### Simulation Test #3  
Simulation test #3 aims to evaluate the navigation algorithm ability to estimate the position of a stationary target within the operational scenario. To validate its estimation performance, a comparison was conducted with a centralized version of the KF. In this test, a sample scenario was considered, involving a formation of 10 UAVs flying together to survey the area of interest and locate the target. Each aircraft maintains a constant speed of 2 m/s, flying in the same direction at an altitude of 100 m above the terrain. Communication capabilities are limited to two neighboring agents, forming a cycle graph, while each UAV is equipped with an additional receiver to detect the signal emitted by the target within a range of \(d_{sens}=200\) m. To account for the noise in the target transmitter signal, the simulation parameters outlined in Table 1 are augmented with the bias and noise covariance values specified in Table 5.  
The aircraft navigate towards the target position located at \((212.1,362.1,0)\) m, starting from their respective initial positions as presented in Table 6 and Figure 8.
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Figure 9-11 depict the estimated components of the target position vector, providing a comparison among the actual value, the estimation obtained from the centralized KF and that derived from the proposed decentralized KF. As observed in the figures, during the initial phase of the simulation, the target position remains unknown as it lies outside the sensor range of the UAVs. At \(t=10\) s, the target enters the sensor range of \(UAV_{1}\), but localization is not yet feasible. It is worth noting that for localization problems based on fusion algorithms, a minimum of three aircraft measurements is required to accurately determine the target location [44; 45; 46]. From \(t=30\) s, the target comes within the sensor range of \(UAV_{1}\), \(UAV_{2}\), \(UAV_{3}\) and \(UAV_{10}\), thus becoming localizable. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Agent** & \(\mathbf{X(0)(m)}\) & \(\mathbf{Y(0)(m)}\) & \(\mathbf{Z(0)(m)}\) \\ \hline \(UAV_{1}\) & \(56.6\) & \(234.8\) & \(100\) \\ \(UAV_{2}\) & \(84.8\) & \(206.6\) & \(100\) \\ \(UAV_{3}\) & \(70.7\) & \(150\) & \(100\) \\ \(UAV_{4}\) & \(70.7\) & \(79.3\) & \(100\) \\ \(UAV_{5}\) & \(0\) & \(79.3\) & \(100\) \\ \(UAV_{6}\) & \(-56.6\) & \(65.1\) & \(100\) \\ \(UAV_{7}\) & \(-84.8\) & \(93.4\) & \(100\) \\ \(UAV_{8}\) & \(-70.7\) & \(150\) & \(100\) \\ \(UAV_{9}\) & \(-70.7\) & \(220.7\) & \(100\) \\ \(UAV_{10}\) & \(0\) & \(220.7\) & \(100\) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Simulation Test #3—UAVs starting position. Figure 10: Simulation Test #3—Comparison of the estimates of the target position. \(Y_{t}\) represents the real \(Y\)-coordinate of the target, while \(\hat{Y}_{t}^{1}\) and \(\hat{Y}_{t}^{com}\) are, respectively, the estimate made by \(UAV_{1}\) that uses the HCMCI algorithm, and that of the centralized scheme. Figure 9: Simulation Test #3—Comparison of the estimates of the target position. \(X_{t}\) represents the real \(X\)-coordinate of the target, while \(\hat{X}_{t}^{1}\) and \(\hat{X}_{t}^{com}\) are, respectively, the estimate made by \(UAV_{1}\) that uses the HCMCI algorithm, and that of the centralized scheme. The estimated target position definitively converges around \(t=43\) s.  
The estimation error made by the \(i\)-th UAV, relative to the position of the target at the time instant \(k\), is:  
\[e_{i}^{\eta}(k)=\|\hat{\eta}_{i}(k)-\eta(k)\| \tag{51}\]  
where \(\hat{\eta}_{i}(k)\) indicates the position component of the target estimated by the aircraft \(i\).