## 4 Distribution Method for Observation Scheduling in the AEOS Constellation
### Consensus and Target Removal Phase
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Sender \(c\) Thinks \(Z_{sg}\) Is** & **Receiver \(s\) Thinks \(Z_{sg}\) Is** & **Receiver’s Action** \\ \hline \multirow{4}{*}{\(c\)} & \(s\) & if \(Q_{cg}>Q_{sg}\): Update \\ \cline{2-3}  & \(c\) & Update \\ \cline{2-3}  & \(k\
otin\{c,s\}\) & if \(u_{ck}>u_{sk}\) or \(Q_{cg}>Q_{sg}\): Update \\ \cline{2-3}  & none & Update \\ \hline \multirow{4}{*}{\(s\)} & \(s\) & Leave \\ \cline{2-3}  & \(c\) & Reset \\ \cline{2-3}  & \(k\
otin\{c,s\}\) & if \(u_{ck}>u_{sk}\): Reset \\ \cline{2-3}  & none & Leave \\ \hline \multirow{4}{*}{\(k\
otin\{c,s\}\)} & \(s\) & if \(u_{ck}>u_{sk}\) and \(Q_{cg}>Q_{sg}\): Update \\ \cline{2-3}  & \(c\) & if \(u_{ck}>u_{sk}\): Update \\ \cline{2-3}  & otherwise: Reset \\ \cline{2-3}  & \(k\) & if \(u_{ck}>u_{sk}\): Update \\ \cline{2-3}  & \(\beta\
otin\{c,s,g\}\) & if \(u_{ck}>u_{sk}\) and \(u_{cg}>u_{sg}\): Update \\ \cline{2-3}  & \(\beta\
otin\{c,s,g\}\) & if \(u_{ck}>u_{sk}\) and \(Q_{cg}>Q_{sg}\): Update \\ \cline{2-3}  & \(\beta\) & if \(u_{ck}>u_{sk}\) and \(u_{sk}>u_{ck}\): Reset \\ \cline{2-3}  & none & if \(u_{ck}>u_{sk}\): Update \\ \hline \multirow{4}{*}{none} & \(s\) & Leave \\ \cline{2-3}  & \(c\) & Update \\ \cline{2-3}  & \(k\
otin\{c,s\}\) & if \(u_{ck}>u_{sk}\): Update \\ \cline{2-3}  & none & Leave \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Consensus rules. \[\max_{g\in D\epsilon}\left\{Q_{sg}-w_{sg}\right\}>0 \tag{21}\]  
where \(w_{sg}=F(\mathbf{a}_{s})-F(\mathbf{a}_{s}\odot g)\) is the significance value of target \(g\) computed based on the current sequence \(\mathbf{a}_{s}\). If (21) is satisfied, we remove from \(\mathbf{a}_{s}\) and \(D\epsilon\) the target \(g_{k}=\operatorname*{argmax}_{g\in D\epsilon}(Q_{sg}-w_{sg})\) which is associated with the largest objective increase and set \(Q_{sgk}=0\). Repeat this process until \(D\epsilon\) becomes empty or (21) is no longer met. Finally, if \(D\epsilon\
eq\emptyset\) but (21) is not satisfied, i.e., there are some targets retained in \(D\epsilon\), we reset the observer of each remaining target \(g\) in \(D\epsilon\) as \(s\), i.e., \(Z_{sg}=s\), and update the significance list \(Q_{sg}=w_{sg}\). The consensus and target removal phase can be expressed in Algorithm 5. ```
Input: AEOS \(s\), target sequence \(\mathbf{a}_{s}\), \(\mathbf{Q}_{s}\) and \(\mathbf{Z}_{s}\); Output: New sequence \(\mathbf{a}_{s}\), and updated lists \(\mathbf{Q}_{s}\) and \(\mathbf{Z}_{s}\);
1. Send \(\mathbf{Q}_{s}\), \(\mathbf{Z}_{s}\) and \(\mathbf{u}_{s}\) to satellite \(c\) with \(H(s,c)=1\);
2. Receive \(\mathbf{Q}_{c}\), \(\mathbf{Z}_{c}\) and \(\mathbf{u}_{c}\)from \(c\) with \(H(c,h)=1\);
3. According to rules in Table 2 to update \(\mathbf{Q}_{s}\), \(\mathbf{Z}_{s}\) and \(\mathbf{u}_{s}\);
4. Let \(D\epsilon=\{g\in\mathbf{a}_{s}\,|\,Z_{sg}\
eq s\}\);
5.while\(\max_{g\in D\epsilon}(Q_{sg}-w_{sg})>0\)
6.\(g_{k}=\operatorname*{argmax}_{g\in D\epsilon}(Q_{sg}-w_{sg})\);
7. Remove \(g_{k}\) from \(\mathbf{a}_{s}\) and \(D\epsilon\);
8. Reset \(Q_{sgk}=0\);
9. end
10. Let \(Q_{sg}=w_{sg}\,\,\forall g\in\mathbf{a}_{s}\);
11.if\(D\epsilon\
eq\emptyset\)
12. Let \(Z_{sg}=s\), \(\forall g\in D\epsilon\);
13. End
14. Output \(\mathbf{a}_{s}\), \(\mathbf{Q}_{s}\), \(\mathbf{Z}_{s}\);
```  
**Algorithm 5**Consensus and target removal phase running on each satellite.