# A Star-Identification Algorithm Based on Global Multi-Triangle Voting
## 3 Simulations and Results
### Comparison and Analysis
When the magnitude noise is 0.5 Mv, the identification rate of our algorithm is 6.92% higher than the grid algorithm and 7.86% higher than the geometric voting algorithm. The reasons for this are as follows: some dimmer stars' appearance and some brighter stars' disappearance due to magnitude noise cause the wrong closest neighbor star selection and the building of an incorrect grid pattern. For the geometric algorithm, the wrong brighter stars are chosen and receive false votes in the identification process. However, the dimension in the algorithm of the vote unit feature is higher, and it needs fewer correct  
Figure 12: Identification rate versus positional noise. brighter stars to generate vote units to obtain reliable identification results, so it is more robust to magnitude noise. (3). Robustness toward false stars: Figure 14 illustrates the identification rates of star images for the three algorithms as the false star number increases linearly from 0 to 5. In this test, the star position noise and magnitude noise are kept at 1.0 pixels and 0.3 Mv, respectively, while the magnitude value of false stars added to simulated star images varies from 3.5 Mv to 5.5 Mv randomly. As shown in Figure 14, the proposed algorithm obtains a higher identification rate than reference algorithms as the number of false stars increases from 1 to 5. For our algorithm, the identification rate decreases from 99.16% to 91.02% with false stars increasing, while the identification performance of the geometric voting becomes unsatisfactory when five false stars are added to the image, where it drops significantly to 59.48% and decreases by 33.54% compared with only one false star. The identification rate of the grid algorithm is similar to our algorithm with five false stars, but its identification performance is poorer than our algorithm. It is obvious that false stars have less influence on the identification performance of the proposed algorithm compared with the other two algorithms. When five false stars are  
Figure 14: Identification rate versus false star. Figure 13: Identification rate versus magnitude noise. added to the star images, the identification rate of the algorithm is 31.54% higher than the geometric voting algorithm and 0.28% higher than the grid algorithm. In fact, false stars may be selected as the closest neighbor stars or cause main stars to be identified, which causes the wrong grid pattern to be built, degrading the performance of the algorithm to some extent. Likewise, incorrect vote star pairs are generated when brighter false stars are selected and wrong candidates are obtained in the geometric algorithm. Our algorithm can utilize fewer correct brighter stars to obtain reliable vote results in the identification process, which makes it robust to false stars. (4). Memory and time performance: Table 2 lists the memory size and running time of the proposed algorithm and the other two reference algorithms, in which memory size is defined as the memory size of the onboard database containing the guide star table and feature table in the algorithm, and run-time is the average time spent identifying a star image with a 1.0-pixel star position noise and 0.3 Mv magnitude noise. In terms of the run-time performance, our algorithm is 18.36 ms, which is much faster than the grid algorithm (72.71 ms) and geometric voting algorithm (96.86 ms) due to the adopted PCA dimensionality reduction and two-dimension lookup table. It should be noted that the onboard memory size was very limited in the past, so it is important to pursue a lower database to reduce the required memory cost in algorithm design. However, embedded systems can easily store 5 MB data, and memory size is gradually become a less significant part of the algorithm compared with the identification rate and run time in the star-identification technique. Considering the above factors, it is still acceptable that the proposed algorithm occupies 1.5 MB, which is larger than the reference algorithms.