## 5 Simulation Debugging  
### Algorithm Accuracy Analysis  
In order to verify the effectiveness of the above algorithm, the algorithm is used to simulate the dynamic star map under the MATLAB R2022a software environment, and the simulation is carried out with resolutions of \(q_{1}=0.109382\), \(q_{2}=0.234570\), \(q_{3}=0.875246\), and \(q_{4}=0.408218\). The coordinates and grayscale of the pixels of the star points in the star map are obtained. The star catalog global traversal algorithm and the algorithm in the literature [16] are simulated in MATLAB, and the results of the computation of the pixel coordinates are retained to four digits after the decimal point. The calculations show that all 45 star points are present, so there are no missing star points. Some of the star points are calculated as shown in Table 3.  
Figure 8: Gaussian template weight distribution. Figure 9: Gaussian filtering data flow diagram. The computational results of the algorithms in the article and the global traversal algorithm are subtracted from the results of the algorithm in the literature [16] to obtain the deviation values, respectively. Figure 10a,b represent the deviation of the computational results of the algorithm in this article and the global traversal algorithm in the x-axis and y-axis directions, respectively. By analyzing the digital star map generation method, the positional deviation of the star point pixels is generated by the following three main factors:  
1. Deviations arising from insufficient precision of the right ascension and declination. 2. Deviations arising from insufficient precision of the quaternion. 3. Deviations during lookup tables and divider computation on FPGA-based platforms. In MATLAB, Figure 11a,b are obtained by adding each of the three deviations separately to the algorithm of the literature [16]. The precision of the right ascension and declination produces a high deviation between the different star points. The mean values of deviation in the x-axis direction and the y-axis direction are 0.1874 and 0.1917, respectively. The deviation of the quaternion causes a deviation in the calculation of the optical axis \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Star Point Number**} & **Algorithms of the** & **Global Traversal** & **Algorithms in** \\  & **Article** & **Algorithm** & **Literature [16]** \\ \hline
1 & (1344, 52) & (1343.6290, 52.3454) & (1343.1869, 52.4629) \\
2 & (1061, 140) & (1060.8745, 140.0319) & (1060.5171, 140.6719) \\
3 & (916, 118) & (916.4424, 118.2077) & (916.2079, 118.7047) \\
4 & (856, 59) & (856.3491, 58.9552) & (856.1927, 59.4249) \\
5 & (1831, 458) & (1830.8544, 457.6822) & (1830.6509, 457.8170) \\
6 & (1788, 571) & (1788.0021, 570.7881) & (1787.8998, 571.2094) \\
7 & (1760, 525) & (1760.3848, 524.7738) & (1760.0700, 524.7066) \\
8 & (1620, 470) & (1619.9463, 469.7154) & (1619.8961, 470.1568) \\
9 & (1507, 301) & (1506.5255, 301.4758) & (1506.4625, 301.9288) \\
10 & (1441, 319) & (1440.7954, 318.6252) & (1440.2570, 319.1484) \\
11 & (1426, 428) & (1426.2083, 427.5948) & (1426.0594, 428.0663) \\
12 & (1372, 273) & (1371.7320, 273.2372) & (1371.4097, 273.7248) \\
13 & (1335, 261) & (1335.0012, 261.1535) & (1334.6780, 261.6318) \\
14 & (1341, 289) & (1340.8006, 288.8830) & (1340.2432, 289.0485) \\
15 & (1738, 597) & (1737.6861, 597.0918) & (1737.6717, 597.5124) \\
16 & (1613, 768) & (1613.1615, 768.0119) & (1613.1064, 767.9271) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Calculation of star points. Figure 10: (**a**) Integrated deviation in the x-axis direction; (**b**) Integrated deviation in the y-axis direction. pointing; therefore, its error produces a small overall shift in all the star points in the chart. The precision of quaternions produces a higher average deviation. The mean values of deviation in the x-axis direction and the y-axis direction are 0.3236 and 0.26, respectively. The lookup tables and the dividers have little effect on the final result during the calculation.