# On-Board Decentralized Observation Planning for LEO Satellite Constellations
## 3 Improved CBBA
### Bundle Construction
DMG(P-L) focuses on not only the profit of the task itself but also the loss mentioned above. The comparison results of DMG(P) and DMG(P-L) on regional targets are shown in Table 3.

Take \"global targets-1500-90/3/1\" and \"regional targets-1500-90/3/1\" as examples; the number of repeated claims for the whole constellation after bundle construction at each iteration is shown in Figure 3a,b respectively. The reduction in the number of repeated claims proves that the consensus check phase plays an important role in the convergence of ICBBA. In order to test the responsiveness of ICBBA to dynamically arrived tasks, taking \"global targets-1500-90/3/1\" and \"regional targets-1500-90/3/1\" as examples, 100 tasks are set to arrive at the 30 th iteration of the algorithm running process. The results of DMG(P) with tasks arriving dynamically are shown in Table 4. The number of repeated claims for the whole constellation after bundle construction at each iteration is shown in Figure 4a,b, respectively, which records the process of re-convergence in the face of dynamically arrived tasks during the running process. Figure 3: The number of repeated claims for the whole constellation after bundle construction varies according to iteration times: (**a**) Global targets-1500-90/3/1; (**b**) Regional targets-1500-90/3/1. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Target Type**} & \multirow{2}{*}{**Target Number**} & \multirow{2}{*}{**Constellation (\(\mathbf{\text{N/P/P}}\))**} & **Available Target Number** & \multirow{2}{*}{**Communication Number**} & \multirow{2}{*}{**Completion Number**} & \multirow{2}{*}{**Rate (\%)**} & **DMG(P)** & & \multirow{2}{*}{**Completion Number**} & \multirow{2}{*}{**Rate (\%)**} & **Total** \\  & & & & & & & & & & \\ \hline \multirow{8}{*}{Regional targets} & \multirow{3}{*}{500} & 30/3/1 & 256 & 4321 & 222 & 86.72 & 16,472.5 & 224 & 87.50 & **16,488.1** \\  & & 60/3/1 & 274 & 15,457 & 262 & 95.62 & 19,161.4 & 272 & 99.27 & **19,668.8** \\  & & 90/3/1 & 282 & 33,502 & 277 & 98.23 & 20,861 & 281 & 99.65 & **20,992.1** \\ \cline{1-1} \cline{2-10}  & \multirow{3}{*}{1000} & 30/3/1 & 546 & 5641 & 370 & 67.77 & 28,473.4 & 374 & 68.50 & **28,548.2** \\  & & 60/3/1 & 580 & 22,816 & 510 & 87.93 & 38,045.9 & 524 & **90.34** & **38,773** \\  & & 90/3/1 & 586 & 46,540 & 558 & 95.22 & 41,911.1 & 577 & 98.46 & **42,943.7** \\ \cline{1-1} \cline{2-10}  & \multirow{3}{*}{1500} & 30/3/1 & 836 & 5627 & 426 & 50.96 & 34,647.4 & 454 & **54.31** & **35,541.6** \\ \cline{1-1}  & & 60/3/1 & 876 & 24,869 & 680 & 77.63 & 52,207.9 & 690 & **78.77** & **52,341.7** \\ \cline{1-1}  & & 90/3/1 & 864 & 55,574 & 770 & 89.12 & 57,981.3 & 811 & 93.87 & **60,182.9** \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The comparison results of DMG(P) and DMG(P-L) on regional targets. (The highest value of task completion rate and total profit in each instance are marked in bold. )From the experimental results, the following observations can be made:

(1) Communication cost analysis: From Tables 2 and 3, we can see that for both global and regional targets, the communication number increases with the number of satellites \(N\) and the number of tasks \(M\). However, there are still a few exceptions, such as \"global targets-500-30/3/1\" and \"global targets-1000-30/3/1\". The target number increases from 500 to 1000 and the available target number increases from 282 to 556, while the communication number decreases from 3552 to 3241. Therefore, this positive proportional relationship is not simply linear or exponential. Compared with other decentralized algorithms, such as Contract Network Protocol (CNP) [18], the communication number of ICBBA is significantly lower than \"\(N\cdot M\)\". In addition, by comparing each corresponding instance in regional and global targets, the communication number for regional targets is always higher than that for global targets. Because there are more conflicts between tasks for regional targets, this coupling needs more communication to resolve.