## 1 Introduction  
A signal represents the physical quantity of a message. Humans can collect important information about the environment through a signal, especially a sound source signal [1; 2; 3; 4; 5], which is a sound wave generated by the vibration of an object, as well as the movement of a sound wave through any material. As a kind of wave, sound with a frequency between 20 Hz and 20 kHz can be recognized by the human ear [6; 7]. Moreover, a target sound source can be located by receiving the sound source signal and applying an algorithm. Microphone arrays [8; 9; 10; 11] perform functions such as noise elimination and target tracking. They can also be used to passively receive sound source signals, making it practical for researchers to collect signals. A microphone array system is composed of multiple microphones placed in accordance with a given topological structure that performs real-time processing on spatial sound source signals received from different directions. In recent years, with the rapid development of physics [12], mathematics [13], and signal processing [14], sound source localization technology for microphone arrays has received widespread attention from researchers both domestically and abroad. In addition, research on sound detection technology for the design of microphone arrays and sound source localization algorithms [15; 16; 17; 18; 19] has been conducted. In terms of sound source localization technology, foreign countries have had an earlier start. In 1985, [PERSON] [20] used a linear array as a research tool to determine the available bandwidth as a function of the steering direction, given the number and spacing of receiving microphones, and solved the problem of reducing the available bandwidth of space discrimination when turning away from the normal wave arrival direction. In 1997, [PERSON] et al. [21] used a set of microphones designed to provide a high-quality source localization while attenuating the interference of speech and ambient noise without the need for a local position sensor, an obstructive talking handheld, or a microphone, as a single microphone does not have this function. In 2016, [PERSON] et al. [22] extended traditional triangulation to moving sources. The experiment proved that the moving time difference of arrival (MTDOA) method is superior to traditional triangulation in case of moving sound sources. With the rapid development of modern technology, numerous breakthroughs in sound source detection have been made. In 2010, [PERSON] et al. [23] proposed a moving sound source tracking method based on microphone array measurements that uses the speech linear prediction residual to estimate the time delay, therefore weakening the noise and reverberation effect and significantly improving localization precision. In 2013, [PERSON] et al. [24], using an acoustic array in a robotic system, proposed a tetrahedral array to locate a sound source target. Using the time difference localization method, the paper deduced localization and fallibility formulas. The method not only improves the localization precision, but also reduces the blind space. In 2017, [PERSON] et al. [25] proposed a method to overcome the effect of spatial aliasing via signal processing. A 32-element spherical microphone array was used to extend the frequency range of the microphone array, and experiments verified the precision of the theoretical results to overcome the aliasing. In the same year, [PERSON] et al. [26] proposed a linear microphone array with multiple hypothesis tracking, combined with a novel sound source parameterization, the joint optimization of six sensors, and three landmarks and sound source positions to solve the three-dimensional sound source mapping problem. Due to the unremitting exploration of international researchers, studies on sound source localization technology based on multi-microphone arrays have been rapidly developing. The estimated arrival time delay will cause errors [27; 28; 29], and the errors of ranging and direction-finding are difficult to avoid.