# Path Planning for Localization of Radiation Sources Based on Principal Component Analysis
## 3 Experiments
### Simulations
#### 3.1.2 Condition (b) Multiple Radiation Sources Concentrated in a Specific Area  
A simulation experiment was conducted in an environment where multiple radiation sources were locally concentrated, as illustrated in Figure 12a. The distance between the radiation sources was close; therefore, the identification of one location enables the elimination of all the radiation sources simultaneously. Three sources of cesium-137 (1 MBq) were positioned on a straight line, and the distance between the radiation sources was set to \(1.5\) m. The mobile robot started the measurement at a position \(7\) m from the central radiation source. The threshold for switching the principal component vector was set to \(5000\).  
Figure 12b presents the simulation results obtained when the radiation sources are locally concentrated. Because the number of incident events fell below the threshold up to the \(6\)th measurement point, a path approaching the radiation sources was generated along the direction of the first principal component. Subsequently, a path that moved toward the second principal component and surrounded the radiation sources was generated. At the \(11\)th, \(17\)th, and \(24\)th measurement points, the number of incident events fell below the threshold, such that the robot moved toward the first principal component again to acquire sufficient events. The measurement was completed at the \(26\)th measurement point.  
Similar to the case of a single radiation source, the reconstruction of the radiation source distribution was performed by the simple back-projection method using only the data obtained when the number of incident events per interval exceeded the threshold. Here, it can be confirmed that the reconstructed distribution of radiation sources was  
Figure 12: Simulation condition and result of multiple radiation sources concentrated in a specific area: (**a**) Three 1 MBq cesium-137 were positioned on a straight line, and the distance between the radiation sources was set to \(1.5\) m. (**b**) The blue and red arrows represent the directions of the first and second principal components, respectively. The ground truth of the position of the radiation source is represented by a red dot. The path approaching the radiation source was generated along the direction of the first principal component. Subsequently, a path was generated, which moved toward the second principal component and surrounded the radiation sources.  
estimated around the ground truth. In this case, it is difficult to separate the area corresponding to each radiation source using the k-means algorithm because the radiation sources were too close to each other. However, all the radiation sources can be eliminated simultaneously, even if the location of each radiation source is not specified. The estimated location of the sources was (0.10 m, 0.26 m). The localization error relative to the central radiation source was approximately 0.28 m. Based on this result, we demonstrated that the proposed method can successfully generate a measurement path in an environment where multiple radiation sources are concentrated in a specific area.