# Acoustic TDOA Measurement and Accurate Indoor Positioning for Smartphone
## 4 Experiments and Results
### Experimental Results and Analysis
In indoor spaces, there is a phenomenon where the strongest path lags behind the direct path. This phenomenon is the essential reason for the large TDOA measurement errors in Figure 18. We developed Algorithms 2 and 3 to improve the problem of large TDOA measurement errors. As can be seen from Figure 19, TDOAs measurement average error has significantly decreased compared to Figure 18. In test point 1, the TDOA2 measurement average error is the maximum value (0.6 ms). In test point 2, TDOA3 measurement average error is the maximum value of (1.4 ms). In test point 3, TDOA3 measurement average error is  
Figure 19: TDOA measurement average error in scenario 1 (using Algorithms 2 and 3). Figure 18: TDOA measurement average error in scenario 1 (using cross-correlation). the maximum value (1.2 ms). In test point 4, the TDOA1 measurement average error is the maximum value (1.5 ms). In test point 5, the TDOA3 measurement average error is the maximum value (0.56 ms). All TDOA measurement average errors are less than 1.6 ms (corresponding distance difference error is 54.4 cm), which provides a prerequisite for achieving decimeter-level positioning in scenario 1. When we use the ML algorithm for positioning, the results will be more stable. To further illustrate the better stability of our TDOA measurement method, we will display the data in Figures 18 and 19 by using a line chart. As can be seen from Figure 20, the proposed method has better stability for TDOA measurement. In Figure 20a, the measurement average error of TDOA1 varies between 0.2 ms and 1.6 ms, the measurement average error of TDOA2 varies between 0.2 ms and 1 ms, and the measurement average error of TDOA3 varies between 0 ms and 1.5 ms. In Figure 20b, the measurement average error of TDOA1 varies between 0 ms and 23 ms, the measurement average error of TDOA2 varies between 0 ms and 23 ms, and the measurement average error of TDOA3 varies between 0 ms and 12 ms. So, it can be seen that the proposed method shows good stability. At the same time, it can be seen that the proposed method has a relatively low measurement error in all TDOA measurements. After we obtain TDOAs, we perform the localization function by using the ML algorithm. We refer to the floor tiles to obtain an approximate true value of the smartphone's position. Then we calculate the CDF with two methods (Proposed-ML and Cross-correlated-ML), as shown in the following Figure 21.  
Figure 21: CDF of the positioning errors in the scenario 1. Figure 20: TDOA measurement average error in scenario 1: (**a**) TDOA measurement average error using the proposed algorithm; (**b**) TDOA measurement average error using the cross-correlation algorithm. In Scene 1, we found that the results of using the cross-correlation-ML algorithm for localization at testing points 2 and 4 tend toward infinity. Therefore, in Figure 22, we do not show the localization results for testing points 2 and 4 when using the Cross-correlation-ML method. By using the algorithm proposed in this paper, high-precision localization results were obtained in the localization experiment in Scene 1. In Scene 1, each test point was located 100 times. We used box plots to display the localization results obtained using the proposed algorithm in Scene 1. As can be seen from Figure 22, the indoor acoustic positioning system was tested using a Proposed-ML algorithm to increase its accuracy to the decimeter level in scenario 1. The preparatory work involved coordinating the acoustic nodes and test points using computer software and calibrating them with a plumb line. In scenario 1, five test points were used, each with known coordinates. These test points were triggered every two seconds by the scheduler, and each point was tested 100 times to increase randomness. The positioning error was evaluated using Formula (9) given in the paper. To verify the accuracy of the system further, data were collected at 20 different test points in scenario 2.