## 1 Introduction  
With the development of science and technology, the robot market has grown quite large for a myriad of applications. The realization of autonomous navigation for robots is an important step in solving the difficult problems of various complicated working environments. Simultaneous localization and mapping (SLAM) [1; 2; 3; 4] of mobile robots is a fundamental and important problem rooting from the related research. In the SLAM problem, the robot needs to perceive its own movement behavior, pose, and information of the current environment through sensors when it is in a known or unknown environment. Visual and optical sensors are classically used as external sensors in solving problems of SLAM [5; 6; 7; 8; 9]. In Reference [10], the technology of the robot environment map-building based on laser radar scanner was studied. However, the beam of the laser radar was extremely narrow, making it difficult to search for targets in space. Its accuracy was also greatly affected by the ground conditions. In Reference [11], a moving camera was applied to adopt environmental information. Then, a visualized SLAM solution was implemented through combining the extended Kalman filtering technology with extracted image features. It needs to be pointed out that visual sensors can only perceive information within the robot's limited field of vision and rely heavily on light. Compared with the above external sensors, sound has the advantages of propagation omnidirectionality, diffraction susceptibility, high-time resolution, and non-limited visibility. In contrast to the classical context of SLAM, this paper presents an algorithm to perform SLAM using acoustic signals. Acoustic SLAM hasthe potential for wide application in areas including autonomous robots, hearing aids, smart cars, and virtual reality devices [12; 13]. An audition system is a very important feature for an intelligent robot [14; 15; 16]. In the auditory field, there are several research issues such as sound source localization, localization of moving microphone arrays, speech separation and enhancement, etc. [17; 18; 19; 20; 21; 22]. Time delay of arrival (TDOA) between sound sources and corresponding microphones was always used in the studies mentioned above [23]. The localization of microphones may help to solve a number of problems for mobile robots. In this paper, acoustic SLAM typically applied microphone localization as a pre-processing step to the extended Kalman filter (EKF) procedure. The distances between the sound sources and detected microphones were calculated according to the TDOA obtained, and then they were used as direct measurement information for microphone localization. The time delay estimation method has a small number of calculations and strong real-time performance. Commonly used time delay estimation algorithms include generalized cross-correlation (GCC) [24], cross-power spectral phase (CSP) [25], adaptive filtering [26], etc. Among them, the GCC method exhibits superior performance in suppressing noise and reverberation. [PERSON] et al. [27] proposed a natural way of human-computer interaction in which people as passive users did not need to interact with the robot through keyboards, mice, etc. The method assumed that the sound source was located in front of the robot, and the cross-correlation method could be used to estimate the time difference of the sound, and then the far-field sound source was located by the far-field approximation geometric method. [PERSON] et al. [28; 29] used the generalized cross-correlation method based on feature structure to estimate the time difference of sound of multiple sound sources. This paper estimates time delay between sound source and microphone by use of the GCC method. At present, solutions to the SLAM problem are roughly divided into two categories: methods based on probability estimation and methods based on non-probabilistic estimation.