## 3 System Model and Problem Description  
### System Model  
In this paper, we adopt the classical Earth observation system model, as shown in Figure 1. The Earth observation satellite orbits the Earth at a particular inclination turns on the onboard remote sensor payload when it flies over the ground target, and performs the observation operation by pushing and sweeping the image. The satellite observation area corresponds to an observation strip on the Earth's surface parallel to the satellite's subsatellite trajectory, and the missions within the coverage of the observation strip are considered to be observed. The satellite performs the observation by turning the side-swing angle of the remote sensor in the direction of the perpendicular satellite orbit to deviate the observation strip from the satellite subsatellite trajectory to cover more missions.  
Let there be a total of \(M\) Earth observation satellites with observation missions in the system, and each satellite carries an imaging remote sensor. \(N\) missions to be observed are randomly distributed on the Earth's surface, and the missions are meta-missions that can be observed by a single transit of the satellite, and the following system model is established.  
The set of meta-tasks \(GT=\left\{T_{1},T_{2},\cdots,T_{N}\right\},\) any meta-task in the set can be described by a triplet \(t_{i}=(lon_{i},lat_{i},d_{i})\), \(lon_{i}\) and \(lat_{i}\) denote the longitude and latitude where the meta-task is located, respectively, and \(d_{i}\) denotes the continuous execution time required for the meta-task \(T_{i}\).  
The set of satellite resources \(GS=\left\{S_{1},S_{2},\cdots,S_{M}\right\}\), any satellite resource in the set can be described by a six-tuple \(S_{j}=\left\{o_{j},\sigma_{j},\omega_{j},at_{j},oe_{j},se_{j}\right\}\), where \(o_{j}\) denotes the orbit information of the satellite, the rest is the information related to the remote sensor carried by the satellite, \(\sigma_{j}\), \(\omega_{j}\), and \(at_{j}\) denotes the field of view, side-swing rate and maximum on-time of the remote sensor, respectively. \(oe_{j}\) denotes the energy consumption per unit time inland when the remote sensor performs the observation activity and \(se_{j}\) denotes the energy consumption per unit angle when the remote sensor performs a side-swing activity.  
\(GTW_{i,j}\) denotes the set of observation time windows of the satellite \(S_{j}\) for the mission \(T_{i}\) during the mission planning cycle, which is calculated from the orbit information of the satellite, the parameter information of the remote sensor carried by the satellite, and the geographical location of the mission target. Any observation time window \(tw_{i,j}\in GTW_{i,j}\) in the set can be described by a triplet \(tw_{i,j,k}=\left\{s_{i,j,k},te_{i,j,k},\theta_{i,j,k}\right\}\), \(ts_{i,j,k}\) and \(te_{i,j,k}\) denotes the earliest start time and the latest end time of the observation performed by the satellite in the observation time window, \(\theta_{i,j,k}\) denotes the ideal side-swing angle of the remote sensor when the satellite performs the observation under the observation time window \(tw_{i,j,k}\), i.e., the angle that the satellite remote sensor side-swing needs to turn when the center point of the observation strip formed on the ground when the satellite performs the observation coincides with the position of the mission target.