# Modeling and Simulation of Sky Survey
## 4 Design of the Model Solving Algorithm
### Overall Arrangement Algorithm
There is a gap between different bands in the CCD field of view, about 5 arcseconds or so. We also consider that stitching needs to require roughly 3% overlap, about 21.6 arc seconds, much larger than the gap interval. Therefore, the minimum area range should be subtracted from the overlap when performing the sky survey area division, but the gap between the filters can be disregarded. In addition, there is a strict limit to the number of angles of CMG rotation per track. It can be seen from Table 4 that if each rotation angle is less than 10\({}^{\circ}\), CMG can rotate 25 times per track, and when the rotation angle is greater than 135\({}^{\circ}\), it can only rotate 2 times. Observation Area Selection:The large scale seamless spectral survey is the main content of the sky survey. The scanning area of the survey is the J2000 flat ecliptic celestial sphere, 25\(\sim\)80 degrees from north to south ecliptic, with a total area of 15,000 deg\({}^{2}\) for seamless spectral survey in Figure 3. The observation area is divided into small observation areas under the ecliptic coordinate system according to the mission objectives, and the projected coordinates of the sky area boundaries are calculated according to the telescope field of view. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \(Angle\) & \([5,10]\) & \([10,20]\) & \([20,35]\) & \([35,45]\) & \([45,75]\) & \([75,90]\) & \([90,135]\) & \([135,180]\) \\ \hline \(c_{p}\) & 25 & 15 & 10 & 8 & 5 & 4 & 3 & 2 \\ \hline \end{tabular}
\end{table} 
Table 4: The maximum number of rotations corresponding to different angles of rotation in each cycle of CMG. Algorithm Parameters: There are several important parameters in the algorithm that need to be set. First, there are two parameters (\(\epsilon_{1}\) and \(\epsilon_{2}\)) of the limitation of the tangential angle of the sunlight and the moonlight to the telescope. Then, there are the parameters for the efficiency statistics and the difficult sky area statistics. The two parameters (\(\gamma_{1}\) and \(\gamma_{2}\)) for the efficiency statistics and the difficult sky area statistics directly affect the planning results of the algorithm. Finally, there is the limiting parameter (\(\Delta\)) of the zenith angle at the time of observation. The results of the parameters in the algorithm selected in the experimental part are shown in Table 5.

### Analysis of the Results

Efficiency Statistics: According to the efficiency statistical method in Algorithm 1, the statistics of efficiency for the time period of the test are carried out, and the results are shown in Figure 4. From the results, it can be seen that the maximum number of days in which a complete day can be observed in 10 years is more than 160 days. The time periods with efficiency below the threshold 0.6 corresponding to these days will be prioritized using Algorithm 3. Difficulty Statistics: The observation difficulty of the test time period sky areas is counted, and different difficulty weights are given to different sky areas. The sky areas exceeding a certain threshold are prioritized and reserved in the final complete arrangement for the advance time period. From Figure 5, it can be seen that the observation difficulty of the sky areas at high latitudes is greater, and they need to be given priority in the observation process and given greater observation weights. CMG Rotation Angle Statistics Results: As can be seen from Figure 6, the CMG rotation angle is about 1.1 degrees in the most cases, with 4969 occurrences. The CMG rotation over 108 degrees does not exist. A normal distribution of rotation angles occurs with a mean value of about 13 degrees, indicating that most of the angles are around 13 degrees. The data of rotation angle statistics will show many rotation angles with significantly more numbers than the surrounding data shown in Figure 6a. The reason for this is that the ten-year sky survey mission is cyclical in nature, and the CMG rotation follows the greedy idea of encountering the same situation with the same angle of rotation.