## 1 Introduction  
Orbital objects, such as meteoroids and space debris, are among the serious and inevitable threats to spacecraft [1]. Technically, collisions caused by debris larger than 10 cm can be avoided by using databases that are compiled by debris-tracking systems [2]. Meanwhile, strikes by objects that are smaller than 10 cm lack an efficient detecting approach. A collision may damage the bulkhead of the spacecraft, causing internal pressure to leak, which seriously threatens the flight and the safety of astronauts and leads to severe consequences [3]. Thus, the detection and location of leakages would be of significant use for spacecraft in orbit. For the problem of leak source location, some related findings have been reported. According to different principles, the currently representative methods include the optical imaging method [4],the optical fiber method [5], the helium mass spectrometry method [6], and the acoustic detection method [7]. Compared with other methods, the acoustic detection method can achieve the non-destructive detection and real-time location of leakages in a larger range with a high location accuracy and stability. Moreover, acoustic sensors are easy to integrate with spacecraft structures, thus eliminating the need for complex processes such as laying optical fibers or using noble gases. Therefore, the acoustic detection method is a potential leakage location technology for spacecraft in orbit [8]. For leakage location based on acoustic methods, the key difficulty lies in the continuity of the leakage acoustic signal. For a collision with a time point of occurrence, location can be performed by calculating the time difference of arrival. To solve the above problems, [PERSON] et al. [9; 10] carried out research on cross-correlation and two-dimensional Fourier transform techniques to determine air leakages on the International Space Station (ISS). In the study, two \(16\times 16\) sensor arrays were applied to locate a leak. All possible cross-correlations between the 256 sensor positions in each array were recorded. A large number of sensors and millions of data samples led to a time- and finance-consuming task. [PERSON] et al. [11] proposed a T-mapping method. This method obtains time-domain eigenvalues from a prior meshing experiment and uses a clustering algorithm to identify the position of the signal source. This scheme has good adaptability to complex structures, but the initial workload is huge and it has no application potential for huge spacecraft. In order to reduce the number of sensors and the algorithm complexity of the leak location scheme, the beamforming technique was firstly applied to the method of leakage detections with acoustic emission sensors by [PERSON] et al. [12]. The beamforming algorithm has been primarily used in radar, sonar and exploratory seismology [13]. However, the specimen tested in their experiment was a steel-reinforced concrete bridge ramp instead of a thin plate. The work was based on [PERSON] wave theory, which is not applicable to the thin plates used in spacecraft. [PERSON] et al. [14] tested a thin plate that was equipped with near-field beamforming analysis, which was suitable for Lamb wave theory. Burst acoustic emission signals that were created by breaking a mechanical pencil lead on the surface of the specimens were applied in their tests, and the propagation speeds of the signals were obtained by time difference of arrival (TDOA) techniques. This method is not ideal for a leak-generated continuous signal. However, the difficulties of using beamforming techniques for acoustic emission signal processing lie in the confirmation of wave speeds due to their dispersion. [PERSON] et al. [15] considered the effect of dispersion, but their scheme did not consider the diversity of the frequency bands that are generated by leakage in practical applications.