## 4 Simulation and Analysis
### Comparison between SS-LCBBA and Baseline Algorithms  
The SS-LCBBA was used to track three planned typical trajectories. The improved contract network protocol (ICNP) and blackboard model (BM) were chosen as the baseline algorithms. The ICNP is an autonomous coordination mechanism under the dynamic-distributed structure. According to the characteristics of the satellite constellation tracking system, the ICNP inherits the primary process of the traditional contract network protocol (TCNP) and improves it with an alternate tenderer mechanism, self-check procedure, and regret mechanism. The BM is a global consensus algorithm for distributed structures, and the blackboard is a global database used by knowledge sources to communicate results as blackboard entries. For specific details of the ICNP and BM algorithms, please refer to [35]. The observation distance \(D_{a}\) between the satellite, the vehicle in the mission planning process, the impact of the communication delay \(E_{l}\) between satellites, and the computational delay \(E_{c}\) of satellites on the mission planning calculation are considered in the value function.  
\(D_{l}\) is calculated as follows:  
\[E_{l}=\frac{\sum\limits_{i=0}^{i}D_{l}+D_{n}\cdot n}{C} \tag{29}\]  
where \(D_{n}\) is the distance of neighboring satellites in the same orbit, and \(n\) is the number of single hops in the same orbit of the link. \(D_{l}\) represents the distances of single hops in the different orbits of the link. \(C\) is the speed of light. \(E_{c}\) is calculated as follows:  
\[E_{c}=\sum\limits_{i_{s}=0}^{i_{s}}\left(T_{c}^{c}-T_{c}^{s}\right) \tag{30}\]  
where \(i_{s}\) is the satellite serial number, \(T_{c}^{s}\) is the start time of the planning calculation, and \(T_{c}^{c}\) is the end time of the planning calculation. The tracking distance evaluation value is as follows:  
\[C_{L}=\frac{u_{if}*c_{H}}{\sqrt{2\pi}\sigma}\cdot\exp(-\frac{\left(D_{a}-\frac {\sin\left(\pi-\theta-ar\sin\left(\frac{\left(U_{a}+R_{c}\right)\sin\theta}{Ra +R_{c}}\right)\right)\cdot\left(R_{c}+H_{n}\right)}{\sin\theta}\right)^{2}}{2 \sigma^{2}}) \tag{31}\]  
where \(u_{if}\) shows whether the target is tracked. \(c_{H}\) is the target value. \(H_{s}\) is the satellite orbit altitude. \(\theta\) is the pitch angle of the sensor. \(H_{n}\) is the height of the near space. \(\sigma\) is the standard deviation. The value of the inter-satellite link is evaluated as follows:  
\[C_{i}=\frac{u_{if}*c_{H}}{\sqrt{2\pi}\sigma}\cdot\exp(\frac{E_{l}}{2\sigma^{ 2}}) \tag{32}\]  
The value of planning calculation time is evaluated as follows:  
\[C_{o}=\frac{u_{if}*c_{H}}{\sqrt{2\pi}\sigma}\cdot\exp(\frac{E_{c}}{2\sigma^{ 2}}) \tag{33}\]  
\(\sigma\) is set to \(\sigma=\sqrt{\frac{2}{\pi}}\).  
The value function is shown below:  
\[S=L_{l}\cdot L_{t}\cdot(\omega_{l}\cdot C_{L}+\omega_{l}\cdot C_{i}+\omega_{o} \cdot C_{o}) \tag{34}\]  
where \(L_{l}\) is the pitch loss factor and \(L_{t}\) is the distance loss factor, which are defined in Section 3.1. \(<\omega_{l},\omega_{i},\omega_{o}>\) are the weighting factors. As the tracking distance is more important, the weighting factor is set to \(<0.4,0.3,0.3>\).