# Research on Advancing Radio Wave Source Localization Technology Through UAV Path Optimization
## 3 Materials and Methods
### Location Fingerprinting Method  
This section builds upon prior work by [PERSON] [8], who investigated RSSI-based localization using UAVs and extended the methodology to incorporate not only RSSI \begin{table}
\begin{tabular}{c c} \hline \hline
**Item** & **Value** \\ \hline Model & 3D (Ray launching) \\ Frequency [GHz] & 2.487 \\ Bandwidth [MHz] & 5.00 \\ Number of Reflections & 6 \\ Number of Diffractions & 1 \\ Number of Transmissions & 0 \\ \hline \multirow{3}{*}{\
\begin{tabular}{c} **Rx** \\ \end{tabular} } & Antenna Type: Isotropic \\  & Height [m]: 50/75/100/125/150 \\ \cline{1-1}  & Antenna Gain [dBi]: 2.0 \\ \hline \multirow{3}{*}{
\begin{tabular}{c} **Tx** \\ \end{tabular} } & Antenna Type: Isotropic \\  & Transmission Power [dBm]: 27 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Ray-Tracing Parameters [8]. Figure 4: Candidate The figure illustrates receiver antenna positions at an altitude of 50 m and transmitter placement. Each dot represents a UAV measurement point. The red points indicate candidate receiver (Rx) antenna positions at 50 m altitude, while the green points represent transmitter (Tx) locations on the ground. The horizontal coverage ensures diversity in observation geometry, which is crucial for directional accuracy. but also AOA (angle of arrival), EOA (elevation of arrival), and their fusion (hybrid) to improve accuracy in outdoor environments. The location fingerprinting method is a statistical localization technique that uses location-dependent signal features as fingerprints and estimates the position via pattern matching. It consists of two phases: the learning phase and the estimation phase. In the learning phase, a location fingerprint database is constructed by observing the propagation characteristics at known transmitter positions. In the estimation phase, the received signal at an unknown target location is compared to the database to estimate the position. In this study, multiple radio features are used as fingerprints. For each transmitter located at position \(\mathbf{u}_{k}\), the RSSI, AOA, and EOA values observed by the \(n\)-th sensor are denoted as \(P_{n}(\mathbf{u}_{k})\), \(\theta_{n}(\mathbf{u}_{k})\), and \(\phi_{n}(\mathbf{u}_{k})\), respectively. Each type of fingerprint vector is defined as follows:  
\[\mathbf{F}_{k}^{\text{RSSI}}(\mathbf{u}_{k})=[P_{1}(\mathbf{u}_{k}),\ldots,P_{N}(\mathbf{u}_{k})] \tag{1}\]  
\[\mathbf{F}_{k}^{\text{AOA}}(\mathbf{u}_{k})=[\theta_{1}(\mathbf{u}_{k}),\ldots,\theta_{N}( \mathbf{u}_{k})] \tag{2}\]  
\[\mathbf{F}_{k}^{\text{EOA}}(\mathbf{u}_{k})=[\phi_{1}(\mathbf{u}_{k}),\ldots,\phi_{N}(\bm {u}_{k})] \tag{3}\]  
To further improve accuracy, we define a hybrid fingerprint that concatenates all available features:  
\[\mathbf{F}_{k}^{\text{HYB}}(\mathbf{u}_{k})=[P_{1}(\mathbf{u}_{k}),\ldots,P_{N}(\mathbf{u}_{k} ),\theta_{1}(\mathbf{u}_{k}),\ldots,\theta_{N}(\mathbf{u}_{k}),\phi_{1}(\mathbf{u}_{k}), \ldots,\phi_{N}(\mathbf{u}_{k})] \tag{4}\]  
In the estimation phase, the observed signal at the \(n\)-th sensor from the target is denoted by \(P_{n}^{\text{target}},\theta_{n}^{\text{target}}\), and \(\phi_{n}^{\text{target}}\), and the corresponding hybrid fingerprint is as follows:  
\[\mathbf{F}^{\text{target}}=[p_{1}^{\text{target}},\ldots,p_{N}^{\text{target}}, \theta_{1}^{\text{target}},\ldots,\theta_{N}^{\text{target}},\phi_{1}^{\text {target}},\ldots,\phi_{N}^{\text{target}}] \tag{5}\]  
The estimated position \(\hat{\mathbf{u}}\) is obtained by minimizing the Euclidean distance between the target fingerprint and each database fingerprint:  
\[\hat{\mathbf{u}}=\arg\min_{\mathbf{u}_{k}}\left\|\mathbf{F}_{k}^{\text{HYB}}(\mathbf{u}_{k})- \mathbf{F}^{\text{target}}\right\| \tag{6}\]  
Alternatively, a maximum likelihood approach can be applied by modeling the distribution of each feature.