# Localization of Radio Sources Using High Altitude Platform Station (HAPS)
## 3 Results
### Single Radio Source Localization  
As shown in Figure 7, the urban environment of Shinjuku was used as the simulation model for localization. A single radio source located within this environment was considered for estimation. The position of the transmission source was varied across 1000 different patterns, while the HAPS was placed at 10 different locations, each maintaining a constant horizontal distance from the center of the Shinjuku 3D environment, as shown in Figure 8. Localization was performed for each HAPS placement. The transmission power of the source was set to 10 W, and the distance between the center of Shinjuku and the HAPS was varied from 5 km to 100 km to evaluate the accuracy of the localization.  
Figure 6: Estimated coordinate determination method.  
The obtained evaluation results are presented in Table 3 and Figure 9.  
The detection percentage represents the ratio of successful localizations out of 10,000 trials. The mean error and CDF 90% were calculated only for cases where a valid estimated position was obtained.  
Next, localization was performed for a low-power transmission source under the same conditions. In this case, the transmission power of the source was set to 200 mW. In addition to the standard cylindrical antenna, another simulation was performed using a modified antenna, where the antenna elements were tilted downward by 45\({}^{\circ}\) from the horizontal plane (0\({}^{\circ}\)), as shown in Figure 5. These localization simulations were performed only for the case where the HAPS was positioned 20 km away from the center of the Shinjuku 3D environment. The obtained results are summarized in Table 4 and Figure 10. The standard cylindrical antenna (without element tilt) is defined as type A, while the tilted antenna  
Figure 8: HAPS placement at a fixed distance from the urban area.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & **5 km** & **10 km** & **20 km** & **40 km** & **60 km** & **80 km** & **100 km** \\ \hline Mean Error [m] & 51.8 & 64.7 & 195.4 & 536.8 & 1149.1 & 2104.2 & 2496.6 \\ CDF 90\% [m] & 87.7 & 113.6 & 193.7 & 479.6 & 935.5 & 1704.8 & 2807.4 \\ Detection Percentage [\%] & 90.19 & 84.21 & 76.70 & 65.66 & 56.41 & 49.43 & 44.14 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Localization of a single source.  
Figure 7: Radio sources placed randomly in the environment.  
(elements tilted by 45\({}^{\circ}\)) is defined as type B. For comparison, the results from the previous case with a 10 W transmission source are also included. To ensure meaningful evaluation, cases where the estimation error exceeded 10 km, indicating a failure in identifying the transmission source, were excluded from the analysis.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Type A [10 W]** & **Type A [200 mW]** & **Type B [200 mW]** \\ \hline Mean Error [m] & 101.6 & 145.7 & 112.2 \\ CDF 90\% [m] & 192.8 & 277.5 & 211.1 \\ Detection Percentage [\%] & 76.51 & 75.08 & 76.44 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Localization of a low-power single source.  
Figure 10: Cumulative distribution of localization error for a low-power single source.  
Figure 9: Cumulative distribution of localization error for a single source.  
Next, a localization simulation was performed while considering edge diffraction effects. The transmission power of the source was set to 10 W, and the number of source location patterns was set to 100. The horizontal distance from the 3D environment to the HAPS was set to 5 km and 20 km, and localization was performed for these two cases. The evaluation results are presented in Table 5 and Figure 11. As seen from this figure, we found out that the angle of arrival changed insignificantly when edge diffraction was taken into account, such that the relative degradation of localization accuracy (compared to the absolute value of the error) was not significant. For this reason, analysis of edge diffraction was just partially conducted in this paper.