# A Location and Velocity Prediction-Assisted FANET Networking Scheme for Highly Mobile Scenarios
## 5 Simulation and Analysis
### Node Initialization and Prediction  
Figure 5a presents the initialized node positions. To determine the optimal number of clusters, we calculate the Silhouette coefficients over different numbers of clusters as shown in Figure 5b. It can be observed that the highest average value appears at the number 4, which corresponds to the preset number of clusters. Then, all nodes are grouped into  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameters** & **Values** & **Parameters** & **Values** \\ \hline \(\alpha\) & 0.5 & \(\overline{\theta}\) & \(10^{\circ}\) \\ \(\overline{\eta}\) & 5 m/s & \(\overline{\phi}\) & \(10^{\circ}\) \\ Initial direction & \((\phi_{0},\theta_{0})\) & \((45^{\circ},45^{\circ})\) & Updation interval \(\Delta t\) & 0.1 s \\ Evolution interval & & & \\ \(\Delta t_{\text{evol}}\) & 0.4 s & Total simulation time & 10 s \\ Initial number of & & Maximal random & \\ clusters \(K(t_{0})\) & 4 & speed \(v_{r,\max}\) & 3 m/s \\ Cluster center speed & & 30 m/s & Number of node \(N\) & 80 \\ Initial \(\mathbf{p}_{1}^{C}\) & \([0,0,80]\) m & Initial \(\mathbf{p}_{2}^{C}\) & \([0,80,40]\) m \\ Initial \(\mathbf{p}_{3}^{C}\) & \([80,0,40]\) m & Initial \(\mathbf{p}_{4}^{C}\) & \([80,80,0]\) m \\ \hline \hline \end{tabular}
\end{table}
Table 2: Simulation settings.  
discernible clusters based on the \(k\)-means++ algorithm. To better illustrate the clustering effects, nodes belonging to the same cluster are painted by the same color and lines connecting CMs and CH are also drawn. Obviously, four clusters can be identified and CHs lie at the center of clusters. Consequently, the nodes in Figure 5a are plotted in 4 different colors, where one color indicates one cluster.  
Figure 6 plots the trajectories of all nodes during the whole simulation process, where curves of the same color represent trajectories belonging to the same cluster. It can be observed that nodes deviate slightly away from the desired paths as a result of external disturbances. Nonetheless, nodes belonging to the same cluster still gather together instead of moving in chaos and they can be separated with others easily. Hence, it implies that the proposed RGPM presents a good modeling capability of the group mobility.  
Figure 7 presents the emulated trajectory of the 1 st node from \(t=5\) s to \(t=10\) s, where Figure 7a,c,e denote the speed components on x, y and z axes. Figure 7b,d,f represent those of the position components. In these figures, the true data are denoted by black triangles, the measured data are obtained based on GPS and speed/acceleration sensors. They are marked by red circles. We can find some differences between true data and measured data, which stems from the white Gaussian noise. Furthermore, we plot the Kalman-filter-assisted prediction results, marked by blue stars. It can be learned that the prediction result presents a good fit to the measured results, even though the time-varying data are non-stationary. Then, the predicted data are utilized to assist the networking.  
Figure 5: The initialization of all nodes at time \(t_{0}=0\) s, (**a**) clustering results, (**b**) average Silhouette coefficient values.  
Figure 6: The nodes’ trajectories during the whole simulation process.