookup table by organizing the navigation stars based on distance ratios and angles. The indices of this table are the distance ratios and angles, while the corresponding values represent the relevant navigation star information. This approach enables direct access to navigation stars that meet the requirements during the initial matching phase of dynamic angles, thereby improving the overall search efficiency. Future research will continue to incorporate the characteristics of the navigation star database to construct specific structures, further optimizing the search process and enhancing the execution efficiency of the algorithm.  
Nonetheless, computational efficiency is not the primary focus of this study, nor is it the sole criterion for evaluating the algorithm. Instead, the main objective of this research is to enhance the robustness and accuracy of the star identification algorithm under various adverse conditions, particularly in the presence of uncertainties such as image distortion and focal length variations, while maintaining high identification accuracy.  
We designed focal length variation experiments and image distortion experiments to evaluate the performance of the proposed algorithm under complex conditions. The experimental results demonstrate that the recognition accuracy of the proposed algorithm is barely affected under these extreme conditions, significantly outperforming traditional algorithms under the same circumstances. Even in cases of severe image distortion or substantial focal length changes, the algorithm is capable of accurately recognizing the targets in star images. This performance advantage enhances the reliability of the algorithm in practical applications, especially when performing star identification tasks in challenging environments, ensuring successful task execution and efficient target identification.  
Therefore, although there is some compromise in computational efficiency, the proposed algorithm's advantages in robustness and accuracy enable it to maintain stable performance in various complex and unpredictable environments. This makes the algorithm particularly suitable for practical tasks with extremely high reliability requirements.  
Figure 12: Comparison of algorithm computation time.