## 5 Conclusions  
This paper considers the EKF-SLAM for mobile robots based on microphone landmark observations. A kinematic analysis of the mobile robot was conducted and a kinematic model was established. The method of microphone localization based on sound source array in the auditory field was described, and it was combined with the EKF-SLAM algorithm to solve the SLAM problem of the mobile robot. The observation model was established based on microphone landmark observation. In addition, this paper also discussed the advantages and novelty of sound sources and microphones used as external sensors for the SLAM problem compared with traditional sensors such as laser radar. In this paper, the effectiveness and the robustness of the EKF-SLAM based on microphone landmark observation is demonstrated through simulation and experimental tests from the theoretical and practical perspective, respectively. It should be pointed out that this method can only realize the localization of landmarks in two-dimensional planes, and there are problems such as the missing of environmental features and low detection accuracy. To achieve the SLAM of mobile robots faster and more accurately, applying a method of microphone localization in a three-dimensional space in SLAM is still a work to be studied in the future.  
Conceptualization, X.C. and H.S.; Methodology, X.C. and H.S.; Software, X.C. and H.Z.; Validation, H.S., and H.Z.  
This research was funded by the National Natural Science Foundation of China Youth Fund, grant number 61503118, the National Natural Science Foundation of China, grant number 61773135, the National Natural Science Foundation of China, grant number 61703135, the Natural Science Foundation Youth Fund of Hebei Province, China, grant number F2016202327, and the Natural Science Foundation of Hebei Province, grant number F2017202119.  
The authors declare no conflict of interest.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Actual Position** & **Estimated Position** & **x-Error** & **y-Error** \\ \hline \multirow{8}{*}{**Landmarks**} & (\(-1.775\), 0.135) & (\(-1.788\), 0.114) & 0.013 & 0.249 \\  & (\(-1.775\), 1.157) & (\(-1.646\), 1.347) & 0.129 & 0.190 \\  & (\(-1.775\), 1.833) & (\(-1.606\), 1.993) & 0.169 & 0.160 \\  & (\(-1.775\), 2.735) & (\(-1.579\), 2.873) & 0.196 & 0.138 \\  & (\(-1.775\), 4.092) & (\(-1.568\), 4.234) & 0.207 & 0.142 \\  & (\(-0.915\), 5.479) & (\(-0.712\), 5.617) & 0.203 & 0.138 \\  & (\(-0.125\), 5.479) & (\(0.087\), 5.607) & 0.212 & 0.128 \\  & (\(0.695\), 5.479) & (\(0.898\), 5.598) & 0.203 & 0.119 \\  & (\(-1.775\), 5.187) & (\(-1.554\), 5.332) & 0.221 & 0.145 \\  & (\(1.685\), 5.479) & (\(1.887\), 5.589) & 0.202 & 0.110 \\  & **Standard Deviation** & & 0.195 & 0.169 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Localization results of landmarks. X-error: the error of the landmarks’ positioning in the \(x\)-axis direction. Y-error: the error of the landmarks’ positioning in the \(y\)-axis direction. Y-error: the error of the landmarks’ positioning in the \(y\)-axis direction.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Actual Position** & **Estimated Position** & **x-Error** & **y-Error** \\ \hline \multirow{8}{*}{**Robot’s Position**} & (0, 0) & (0, 0) & 0 & 0 \\  & (0, 0.586) & (0, 0.586) & 0 & 0 \\  & (0, 1.172) & (0.021, 1.177) & 0.021 & 0.005 \\  & (0, 1.758) & (0.116, 1.806) & 0.116 & 0.048 \\  & (0, 2.344) & (0.185, 2.400) & 0.185 & 0.056 \\  & (0, 2.930) & (0.187, 3.045) & 0.187 & 0.115 \\  & (0, 3.516) & (0.201, 3.643) & 0.201 & 0.127 \\  & (0.586, 3.516) & (0.785, 3.646) & 0.199 & 0.130 \\  & (1.172, 3.516) & (1.371, 3.646) & 0.199 & 0.130 \\  & (1.758, 3.516) & (1.840, 3.646) & 0.082 & 0.130 \\  & **Standard Deviation** & & 0.132 & 0.082 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Localization results of a mobile robot. X-error: the error of the robot’s positioning in the \(x\)-axis direction. Y-error: the error of the robot’s positioning in the \(y\)-axis direction.