# Modeling and Simulation of Sky Survey
## 4 Design of the Model Solving Algorithm
### Overall Arrangement Algorithm
The area of the sky area left for observation becomes less and less, so the observation efficiency gradually decreases in the later stage. Figure 7c shows the results of the growth of the covered area according to the annual statistics. As can be seen, a maximum of more than 2600 deg\({}^{2}\) of the sky area is observed in the third and fourth years. The eighth year has a total observation area of more than 500 deg\({}^{2}\) in nine months, which is 75% of the time. However, it is 25% of the time of the

Figure 6: CMG rotation angle statistics results. (**a**) Represents the main graph with an angular statistic interval of 0.1\({}^{\circ}\). (**b**) A zoomed-in display of rotation angles below 10\({}^{\circ}\). (**c**) Counts the statistics at 10\({}^{\circ}\) intervals. first year, indicating that the eighth year is in the stage of replenishing the sky area. In addition, the areas that are difficult to observe in the previous years are replenished with observations in the ninth year. From Figure 9g, it can be seen that the area observed in the ninth year is very small and mainly concentrated in the sky areas that are difficult to observe in the previous years. Figure 8: The results of the first year of sky surveys, with different colors representing different numbers of observations. Figure 7: Statistical results of sky survey coverage efficiency. (**a**) The cumulative statistical results according to the daily coverage efficiency. (**b**) The cumulative coverage efficiency according to the monthly statistics and the results of each month. (**c**) The cumulative results of the coverage efficiency according to the annual statistics and the data of each year. Figures 8 and 9 show the display of the effect of the sky survey observations from the second to ninth year. The two elliptical sky regions with dimensions near the South Pole and the North Pole are observed first, because they are found to be more difficult to observe after several planning sessions. The weighting factors of the regions are increased, so that they are observed first. Figure 9: Presentation of observation results from the second year to the ninth year with parameter \(\gamma_{1}=0.6\). ### Experimentation of Algorithm Parameters

Three of the five parameters shown in Table 5 are designed according to the satellite orbit, and two parameters are related to the algorithm design. The two parameters of the algorithm design are set differently, and the results of the sky survey planning are different. In order to study the specific effect of parameter settings on the sky survey effect, this section conducts experiments on the controlling efficiency parameter \(\gamma_{1}\). The results of the sky survey area with different parameters are shown in Figure 10. It can be seen that the first to fifth years of the sky survey are slow with the parameter (\(\gamma_{1}=0.7\)), increasing the area by about 1600 deg\({}^{2}\) at most. The sixth year increases the most, about 5200 deg\({}^{2}\) of the sky survey area, indicating that some of the sky areas accumulated in the previous years with an insufficient number of observations are observed a lot in the sixth year. This breaks through the single-year observation area of more than 5000 deg\({}^{2}\). The case of parameter 0.7 is slightly different from the case of parameter 0.6. Since the increase of the efficiency parameter makes it so that the sky areas that are not prioritized in the previous years are scheduled, it can be seen from Figure 10a that the observed sky area is more homogeneous compared with the case of parameter 0.6. In addition, the increase in observations is slow before the sixth year, and a rapid increase occurs in the sixth year. The eighth year of the resultant observations can complete 16,492 deg\({}^{2}\) of the sky area. For the case of parameter 0.6, it is a slow-growing type overall, with a maximum increase of no more than 3000 deg\({}^{2}\) in a single year, illustrating the stable growth.