## 4 Simulation and Experiment Results
### Experimental Results in a Realistic Environment
#### 4.2.3 Experiment Results  
We programmed the method to acquire sound signals only when the robot stopped. The experimental verification process of the method is as follows:  
The robot center point is considered to be the origin. At the initial time, the origin of the robot coordinate system coincides with the origin of the world coordinate system, and the current position of robot is (0, 0). These ten microphones need to be measured one by one to determine the difference in sound time between them and the reference microphone. 1. For the first microphone to be positioned (m1), use the calibration method described in Section 4.2.2, to obtain the precise value of time delay of arrival between m0 and m1 (TDOA1). 2. Similar to Step 1, first s0 sounds, and then s2 sounds. Finally, TDOA2 between m0 and m1 is obtained. When it is s3, TDOA3 is obtained too. 3. Distances between m1 and the three sound sources (d1, d2, d3) is calculated by Equations (6) and (7). 4. Evaluate whether m1 is a valid characteristic landmark, and if it is, put m1 into the dataset or abandon it. The evaluation method is described as follows and the evaluation standard value is obtained from actual experimental data analysis in this paper. 5. Repeat Steps 1-4 and the other valid microphones are detected in sequence. 6. The method of EKF-SLAM based on microphone landmark observations described in Section 3.3 is applied to this procedure. 7. The robot insists on moving to the next position and performing the above operations until the end of the experiment. As shown in Figure 16, there are two sound sources, S0 and S1. S1 is used as the main sound source, and S0 is used as the \"calibration sound source\". Also, there are two microphones, MIC0 and MIC1. MIC0 is used as the reference microphone, and MIC1 is used as the microphone to be positioned. The distance between S1 and MIC0 is known for 1 m. Assuming that the distance between MIC1 and S1 is unknown, and it is estimated by the TDOA estimation method introduced in Section 2. Firstly, place MIC1 two meters away from s1, and then move MIC1 in units of one meter to the right to do multiple measurements. Finally, by comparing the estimated distance value with the real, it is found that when the microphone is placed less than 3 m away from the sound source, the acquired sound signal is the most reliable for this method. Figure 15: Partially enlarged view of the first speech segments. To verify the feasibility of the SLAM method presented in this paper, the robot (Pioneer3-DX) was moving through a specifically designed path to avoid some improper situations for TDOA estimation and range-only SLAM, as depicted in Figure 17. The origin was the point where the robot started to move in an 6.05 m \(\times\) 4.10 m \(\times\) 2.22 m experimental area. In the robot coordinate system, three sound sources and the reference microphone at a height of 0.7 m were at s1 = (0, 0.3) m, s2 = (\(-\)0.26, \(-\)0.15) m, s3 = (0.26, \(-\)0.15) m, and m0 = (0, 0) m. Ten microphones to be positioned were dispersedly mounted on the wall in the same plane as the sound source. It can be seen that it was L-shaped. The calibration speaker can be moved when needed. The robot stopped at 10 waypoints to record the acoustic data. It stopped for approximately 120 s to ensure the recording of the sound signal. The speed of robot was fixed when moving. Figure 16: Schematic diagram of the evaluation method. The SLAM results are shown in Figure 18. In Figure 18a, the red, solid line represents the robot's planned trajectory (actual trajectory), and the red star points represent microphones that were distributed in an L-shape in the environment, that is, the actual location of the feature landmarks; The blue, dotted line represents the robot's estimated path trajectory, and the blue circles represent the estimated location of the feature landmarks.