## 1 Introduction
If the distribution of the measured fingerprint is known, we can use the maximum likehood (ML) approach for localization. This is the approach employed in this paper (since this paper focuses on the optimization of the UAV sensor's flight path to improve the localization estimation, the discussion of different machine learning techniques to improve localization accuracy in an NLoS environment is out of the scope of this paper. The interested reader may refer to [3, 4, 7] for further discussion on different machine learning techniques). Figure 1: Statistics of illegal radios in Japan [2]. However, even with fingerprint-based localization, accuracy degradation in out-of-sight communication cannot be completely avoided, and the reliability of the system decreases in an NLoS condition when fixed sensors are deployed [10]. In this study, a UAV is used as a sensor for fingerprint-based localization, which allows the sensor to move freely in the air and ensures LoS communication to directly receive radio waves from the target, thereby improving localization accuracy. Furthermore, employing a UAV as a sensor enables the capability of determining an optimal flight path, on which optimal UAV's sensing points can be selected to improve localization accuracy. Compared to the conventional system of fixed ground-based sensors, our approach is more cost-efficient since only one UAV sensor is required instead of the requirement for the deployment and installation of multiple fixed ground-based sensors. For this purpose, we propose an outdoor localization system using fingerprint-based localization and aim to realize a low-cost and high-efficiency localization system by optimizing the flight path of UAVs in this paper. The improved accuracy might depend on the selection of a suitable optimization algorithm, as explained in Appendix A of this paper. Particularly, a free-path route optimization is further considered in this paper in constrast to our previous work in [11], where only a restricted circular orbit was investigated. Numerical results will reveal the superiority of the free-path route optimization compared to the circular case, owing to the higher mobility freedom of the UAV sensor. Compared to our previous work in [11], the main contributions of this work include:  
* The investigation of a free-path trajectory that helps to further improve estimation accuracy;
* Detailed explanations of each process of our proposed system;
* Comparison of different optimization solving techniques;
* Discussions about future directions/applications of the UAV-based localization system proposed in this paper. This paper is organized as follows. Section 2 describes conventional localization methods and the proposed fingerprint-based mechanism using UAVs. The simulation setup is explained in Section 3. Numerical results and discussions are given in Section 4. Finally, Section 5 concludes this paper with our future works. Table 1 summarizes all the abbreviations used in this work. \begin{table}
\begin{tabular}{c c} \hline \hline
**Abbreviation** & **Meanings** \\ \hline LoS & Line-of-Sight \\ \hline NLoS & Non-Line-of-Sight \\ \hline UAV & Unmanned Aerial Vehicle \\ \hline PSO & Particle Swarm Optimization \\ \hline GA & Genetic Algorithm \\ \hline RF & Radio Frequency \\ \hline MIC & Ministry of Internal Affairs and Communications \\ \hline DEURAS & Detect Unlicensed Radio Stations \\ \hline DEURAS-D & DEURAS Direction Finder \\ \hline GPS & Global Positioning System \\ \hline RSSI & Received Signal Strength Indicator \\ \hline TDOA & Time Difference of Arrival \\ \hline AOA & Angle of Arrival \\ \hline FDTD & Finite-Difference Time-Domain \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Summary of abbreviations used in this manuscript.