## 4 Experimental Simulation  
### Simulation Condition  
Hardware environment: Windows 10 operating system and Inter Core i7 processor. MATLAB 2016b and the System Tool Kit (STK) software were used to randomly generate 50 tasks within a certain satellite orbit. The simulation start time: 01 Apr 2018 00:00:00. The following Tables 1 and 2 show the other parameters:  
These parameters are classic orbital elements. \(a\) is the semimajor axis, it describes the orbit's size. \(e\) is eccentricity, it describes the orbit's shape. \(i\) is inclination, it describes the tilt of the orbital plane with respect to the fundamental plane. \(\Omega\) is the right ascension of the ascending node, it describes the orbital orientation with respect to the principal direction. \(\omega\) is the argument of perigee, it describes the angle from the ascending node to perigee. \(v\) is the true anomaly, it describes the angle from the perigee to the spacecraft's position. The orbit parameters selected in this paper belong to the low Earth circular orbit, it is mainly for ground observation objects, and we hope to design the mission planning for some special areas in China. If two tasks can cluster, the time window interval is \(\Delta\mathrm{t}=35\). Ground task selection: Fifty target points were randomly selected between 40 and 45\({}^{\circ}\) (N) latitude and 117 and 130\({}^{\circ}\) (E) longitude. Figure 7 is the distribution map of these 50 tasks. The point tasks generated above are arranged in chronological order from small to large according to the starting time of the observation. The parameters of the 50 tasks are given in Table 3. The first four tasks are those that cannot be detected by the satellite sensor in this orbit, they are invalid tasks. The priority range of this paper is 1-10, and the observation duration is 5-15. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**a (km)** & **e** & **i** & \(\Omega\) & \(\omega\) & \(v\) \\ \hline
7000 & 0 & 60 & 285 & 0 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Satellite orbital parameters. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**FOV (\({}^{\circ}\))** & **maxT (s)** & **max\(\theta\) (\({}^{\circ}\))** \\ \hline
10 & 150 & \(\pm\)40 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Satellite sensor parameters. Figure 7: Task objects. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**No. **} & **Time Window** & **Time Window** & **Slew** & **Observation** & **Observation** & **Time Window** & **Time Window** & **Slew** & **Observation** \\  & **Start (s)** & **End (s)** & **Angle (\(\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\bmbmbmbmbmbmbmbmbm                              }}}}}}}}}}}  
When the number of tasks is different, the final optimal fitness value is different. If there are more original tasks, the final fitness value is lower. When the original number of tasks is 50, the final fitness value is 0.6294. When the original number of tasks is 100, the final fitness value is 0.3718. When the original numbers of tasks is 150, the final fitness value is 0.2833. In one orbit, the energy, storage and observation times of the satellite are limited, and satellite observations are also restricted by other constraints. Thus, satellites can execute a certain number of tasks in one orbit. As the number of satellite tasks increases, the fitness value become low. We also compared the GA-SA algorithm with a single GA algorithm and a single SA algorithm when the number of original tasks is different. Figure 11 shows the average fitness values and variance values of the three algorithms. Each algorithm runs ten times when the original number of tasks is 50, 100, and 150 and compares the average fitness value and variance value of the three algorithms. When the original number of tasks is 50, the average fitness value is 0.63195, and the variance value is about \(3.266\times 10^{-7}\).