# Path Planning for Localization of Radiation Sources Based on Principal Component Analysis
## 1 Introduction  
Although radiation sources are applied in various fields such as energy, medical, and manufacturing, gamma rays, which are emitted from high-dose radiation sources, such as those exceeding 5 Sv, can cause serious damage to the human body. Consequently, the application of radiation sources is strictly regulated by law. However, there are cases where radiation sources are stolen or leaked out, and this has become a critical social problem. There have been some cases in which radiation sources were stolen. In Georgia, five suspects were arrested for the illegal trade of radioactive uranium [1]. Accordingly, illegally traded radiation sources possibly fall into the hands of terrorist organizations, and are harnessed to create dirty bombs comprising explosives and radiation sources, or silent source attacks that leave high-dose radiation sources to harm humans. In addition, radiation sources can cause great damage when used in urban areas or important facilities. However, the detection and removal of radiation sources currently relies on human workers, even though it is extremely dangerous to approach and investigate these sources [2]. Owingto the high risk of exposure to radiation, it is necessary to develop a radiation source exploration system with mobile robots in urban areas and various facilities [3; 4]. Accordingly, a method for the localization of radiation sources in an environment using a radiation detector has been studied. Radiation caused by radioactive decay can be categorized into electromagnetic radiation, such as gamma rays, and particulate radiation, such as alpha and beta rays. Although, alpha and beta rays can be easily blocked by thin materials, gamma rays exhibit high penetration power. Hence, gamma-ray detection is the conventional method for detecting radiation sources. The conventional search approach, such as uniform search, is based on a predefined path that scans the area. [PERSON] and [PERSON] proposed a uniform search method to detect a radiation source [5]. [PERSON] et al. also proposed a strategy of searching along a predefined path while adaptively optimizing detection time [6]. In addition, information-driven approaches have been studied. Various information gains, such as entropy and Fisher information, have been proposed to determine the best next measurement position. [PERSON] et al. used the maximum entropy sampling concept to determine optimal measurement positions [7]. [PERSON] et al. designed a method for maximizing the information gain in the Renyi divergence sense to determine subsequent measurement positions and detection times [8]. [PERSON] and [PERSON] proposed a double Q-learning algorithm [9], a data-driven approach. These studies were essentially designed to use a radiation detector more as a counter rather than as an imager. A counter-type detector counts the number of incident gamma rays or obtains the radiation dose rate. However, the incident gamma ray direction is not determined. As an alternative to the aforementioned techniques, gamma camera-based searching, which allows for determining the incident gamma ray direction, has been studied. [PERSON] et al. proposed a method for three-dimensional (3D) reconstruction of the radiation source distribution in an environment using a mobile robot equipped with a Compton camera [10]. [PERSON] et al. proposed a method for estimating the radiation source distribution using an unmanned helicopter equipped with a Compton camera [11]. However, these techniques are based on a predefined path. Search path planning using a gamma camera has not been extensively studied. Because high-dose radiation sources exceeding 5 Sv can cause significant damage to the human body, it is necessary to detect and eliminate it at an early stage. Therefore, an investigation that sequentially scans the entire environment is ineffective when the target environment is large.