## 1 Introduction  
Pipelines are used to transport natural gas, water, oil products and other easy-flowing products, and pipeline leakage is a common phenomenon in the continuous transportation process due to the corrosion of pipe walls [1], third-party interference [2], aging of the pipes [3], etc. Leakage may lead to environmental pollution, energy loss, injuries, and even fatalities. Therefore, leakage location is one of the paramount concerns of pipeline operators and researchers. Pipeline leakage detection methods include direct and indirect methods [4]. Direct methods detect the leaked product outside the pipeline using fiber optic sensing, moisture measurements, gas tracing, vapor sensing, etc. [5]; however, these methods suffer from low sensitivities and expensive sensors. Indirect methods detect the leakage by measuring the pipeline gas pressure, flow, temperature, etc. using sensors mounted inside the pipeline; however, many pressurized vessels in industry are inaccessible, which necessitates nondestructive testing. Acoustic emission (AE) [6] is a nondestructive testing technique that provides the ability to rapidly locate small-scale leaks [7]; it has thus now become a common leak location method. AE signals can be generated by friction, cavitation, impact, or leakage in a high-pressure pipe. In this study, the AE signals in the pipe wall are detected by AE sensors mounted on the pipe's exterior surface. Leakage location commonly relies on attenuation-based methods or time-of-flight-based methods [8]. The former methods are based on the reduction in the AE signal strength as the propagation distance increases. The prerequisite for the latter methods is that the wave speed is a known constant; however, the wave speed varies as a function of frequency due to the group speed dispersion nature of gas-leakage-induced guided waves [9]. To determine the speed of the AE signal, [PERSON] et al. [10] derived the wavenumber formulae to predict the wave speeds, and thereby halved the location error compared to that using the theoretical wave speed. [PERSON] and [PERSON] [11] derived the motion equation of the pipe for the simply supported boundary condition by the standard form of [PERSON]'s nonlinear cylindrical shell theory. [PERSON] et al. [12] generated wide-band cylindrical waves in aluminum pipes by the laser-ultrasonic method; the experimental results showed good agreement between the theoretical and experimental group speed dispersion curves. In this study, the group speed of the leakage-induced signal was estimated by its peak frequency in combination with the group speed dispersive curve of the fundamental flexural mode. When leakage-induced signals transmit along the pipe wall, signal distortion arises due to energy attenuation, dispersion effect [13] and reverberation. The cross-correlation function (CCF) can determine the time delay based on the similarity of two signals. However, the degree of signal distortion affects the similarity of two signal waveforms measured by two AE sensors, and this interference degrades the performance of the CCF method. To improve the leakage location accuracy, [PERSON] and [PERSON] [14; 15] located a leak on a high-pressure gas pipe by wavelet transform, filtering technique, and CCF. [PERSON] et al. [16] located the leakage by dual-tree complex wavelet transform and singular value decomposition. [PERSON] et al. [17] estimated the time delay between two channels by the time and frequency domain methods, with almost identical test results being obtained. [PERSON] et al. [18] proposed a leakage aperture recognition and location method using the root mean square entropy of local mean deposition and Wigner-Ville time-frequency analysis. [PERSON] et al. [19] proposed an adaptive noise cancellation method using the empirical mode decomposition, the test result showed that the time delay estimation of the leakage-induced signal is more accurate. [PERSON] et al. [20] estimated the characteristics related to the two propagation channels by blind system identification.