# Multi-UAV Area Coverage Based on Relative Localization: Algorithms and Optimal UAV Placement
## 5 Simulation Results  
In this section, the performance of the coverage algorithm proposed in this paper is evaluated using the simulation tests. The parameters used in the simulations are listed as follows: 4 UAVs are assigned randomly in the given square region for coverage task. The size of the coverage area is 15 m \(\times\) 15 m. The UAVs move at an average speed of 0.2 m/s, and the communication frequency is 10 Hz. In the global position estimation KF algorithm, the process noise is set as \(\boldsymbol{\varphi}_{i;k-1}\sim N(0,0.1^{2})\). In the relative location estimation EKF algorithm, \(\boldsymbol{\xi}_{k-1}^{i,j}=\boldsymbol{\varphi}_{i;k-1}-\boldsymbol{\varphi }_{i;k-1}\) and \(\boldsymbol{\xi}_{k-1}^{i,j}\sim N(0,0.02^{2})\), and the displacement measurement noise \(\eta_{k}^{i,j}\sim N(0,0.01^{2})\) and \(\boldsymbol{\upsilon}_{k}^{i,j}\sim N(0,0.02^{2})\). The velocity of UAVs and the communication frequency are obtained from our real experimental equipment. The gaussian noise of position estimation is obtained from our truly flight test. The approach we proposed has a complexity of \(\mathcal{O}(N^{3})\) because the matrix inverse calculation is involved in the process of position estimation. The average computing time ranged from 0.013 to 0.028 s, and the processer used was Intel i7-1165G7. In the simulations, the real position and the initial position guess of the UAVs are shown in Figure 3. Voronoi partition is based on the estimated position of the UAVs. Figures 4 and 5 show the initial to medium stages of the RL-based coverage placement. In the figures, a straight line is used to represent the boundary of the Voronoi partitions. Curves represent the flight trajectories of the UAVs. As we can see in Figure 4, the location estimation uncertainty of the UAVs is pretty large at the initial stage; hence, \(\boldsymbol{u}_{i;k}^{{}^{\prime\prime}}\) dominates the control input and UAVs have to keep close to each other to ensure the precision of relative localization. With the execution of the coverage task, the covariance measure of the position estimation decreases gradually and then \(\boldsymbol{u}_{i;k}^{{}^{\prime}}\) dominates the control input, as shown in Figure 5.  
The relative localization performance results are shown in Figure 6. The root-mean-square error (RMSE) is utilized as the localization accuracy metric. From the figure, we can see that the RMSE of the position estimate of follower UAVs converge to 0 gradually and remain accurate until convergence of the coverage task. We choose different values of \(T\) (threshold used in the weight setting in (36)). Compared with the one without considering the control input originated from the localization optimization, by using the join force strategy (35), localization performance is better. We also compared the change in coverage cost value with other published approaches. Our work considers the coverage with relative localization of UAVs and optimal UAV placement. As shown in Figure 7, the coverage performance is better using the approach we proposed. The location uncertainty ellipse of the follower UAVs is shown in Figure 8. As we can see from the figures, the location uncertainties of follower UAVs is pretty large at the initial stage. Localization errors decrease gradually while performing cooperative localization. The overall process of the RL-based multi-UAV coverage task is shown in Figure 9. In the figure, the whole procedure is shown, i.e., from initial RL dominated stage to the final coverage control dominated stage. By using our proposed RL-based coverage control strategy, even with most of the UAVs having no location information or having large uncertainties a priori, UAVs can estimate their location using RL methods and can simultaneously fight the centroid of their Voronoi regions in a given area, as shown in [1], and complete the area optimal placement coverage task.