# Star Identification Algorithm Based on Dynamic Distance Ratio Matching
## 4 Supplementation with Adjacent Stars and Distortion Correction  
Due to the limitations of optical systems and the degradation of performance during on-orbit operations, actual observed star maps may exhibit various distortions. Typically, the degree of distortion increases with the distance from the center of the image. As a result, in distorted conditions, only a few stars near the center of the field of view can be successfully identified. Additionally, the sparse distribution of some stars or the presence of certain stars in edge regions of the image, where there are fewer neighboring stars providing information, can also lead to incomplete identification.  
We propose a method for supplementing neighboring stars by further utilizing the information from various neighboring stars during the matching process to increase the number of identified stars. By employing this method, the actual stars affected can be obtained, while also providing data support for subsequent distortion correction of the star image.  
By analyzing the previous stellar identification process, it was found that some neighboring stars' positional information was not fully utilized. In star identification, the reference star relies on the features provided by its neighboring stars. If the reference star is correctly identified, these neighboring stars should also be uniquely determined. Therefore, when constructing the navigation star catalog, in addition to recording the distance and angle features of each navigation star, it is also necessary to record the corresponding neighboring star numbers in counterclockwise order for each set of features.  
The matching process is conducted in a fixed order. When a star is successfully identified, some neighboring stars' numbers have also been determined throughout the matching process. For the identified navigation star, by combining the order of feature matches during the process and the neighboring star numbers stored in the navigation star database, the true star numbers of each neighboring star can be inferred, thereby restoring these neighboring stars' numbers sequentially.  
Using this method, it is possible to extend the identification from a single recognized star to multiple neighboring stars, significantly increasing the number of identified stars.  
In Figure 7, the left side represents the ideal star pattern, while the right side shows the actual star pattern. As discussed in the previous sections, when the navigation star is correctly identified, the number of neighboring star features that are currently matched is 6, meaning that neighboring stars 1, 2, 4, 5, 6, and 7 have all completed matching.  
When constructing the star catalog, the star numbers of each neighboring star are recorded in counterclockwise order, and the matching order is documented during the  
Figure 7: Schematic diagram of the adjacent star.  
matching process to derive the theoretical star numbers for neighboring stars 1, 2, 4, 5, 6, and 7. With our method, the number of identified stars can be further expanded.  
In our method, it is possible to supplement multiple neighboring star numbers while only identifying one star. Additionally, when multiple stars are recognized, each recognized star can supplement its own neighboring stars, and a neighboring star is considered a valid supplementary star only when the results are consistent across different recognized stars. This approach allows for mutual verification between neighboring stars, further enhancing the reliability of the supplementary neighboring star identification.  
Combined with the identification algorithm presented in this paper, the method of neighboring star supplementation can fully utilize the information between various stars, especially in cases where there is significant distortion in star images or a limited number of recognized stars, resulting in a notable improvement in performance.