# A Study on a Radio Source Location Estimation System Using High Altitude Platform Stations (HAPS)
## 3 Numerical Analysis and Results
### Location Estimation Simulation
#### 3.2.5 Results of Location Estimation Simulation  
The 3D city model shown in Figure 7 was used to randomly generate 1000 radio wave sources, and the location of each source was estimated using the method described in the previous section. The horizontal distance between the center of the urban area with illegal radio sources and the hovering sensors was varied with different scenarios, as seen in our evaluation results below. Three scenarios of sensor altitudes, i.e., HAPS, UAV, and DEURAS, are also separately evaluated in this section. * HAPS altitude  
Table 3 shows the results of localization using the HAPS at three points 5 km away from the urban area. The Beamformer and MUSIC methods were used to estimate the direction of arrival. The estimation probability denotes the percentage that the emitter can be identified (with localization errors) via our proposed system, as mentioned in Figure 16. The stochastics of the estimation errors were derived only from emitters, which were identified by our proposed method. From Table 3, it is observed that there was no significant difference in the results between the Beamformer and MUSIC methods, and 90% of the estimated locations were within 30 m of the true coordinates. Table 4 shows the results of the estimation using the HAPS at three locations 10 km away from the urban area. Since the sensors are more distanced from the sources compared to the 5 km case, we can observe a slight degradation in terms of localization accuracies as compared to these in Table 3.  
Furthermore, Table 5 shows the results of the estimation using the HAPS at three locations 20 km away from the urban area. Similar to the two aforementioned scenarios, neither the Beamformer nor the MUSIC method showed a significant difference in results. \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Beamformer** & **MUSIC** \\ \hline Mean error [m] & 28.2 & 28.4 \\ \hline CDF90\% [m] & 57.8 & 58.4 \\ \hline Detection percentage [\%] & 92.1 & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Results with the HAPS 10 km away. Figure 16: Location estimation method. \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Beamformer** & **MUSIC** \\ \hline Mean error [m] & 16.4 & 17.0 \\ \hline CDF90\% [m] & 30.0 & 30.7 \\ \hline Detection percentage [\%] & 95.6 & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Results with the HAPS 5 km away. Also, the accuracy of the estimation was poorer at greater distances compared to the cases at 5 km and 10 km. Furthermore, only about 83.6% of the radio transmitting sources in urban areas could be obtained. The CDF of localization errors for these scenarios is summarized in Figure 17.  
UAV altitude  
Similarly, a simulation was conducted assuming a UAV, with the height of the receiving antenna changed to 200 m. In addition, because the effect of reflections is likely to increase at the altitude of the UAV, the simulation was performed considering radio waves that can be reflected up to four times. Tables 6-8 show the results of the estimation using UAVs at three locations (5 km, 10 km and 20 km away from the urban area, respectively). \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Beamformer** & **MUSIC** \\ \hline Mean error [m] & 205.1 & 204.9 \\ \hline CDF90\% [m] & 424.9 & 421.5 \\ \hline Detection percentage [\%] & 21.1 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Results with UAV 5 km away. Figure 17: CDF of errors using the HAPS at different distances against the emitting sources. In Table 6, only 20% of the total number of radio sources could be identified due to the low LoS ratio, as described in Section 3.1. The localization estimation error of the radio sources that could be identified was also larger than that of the HAPS case. Table 7 shows the results of the estimation using UAVs at three locations 10 km away from the urban area. As in the 5 km case, the number of radio sources that could be identified was small. However, the estimation error and the CDF90% value was slightly improved against the 5 km case.