## 3 System Model and Problem Description
### Problem Description
\begin{table}
\begin{tabular}{c c} \hline \hline
**Symbol** & **Description** \\ \hline \(GT\) & Meta-task set \(\{T_{1},\cdots,T_{N}\}\) \\ \(d_{i}\) & The continuous execution time required for meta-task \(T_{i}\) \\ GS & Satellite resource set \(\{S_{1},\cdots,S_{M}\}\) \\ \(S_{j}\) & The six-tuple of satellite resource \(S_{j}\) (\(o_{j},\sigma_{j}^{\prime},\omega_{j},at_{j},oe_{j},se_{j}\)) \\ \(o_{j}\) & Orbital information for satellite \(S_{j}\) \\ \(c_{j}\) & FOV angle of satellite resource \(S_{j}\) \\ \(\omega_{j}\) & Side-wing rate of remote sensor on satellite \(S_{j}\) \\ \(at_{j}\) & Maximum continuous working time of remote sensor on satellite \(S_{j}\) \\ \(oe_{j}\) & Energy consumption rate of remote sensor on satellite \(S_{j}\) when observing \\ \(se_{j}\) & Energy consumption per unit angle of remote sensor on satellite \(S_{j}\) \\ \(GTW_{i,j}\) & Observation time windows of meta-task \(T_{i}\) on satellite \(S_{j}\) \\ \(tw_{i,j,k}\) & Observation time window tuple \((ts_{i,j,k},te_{i,j,k},\theta_{i,j,k})\) \\ \(ts_{i,j,k}\) & The earliest observation time of task \(T_{i}\) under window \(k\) using satellite \(S_{j}\) \\ \(te_{i,j,k}\) & The latest observation time of task \(T_{i}\) under window \(k\) using satellite \(S_{j}\) \\ \(\theta_{i,j,k}\) & Ideal sensor swing angle for mission \(T_{i}\) under window \(k\) using satellite \(S_{j}\) \\ \(GC\) & Aggregated task set \(\{C_{1},\cdots,C_{L}\}\) \\ \(C_{k}\) & Aggregated task elements \((M_{k},l_{k},s_{k},e_{k},\delta_{k})\) \\ \(M_{k}\) & The set of meta-tasks contained in task \(C_{k}\) \\ \(l_{k}\) & Resources required to execute aggregation task \(C_{k}\) \\ \(st_{k}\),\(et_{k}\) & Start and end times of task \(C_{k}\) \\ \(\delta_{k}\) & Side-swing angle of the remote sensor during execution aggregation task \(C_{k}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Symbol descriptions for satellite operations. s.t. \[ \begin{cases}(a)\max_{T_{pq}\in T_{p}}\left\{\theta_{pq,j,k_{pq}}\right\}-\min_{T _{pq}\in T_{p}}\left\{\theta_{pq,j,k_{pq}}\right\}\leqslant\sigma_{j},\\ (b)\max_{T_{pq}\in T_{p}}\left\{te_{pq,j,k_{pq}}\right\}-\min_{T_{pq}\in T_{p}} \left\{ts_{pq,j,k_{pq}}\right\}\leqslant at_{j},\end{cases}  \tag{4}\]  
The observation time window constraint indicates that the satellite can perform all meta-tasks in the aggregated mission in a single observation campaign. The observation time window constraint consists of a side-swing angle constraint and a time constraint. \((a)\) in Equation (4) is the side-swing angle constraint, which indicates that the satellite can adjust the side-swing angle of the remote sensor to cover all the tasks in the aggregated mission by the remote sensor field of view when executing the observation activity. \((b)\) in Equation (4) is a time window constraint, which indicates that the satellite can complete the observation activities of all meta-tasks in the aggregation task within the maximum power-on time of the remote sensor, i.e., the observation time length of the aggregation task is less than the maximum power-on time of the remote sensor. Since the observation time interval of the aggregated tasks is dynamically changing during the task aggregation process, the difference between the earliest time and the latest time of the observation time window of all meta-tasks in the aggregated tasks is chosen here as the judgment criterion to ensure that the execution time of the aggregated tasks must be less than the maximum power-on time of the remote sensor.