## 1 Introduction
The basis of the probabilistic estimation method is mainly Bayesian theory estimation, which is divided into two major filtering algorithms: Kalman filter and particle filter. A number of studies have been conducted on the basis of them, and several classical algorithms have been proposed, such as the EKF [30], the unscented Kalman filter (UKF) [31; 32], the particle filter and the Rao-Blackwellization algorithm, the particle filter combined with the Rao-Blackwellization algorithm to form RBPF [33; 34; 35; 36], etc. Reference [37] has made a detailed comparison of the above algorithms. Among them, EKF-based SLAM is simple and feasible when dealing with non-linear systems, and it is still widely used not only in land, aviation, and underwater fields, but also in various forms of robotics, such as unmanned aerial vehicles (UAVs) [38], automated guided vehicles (AGVs) [39], and remotely operated vehicles (ROVs) [40]. In this paper, we propose a novel approach to map the positions of microphones passively and to simultaneously localize a moving robot in realistic acoustic environments. The microphone localization process based on sound source array was conducted and then a method of EKF-SLAM for mobile robots based on microphone landmark observation is proposed. To avoid the estimation error of the time delay of sound arrival caused by environmental noise, reverberation [41], and hardware equipment, a method of using calibration to eliminate TDOA estimating errors is presented. In our case, the robot itself carries three sound source units distributed in an equilateral triangle and a reference microphone. The relative distance between the reference microphone and the three sound sources was known. The reference microphone was placed within a range that ensured that the three sound signals could be received clearly. In the same plane as the sound sources, a certain number of microphones were randomly distributed; the microphone which received the three sound signals was defined as a microphone to be positioned (MTP). The reference frames are illustrated in Figure 1.  
Therefore, the novel features of the approach proposed in this paper are (1) the joint estimation of the unknown robot path and the positions of multiple microphones based on the (2) sound source array installed on the robot, and (3) a microphone capable of receiving sound signals which can be directly used as a feature landmark of the robot observation model without feature extraction. Performance results for controlled and realistic room acoustics are presented to analyze the theoretical and practical behavior of the method. Specifically, it is shown that this approach outperforms other methods for SLAM due to its lower complexity and lack of feature extraction, and SLAM research using acoustic sensors has the potential for wide application. The paper is structured as follows: Section 2 describes the strategy of the microphone localization method based on sound source array. Section 3 derives the proposed algorithm involving the microphone localization combined with EKF-SLAM. Section 4 presents the simulation and experimental setup and results. Conclusions are drawn in Section 5.