## 4 Simulation Results
### Towards Realistic Experimental Scenarios
\begin{table}
\begin{tabular}{l c c c c} \hline \hline \multicolumn{5}{c}{**Localization Results Based on 10 Relative Measurements**} \\ \hline
**Method** & **Convergence Rate** & **Localization Error (m)** & **Number of Iterations** & **Computation Time (ms)** \\ \hline Fixed-step GD/Equation (3) (w/o errors) & **100.0\%** & 0.004 \(\pm\) 0.005 & 22.6 \(\pm\) 15.5 & **0.066 \(\pm\)** 0.043 \\ \hline Variable-step GD/Equation (3) (w/o errors) & 96.6\% & 0.004 \(\pm\) 0.005 & 233 \(\pm\) 173 & 1.5 \(\pm\) 1.2 \\ \hline Fixed-step GD/Equation (4) (w/o errors) & **100.0\%** & **0.0000 \(\pm\) 0.0000 & 1237 \(\pm\) 1006 & 5.6 \(\pm\) 5.3 \\ \hline Variable-step GD/Equation (4) (w/o errors) & 94.0\% & **0.0000 \(\pm\) 0.0000 & 526 \(\pm\) 810 & 1.5 \(\pm\) 2.3 \\ \hline Fixed-step GD/Equation (5) (w/errors) & **92.3\%** & **0.130 \(\pm\) 0.032** & 22.9 \(\pm\) 16.7 & **0.076 \(\pm\)** 0.055 \\ \hline Variable-step GD/Equation (5) (w/errors) & 88.9\% & **0.130 \(\pm\) 0.032** & 240 \(\pm\) 177 & 1.8 \(\pm\) 1.3 \\ \hline Fixed-step GD/Equation (6) (w/errors) & 82.0\% & 0.131 \(\pm\) 0.040 & 1218 \(\pm\) 1025 & 2.6 \(\pm\) 3.0 \\ \hline Variable-step GD/Equation (6) (w/errors) & 77.5\% & 0.131 \(\pm\) 0.040 & 471 \(\pm\) 681 & 4.2 \(\pm\) 6.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Comparative localization results using the different formulations of the estimation problem based on 10 relative measurements, with and without taking into account uncertainty models. Figure 10 shows the results of an example drone localization scenario based on inertial measurements and enhanced by integrating distance measurements to anchors when they are located. The localization of each drone is first estimated by integrating the measurements of the inertial unit, which inevitably induces a strong drift depending on the distance traveled. The difficulty is therefore to take measurements at the start of the flight and to quickly locate a set of anchors before the drift and the localization error become too great to make multilateration unusable. When a sufficient number of anchors are located, the resolution of the multilateration localization optimization problem is re-initialized, which results in a significant improvement in the drone localization. The curves also indicate the localization errors in each case, with and without the use of the localized anchors to improve the drone localization. Points marked '+' on the blue curve indicate when anchor positions are made available and are therefore used to correct drift errors in inertial measurements, improving the localization accuracy. Note that the drone has no prior information on the location of the anchors. The positions of the detected anchors are first calculated with reference to the drone's low-drift odometry; they are then exploited to correct the position of the drone, which explains the constant self-localization error. This process continues iteratively, which makes it possible to contain localization errors within a very limited interval. Figure 8: Multi-drone and anchor localization scenario. Fixed anchors with unknown positions are marked with _green_ dots. The ten drones and their local trajectories are represented using solid and dashed curves of different colors. Figure 9: Localization of anchors by a fleet of drones. The colors correspond to the different drones and the corresponding located anchors.