## 4 Simulation and Experiment Results
### Room Simulations  
In this simulation, the data collected by the robot motion model in 0-95 s was selected to test. The control input adds Gaussian noise with a mean value of 0 and a variance of \(\sigma_{\text{rc}}=0.49\) m/s, \(\sigma_{\text{rc}}=0.49\) m/s, \(\sigma_{\gamma}=\left(\frac{7\pi}{180}\right)^{2}\), where \(v_{e}\) and \(v_{c}\) denote the speed of the rear wheel and the center of the robot, respectively, \(\gamma\) represents the robot's steering angle. In the same plane, 15 microphones were randomly distributed, and the observation range was formed within a circle with a radius of 10 m centered on the robot. The observation information was added with Gaussian noise with a mean value of 0 and a variance of \(\sigma_{d1}=0.001\), \(\sigma_{d2}=0.001\), and \(\sigma_{d3}=0.001\), where \(d_{1}\), \(d_{2}\), \(d_{3}\) were the distances from the landmarks to the three sound sources, respectively. The simulation results of the proposed method are shown in Figure 9. In Figure 9a, by comparing the robot's real movement trajectory with the trajectory estimated by the EKF-SLAM algorithm regarding the microphone as a landmark, it was found that the two were basically coincident. At the same time, comparing the actual location of the feature landmarks in the environment with the estimated location, it can also be found that the two were basically coincident. It means that the mobile robot can accurately achieve its own localization and map construction to some extent. However, there was a small difference between the estimated location and the actual location of the robots and landmarks, due to the presence of irregular movements such as steering during the movement of the robot. In addition, sometimes when only one or even no landmarks could be observed during the observation process, it caused errors. Figure 9b,c  
Figure 8: Extended Kalman filter (EKF)-SLAM processing flow chart. show the error analysis of simulation results. It is pointed out that the method can ensure the accuracy of position and map estimation. Figure 9: Simulation results for SLAM with no noise in the sound signal: (**a**) EKF-SLAM for a mobile robot based on microphone landmark observations; (**b**) robot position errors in the \(x\)- and \(y\)-directions; and (**c**) landmark position errors in the \(x\)- and \(y\)-directions. In actual real-world environments, there are often various kinds of noises around the sound source. Sound signals are usually noisy sounds formed by pure sound and aliased noise. For a noisy signal, the amount of noise it carries can be represented by a physical signal-to-noise ratio (SNR). The SNR is defined as the average energy ratio between each speech source and the noise. \[\text{SNR}=10\log_{10}\frac{\sum\limits_{n=0}^{N-1}s^{2}(n)}{\sum\limits_{n=0}^ {N-1}d^{2}(n)} \tag{21}\]  
Gaussian white noise was added to the speech signal. In Equation (21), \(\sum\limits_{n=0}^{N-1}s^{2}(n)\) denotes the energy of the signal; \(\sum\limits_{n=0}^{N-1}d^{2}(n)\) denotes the energy of the noise. Thus, in this paper, simulation experiments were also carried out on the basis of the addition of noise with a SNR with 65, 50 (dB) to the sound signal. The simulation results are shown in Figures 10 and 11. The results of Figure 11 were generated when more noise was added than previously seen in the results in Figure 10. The SD of the robot's position and landmark position under SNRs of 50 and 65 dB is shown in Tables 1 and 2. Standard deviation is defined as  
\[\text{SD}=\sqrt{\frac{1}{N_{T}-1}\sum\limits_{i=1}^{N_{T}}\left(\hat{D_{i}}-D_{ i}\right)^{2}} \tag{22}\]  
where \(N_{T}\) is the total number of estimations (i.e., total number of estimated position for the robot and ten microphones), \(\hat{D_{i}}\) is the \(i\)-th estimation and \(D_{i}\) is the \(i\)-th correct position.