# Distributed Extended Kalman Filtering Based Techniques for 3-D UAV Jamming Localization
## 6 Results and Discussion  
We considered the first scenario in which the jammer UAV hovers in three-dimensional space \((x,y,z)\) with constant acceleration equal to zero and variable velocity at each time step in order to evaluate the performance of the proposed algorithm. The boundary node or the tracker is located at the position \((15,30,0)\) with transmitting power \(-35.5\) dBm. The neighbor node near the boundary is located at \((10,30,0)\) with the same transmitting power as that of the boundary node. The jammer UAV starts at position \((10,20,12)\) with starting time \(t_{0}\) equal to zero and transmitting power equals to \(-20\) dBm. The sensing range of the boundary node is equal to \(16\) meters and the jammer UAV transmitting range is around \(90\) m. In the first experiment, the initial position for the original trajectory and UAV are \((10,20,12)\). It can be depicted with the results that are shown in Figure 5a that the proposed the DEKF-DR has better localization performance in comparison with the DEKF and the EKF-Centr. To measure the performance and the robustness of the proposed algorithm, we have set the starting positions different for both the original trajectory and the UAV, such that the original trajectory started at position \((0,0,5)\), while the initial positions for the UAV are \((5,4,8)\) in Figure 5c and (13,9,14) Figure 5e. It can be easily seen that the proposed DEKF-DR has outperformed its counterparts in both experiments and able to estimate the jammer more accurately. In contrast, the DEKF and EKF-Centr had a shift in tracking the jammer's location, as shown in Figure 5c,e. Here, the blue triangle and the green triangle represent the boundary nodes and the neighbor nodes, respectively. The second scenario is to evaluate the centralized EKF, where the four boundary nodes located at positions \((10,15,0)\), \((5,25,0)\), \((15,5,0)\) and \((20,30,0)\), as shown in Figure 5. The system threshold value \(\gamma\) and the path loss factor \(n\) for free space set to 2, as in Table 2. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Meaning** & **Assigned Values** \\ \hline \(L\) & Range of network & \(100\) \\ \(N\) & Number of nodes & \(1\) \\ \(N_{j}\) & Number of jammer & \(1\) \\ \(P_{l}\) & Jammer’s transmission power (dBm) & \(-20\) (dBm) \\ \(P_{l}\) & Sensor’s transmission Power (dBm) & \(-35.5\) (dBm) \\ \(R_{J}\) & Jammer’s transmission range (m) & \(90\) (m) \\ \(R_{N}\) & Node’s transmission range (m) & \(16\) (m) \\ \(k_{0}\) & Initial time & \(0\) s \\ \(t\) & End time & \(1000\) s \\ \(\Delta t\) & Time step & \(1.0\) s \\ \(v_{x}\) & Initial velocity on x axis & \(1\) m/s \\ \(v_{y}\) & Initial velocity on y axis & \(0\) m/s \\ \(a\) & acceleration & \(0\) m/s\({}^{2}\) \\ \(\gamma\) & System threshold value & \(2\) \\ \(n\) & Environmental factor & \(2\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The Simulation Parameters. Figure 5: The UAV localization based on distance ratio \((\beta)\) and Distributed Extended Kalman Filter (DEKF-DR) when compared to Centralized Extended Kalman Filter (EKF-Centr) and DEKF where the jammer UAV hovers over the target area to jam the base stations on the ground. (**a**) trajectory and UAV initial position \((10,20,12)\), (**b**) Zoom in of (**a**). (**c**) trajectory starting position \((0,0,5)\) and UAV initial position \((5,4,8)\), (**d**) zoom in (**b**). (**e**) trajectory starting position \((0,0,5)\) and UAV initial position \((13,9,14)\), and (**f**) zoom in of (**e**). Figure 6a shows the position errors in three-dimension space (x, y, z) at each time step. Here, the jammer UAV is moving in 1000 steps to measure the performance of the EKF-DR. The proposed algorithm can estimate the jammer position more accurately when compared to the EKF-Centr and the DEKF. The maximum position error is less than 0.6 meters compared to 2.9 m and 2.4 m for the DEKF and the EKF-Centr, respectively.