## 1 Introduction  
Acoustic emission (AE) is defined as a phenomenon whereby a transient elastic wave is generated by the rapid release of energy from a localized source of damage [1]. Various types of AE sources, such as fiber breakage [2], fatigue cracks [3], rubbing [4], and impact of foreign objects [5] can generate the propagation of AE waves. The process of locating the source of these acoustic waves, by recording the propagating acoustic signals from various sensors and properly analyzing them, is commonly known as the AE localization technique. It is an important step for structural health monitoring (SHM) [6]. The AE localization technique is one of the key issues in AE technology research. The accuracy of the localization reflects the degree of compliance between the detection location of the AE source and real location. Many scientists have conducted a mass of research on the source localization of AE, and have proposed many efficient localization methods. [PERSON] [6] reviewed the research status of AE source localization research technology. [PERSON] [7] is a pioneer in the study of AE source localization in isotropic materials. The triangulation method proposed by [PERSON] is the most commonly used method for isotropic materials, which determines the location of the AE source based on the time difference of arrival (TDOA) between the AE waves reaching different sensors. But only when the precise wave velocity of elastic wave propagation in the material is obtained can an accurate location result be obtained. In response to this limitation, [PERSON] et al. [5] improved the triangulation method and proposed an AE source localization method suitable for isotropic materials without wave velocity. However, the localization accuracy of the TDOA method is affected by noise, dispersion effect, energy attenuation, and other factors during the propagation process [8]. Moreover, the application of TDOA method in two-dimensional or three-dimensional large and medium-sized structures generally requires the sensors to be sparsely arranged. In response to this situation, [PERSON] et al. [9] carried out non-destructive testing research based on the beamforming method to achieve the location of AE sources for structural damage in the field of civil engineering. [PERSON] et al. [10] introduced the near-field beamforming method into the processing of AE signals in thin-plate structures, and studied a new method of arranging a small number of sensors in small areas to realize the localization of AE sources. In order to locate the acoustic emission source in an anisotropic material, [PERSON] et al. [11; 12] extended the beamforming method into anisotropic materials. But it is necessary to measure the propagation velocity of AE waves in different directions in anisotropic materials. [PERSON] et al. [5; 13; 14], [PERSON] et al. [15], and [PERSON] et al. [16] improved the TDOA method and successfully applied it to AE source localization of anisotropic materials. The localization accuracy of these methods depends on the measured wave velocity, and the relevant properties of the material need to be obtained in advance. In order to overcome the influence of wave velocity on the localization accuracy of AE sources in anisotropic materials, [PERSON] et al. [17; 18] proposed an AE source localization method that does not require wave velocity. Only six acoustic emission sensors are needed to locate AE source in an anisotropic plate. In summary, the localization research of AE source mainly includes the TDOA method and the beamforming method. These methods can be applied to actual engineering structures. For example, fuselages of aviation structures [19], aircraft engines [20], and vehicle welding structures [21]. Although the TDOA method is mature and easy to use, its localization effect is highly dependent on the accuracy of the obtained TDOA. The beamforming method based on the delay-and-sum algorithm is accurate in localization.