# Multi-Satellite Observation-Relay Transmission-Downloading Coupling Scheduling Method
## 2 Problem Description
The higher the weighted sum of the target values, the greater the overall benefit. The objective function signifies the weighted profit of all targets observed, transmitted, and ultimately downloaded to the ground station by the satellite cluster. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Meaning** \\ \hline \(t_{skimi}\), \(t_{skimi}\) & Satellite \(k\)’s start time and end time for transmitting observation data of target \(i\) to ground station m. \\ \hline \(t_{rOutskli}\), \(t_{rOutskli}\) & Satellite \(k\)’s start time and end time for transmitting observation data of target \(i\) to satellite \(l\). The transmitting direction is satellite \(k\) to satellite \(k\) to satellite \(k\) to satellite \(l\). The transmitting direction is satellite \(k\) to satellite \(l\). The transmitting direction is satellite \(k\) to satellite \(l\). The transmitting direction is satellite \(k\) to satellite \(l\). The transmitting direction is satellite \(l\) is satellite \(l\) is satellite \(l\) is satellite \(l\) receives target \(i\)’s observation data from satellite \(k\), i.e., \(t_{rOutskli}=t_{rInskli}\), and \(t_{rOutskli}=t_{rInskli}\). \\ \hline \(\Delta t_{o}\) & The observation time of single target \\ \hline \(\Delta t_{Al,j}\) & The attitude maneuver time required for observation missions’ attitude transition of satellite \(k\) \\ \hline \(\Delta t_{prk}\) & The device switching time between two inter-satellite data transmission missions to different satellites of satellite \(k\) \\ \hline \(\Delta t_{pdk}\) & The device switching time between two data downloading missions to different ground stations of satellite \(k\) \\ \hline \(W_{k}\), \(W_{kTotal}\) & Satellite \(k\)’s the available electrical energy and satellite \(k\)’s electrical energy capacity of the battery. \\ \hline \(M_{k}\), \(M_{kTotal}\) & Satellite \(k\)’s occupied memory capacity and satellite \(k\)’s total memory capacity. \\ \hline \hline \end{tabular}
\end{table} 
Table 1: _Cont._The observation time window and the data transmission time window in the problem description are calculated through the preprocessing process and the state calculation process. In this article, the satellites are agile, capable of adjusting their attitude through pitch and roll maneuvers to observe targets within their field of view. The observation time window for a satellite to observe a target represents the earliest and latest times during which the satellite can observe the target within the allowable range of satellite attitude maneuvers. The observation time window [\(t_{\textit{outside}}\), \(t_{\textit{outside}}\)] is calculated based on the relative position between satellite \(k\) and target \(i\), considering the satellite's maximum allowable maneuver cone angle constraints. The satellite-ground data transmission time window [\(t_{\textit{duskm}}\), \(t_{\textit{duskm}}\)] is the period when the \(k\)th satellite's antenna and the \(m\)th ground station's antenna are visible to each other. During the satellite-ground data transmission time window, the satellite can download data to the ground station. The calculation of the satellite-ground data transmission time window relies on satellite orbital information and attitude history \(A_{k}(t)\). Similarly, the inter-satellite data transmission time window [\(t_{\textit{rnsklp}}\), \(t_{\textit{rnsklp}}\)] is the period when satellite \(k\) and satellite \(l\) are visible to each other. During the time window, an inter-satellite link can be established between the two satellites for data transmission. The constraints that should be considered in the mission scheduling problem are as follows:  
\[t_{\textit{oski}}\geq t_{\textit{ovskio}}\wedge t_{\textit{ooki}}\leq t_{ \textit{owskio}}\quad\exists o,1\leq o\leq n_{\textit{outki}}, \tag{2}\]  
\[t_{\textit{oskij}}-t_{\textit{ooki}}\geq\Delta t_{Ai,j}\quad g_{ki,j}=1, \tag{3}\]  
\[\left\{