### Simulation Test #5, a Post-Avalanche Scenario
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Cruise speed \(V_{c}\) (m/s) & \(3\) \\ Minimum speed \(V_{min}\) (m/s) & \(0\) \\ Maximum speed \(V_{max}\) (m/s) & \(10\) \\ Minimum normal acceleration \(a_{min}^{\perp}\) (m/s\({}^{2}\)) & \(-5\) \\ Maximum normal acceleration \(a_{max}^{\perp}\) (m/s\({}^{2}\)) & \(5\) \\ Minimum tangential acceleration \(a_{min}^{\parallel}\) (m/s\({}^{2}\)) & \(-10\) \\ Maximum tangential acceleration \(a_{max}^{\perp}\) (m/s\({}^{2}\)) & \(10\) \\ Safety distance \(d_{safety}\) (m) & \(3\) \\ Desired distance \(\overline{d}\) (m) & \(20\) \\ UAV size \(\overline{r}_{\gamma}\dot{\gamma}=1,...,N\) (m) & \(1\) \\ MPC weight matrix for tracking error \(\mathbf{Q}_{MPC}\) & diag([10,10,10,10]) \\ MPC weight matrix for control effort \(\mathbf{R}_{MPC}\) & diag([1,1]) \\ Number of steps of the MPC prediction horizon \(n_{P}\) & \(10\) \\ Number of steps of the MPC control horizon \(n_{c}\) & \(5\) \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Simulation Test #5—Parameters of the integrated GNC model. Figures 21 and 22 show trajectories of \(UAV_{2}\) and \(UAV_{3}\) as estimated by \(UAV_{1}\), compared with reference paths. As can be seen, \(UAV_{1}\) is always able to estimate its neighbors' trajectories. It is worth remembering that each UAV in the swarm, at the beginning of the simulation, knows only its position, and the estimates start at random values. As can be seen, the estimates made by \(UAV_{1}\) converge to the correct values after a few time instants, necessary for the convergence of the consensus algorithm. Figure 19: Simulation Test #5—UAV trajectories in the search of the missing skier along the search patterns. Solid black line represents the reference trajectory to be followed by the formation. Colored circular markers indicate positions of UAVs at different time instants. Green straight lines are used to highlight the connection graph. (**a**) Scenario #1. (**b**) Scenario #2. Figure 20: Simulation Test #5—Average distance \(d_{mean}\) between adjacent UAVs compared with the desired distance. (**a**) Scenario #1. (**b**) Scenario #2. Figures 23-25 show the effectiveness of the proposed algorithm in the estimation process of the skier position, comparing the real value with the estimation made by \(UAV_{1}\), for both the analyzed case studies. As shown, at the beginning of the simulation the skier position is unknown, still being far from the range of the receivers onboard the UAVs. Once the skier ARTVA transmitter enters the range of at least three aircraft receivers (at \(t=260\) s (#1) and \(t=230\) s (#2)), the estimates tend to the real position, converging definitively after the time necessary for the consensus phase. In case study #1, it is worth noticing that a first convergence estimation is reached at \(t=170\) s. This is due to the particular research path; in fact, as shown in Figure 19a,  
Figure 24: Simulation Test #5—Estimate of the skier position. \(Y_{s}\) represents the real \(Y\)-coordinate, while \(\hat{Y}_{1}^{s}\) is the estimate made by \(UAV_{1}\). (**a**) Scenario #1. (**b**) Scenario #2. Figure 22: (**a,b**) Simulation Test #5, Scenario #2—UAVs positions estimated by \(UAV_{1}\). at \(t=160\) s the skier enters the sensor range of only one UAV of the swarm, whose measurement is still not sufficient to correctly estimate the position of the missing person (see Section 4.4). Table 12 shows mean absolute error (Equation (53)) and standard deviation (Equation (54)) for any component of the target position vector, \(\mathbf{S}_{s}\). These uncertainties in the estimation are graphically represented in Figures 26 and 27 for both the scenarios. The data presented in this section represent the results regarding the accuracy of the proposed algorithm, with standard deviations never exceeding 1 m and MAE values consistently below 0.1 m for the estimation of the X and Y coordinates. Furthermore, the potential application of the proposed GNC model in SAR scenarios is demonstrated.