## 1 Introduction  
In today's age of diversified use of radio waves [1], illegal radio waves that cause interference in wireless communication systems have become a social issue. Illegal radios (or private radios) consist of radio emitters operating without a proper license issued by authorities. The term may also refer to radios that have obtained a license but operate using frequencies outside the ranges specified by their license or transmit using powers much larger than regulations. Statistics of illegal radios in Japan from 2014 until 2021 are available on the MIC website [2], as shown in Figure 1. From the figure, the number of appearances of illegal radios has been gradually increasing in recent years. A large percentage of illegal radios consists of unlicensed citizen band radios, followed by unlicensed amateur radios. Cases have been reported in which the use of radio waves violating the power strength and frequencies regulated by national laws caused interferences to important lifelines such as police, fire, disaster prevention, and aviation radios, as well as television and cellular systems. Also, the occurrence of fires had been reported due to malfunctions of electronic equipment. For example, in June 2015, there were reports of interference to a broadcasting service in Tokyo. The interference source was found to be a wireless transceiver imported from overseas to communicate between shops in a shopping street, and the transceiver was not licensed for use in Japan. In March 2015 in the Tochigi prefecture, an amateur radio station was set up on a dump truck without an amateur radio license. The Japanese Ministry of Internal Affairs and Communications (MIC) has developed and utilized a radio wave monitoring system called DEtect Unlicensed RAdio Stations (DEURAS) to crack down on illegal base stations, but in recent years, with the diversification of radio wave usage, there have been many different types of illegal base stations [2] that prevent the effectiveness of DEURAS. One of the methods used to estimate the location of radio wave sources for radio wave monitoring is the geometric localization method using the angle of arrival (AOA) of the received signal. However, since the geometric localization method assumes an LoS condition between the sensor and the target, the localization accuracy deteriorates significantly in general environments of urban areas with the existence of many scattering objects, where sensors and the radio sources are normally in an NLoS condition [3, 4, 5, 6]. In a geometric localization or triangulation approach, the location of the emitters is predicted as the intersection point of different estimated AOAs from the illegal source toward different received sensors. Due to the existence of multipath components in NLoS environments, AOA estimation errors finally result in a large localization error. Therefore, a statistical localization method, i.e., fingerprint-based localization, has been attracting attention [4]. In particular, statistical approaches, such as machine learning, are expected to enable localization even in NLoS conditions. There are several approaches to perform pattern matching or machine learning of the fingerprints. The reader can find a good survey of pattern matching techniques in [3, 7]. The most conventional approach is calculating the distance between two fingerprints. The most commonly used distance metric is the Euclidean distance, and it was used in [8] under the name Nearest Neighbour in Signal Space (NNSS). One may also use the Manhattan distance as a distance metric [9]. Other deterministic methods include the \(k\)-Nearest Neighbour (KNN), which calculates the weighted or unweighted average of \(k\) training locations, which are closest to the target's fingerprints under a certain distance metric. One may also obtain a large number of snapshots of the training fingerprint and utilize its distribution as a location fingerprint. This is categorized as a statistical approach.