## 1 Introduction  
Speaker recognition is a part of biometric technology. This technology is often used in security detection, such as access control, company punch cards, bank vaults, robots, and smart living. Speaker recognition technologies can be divided into text-dependent [1] and text-independent [2]. In text-dependent speaker recognition, the speaker must utter a sentence with specific content. For example, ref. [1] applied the wake-up word model to speaker recognition. Text-independent speaker recognition has no restrictions on sentence content, and recognition focuses on confirming the speaker's identity. For example, ref. [2] proposed a text-independent speaker verification method in noisy environments by fusing different features. Text-independent forensic speaker recognition was studied in [3]. Forensic speaker recognition means that when a suspect has left sound evidence, speaker identification needs to be found through the sound [4,5]. Text-dependent speaker recognition is easier to train but more limited because the same sentence needs to be spoken during recognition. Text-independent speaker recognition is challenging because it usually requires more data to achieve better results, but it is relatively more flexible in application. Our research aimed to construct a text-independent speaker recognition method. We discuss two main aspects of the speaker recognition process: feature extraction and speaker modeling. In previous studies, many techniques have been developed for extracting features from sound signals. For example, linear frequency cepstral coefficients (LFCC) [2; 6] and mel-frequency cepstral coefficients (MFCCs) [2; 6; 7] use filter-bank coefficients for feature extraction. The differences between LFCC and MFCC are described in [2]. In LFCC, sound signals of all frequencies are regarded as equally important. The design of MFCC considers the degree and influence of the perception of different sound frequencies by the human ear. In reality, the human ear is more sensitive to changes in low-frequency sounds; therefore, the MFCC method emphasizes low-frequency sound signals. The MFCC calculation is described in detail in [8]. [PERSON] and [PERSON] [9] described some text-independent speaker recognition techniques and discussed and recommended feature selection in their paper, including the use of MFCC features. [PERSON] and [PERSON] [10] proposed a new windowing technique for MFCC computation and used speaker recognition accuracy for comparison with past windowing techniques. In reference [7], dynamic time warping (DTW) and features extracted using MFCC were utilized for speaker recognition. The two feature extraction techniques, LFCC and MFCC, have been used to classify insect singing [6]. The performance achieved from both approaches was good, but most insects' sounds are high-frequency signals, so using LFCC as the classifier input provides better results than using MFCC. Spoken language identification utilizes MFCC features and gammatone cepstral coefficient features [11]. Because our research direction is to construct a method of speaker recognition for the human voice, we use MFCC for feature extraction, as it is more suitable for recognizing the human voice. Many models have recently been applied in the field of voice recognition, the primary purpose of which is the recognition output after the model calculates the input data. Hidden Markov models (HMMs) were applied to speaker-independent word recognition for the first time [12]. HMMs use multiple states to construct implicit unknown parameters and are predominantly used for word recognition. [PERSON]. [13] used a Gaussian mixture model (GMM) to calculate the input signal into multiple Gaussian components to represent the spectral shape of the speaker. Because a GMM uses multiple Gaussian components to construct the sound model of the input signal, it is primarily used for identity model construction and recognition. [PERSON].