# A Star-Identification Algorithm Based on Global Multi-Triangle Voting
## 3 Simulations and Results
### Comparison and Analysis  
The influence of the three different types of noise (position noise, magnitude noise, and false stars) on the identification rate of the proposed algorithm, geometric voting algorithm, and grid algorithm is shown in this section. The position noise added to the observed star makes the corresponding projected centroids deviate from their theoretical location coordination. Compared with the star magnitude data listed in SAO, there are some errors in the star brightness for images captured by the star sensor, which leads to some brighter stars, whose magnitude value in the star catalog is less than 5.5 Mv, being lost in star images, while dimmer stars, whose magnitude value in the star catalog is more than 5.5 Mv, are captured by the star sensor and appear in the image. Besides the above two measurement noise sources, false stars may appear in the captured image because planets, observed spacecraft, radiation, space fragments, and hot spots may also appear in the captured image, and these are mistakenly regarded as true stars. In our experiment part, all parameters of the algorithm are fixed, and one noise source increases linearly, while the others are maintained at a typical level. In total, 5000 star images are generated and identified by the three algorithms to evaluate their identification rates with different noise conditions through the Monte-Carlo method. Figure 11: Identification rate versus positional noise with different discretized unit. (1). Robustness toward star positional noise: Figure 12 illustrates the identification rates of star images for three algorithms when the star position noise increases linearly from a 0.0 to 2.0 pixels with a 0.5-pixel step, while the magnitude noise is kept at 0.3 Mv. As shown in Figure 12, the identification rate of the proposed algorithm remains at more than 97.0% when the standard deviation of the position noise added to the star image is 2.0 pixels. As for the grid algorithm, its identification rate decreases quickly from 99.32% to 83.5% as the position noise increases, while the identification performance of the geometric voting is much poorer with large noise, whose identification rate drops significantly from 97.82% to 61.08%, which drops more than 36.74%. It is obvious that the positional noise deviation increase has little effect on the identification performance of the proposed algorithm compared with the two reference algorithms. When the position noise is 2.0 pixels, the identification rate of the algorithm is 35.92% higher than the geometric voting algorithm and 13.50% higher than the grid algorithm. However, the position noise causes the wrong closest neighbor star to be selected as the orientation star, and the incorrect grid pattern is built. For the geometric algorithm, the basic vote unit is star pairs, which is a low-dimension feature and always receives numerous candidate votes due to position error. While the vote unit is undirected and of a higher feature dimension, it is more robust to position noise in the voting process. (2). Robustness toward star magnitude noise: Figure 13 illustrates the identification rates of star images for three algorithms when the star magnitude noise increases linearly from 0.1 to 0.5 Mv with a 0.1 Mv step while the position noise is kept at 1.0 pixels. As shown in Figure 13, the proposed algorithm identification rate drops slightly from 99.9% to 97.14% when the standard deviation of magnitude noise gradually grows from 0.1 to 0.5 Mv. In contrast, the other two reference algorithms obtain a lower identification rate with larger noise; the grid algorithm identification rate decreases to 90.22% while the geometric voting algorithm drops sharply to 89.28% with 0.5 Mv magnitude noise, respectively. We can see that the magnitude noise deviation increase has less of an effect on the identification performance of the proposed algorithm compared with the two reference algorithms.