# Evaluation of Multi-Sensor Fusion Methods for Ultrasonic Indoor Positioning
## 5 Experimental Results  
Some experimental results are presented now, according to the previously studied fusion algorithms. These tests were developed in a hall of the School of Engineering at the University of Alcala. As shown in Figure 1, it is an extended hall located on the second floor of the building, with a volume of \(7\times 8\times 3.5\) m\({}^{3}\). Table 1 already showed the coordinates of the central beacons \(B_{1}\) for every ULPS; note that ULPS-2 and ULPS-3 had different heights and were not placed at the centres of the wall in the hall, due to its complex architecture. The beacons from the three ULPSs were encoded with fifteen different 1023-bit Kasami sequences, whereas a multiple ultrasonic receiver prototype was placed at the seven measurement points (P1-P7) with the same heights \(z_{1}=1.35\) m and \(z_{2}=1.93\) m, in accordance  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Points**} & \multicolumn{6}{c}{\(z_{1}\)} & \multicolumn{6}{c}{\(z_{2}\)} \\ \cline{2-13}  & \multicolumn{2}{c}{**Mean Error (m)**} & \multicolumn{2}{c}{**Std Deviation (m)**} & \multicolumn{2}{c}{**Mean Error (m)**} & \multicolumn{2}{c}{**Std Deviation (m)**} \\ \cline{2-13}  & \(x\) & \(y\) & \(z\) & \(x\) & \(y\) & \(z\) & \(x\) & \(y\) & \(z\) & \(x\) & \(y\) & \(z\) \\ \hline P1 & 0.163 & 0.098 & 0.117 &  
with the previous simulations. Firstly, one hundred measurements were acquired and stored at each position for the three ULPSs. Those measurements were used to compute the variances of each position offline, then stored and used later in the online positioning system, when the variances were needed in the loosely coupled fusion methods. Secondly, thirty measurements were obtained at each point P1-P7 for the online study. These experimental results are provided next, in the same order as they were analysed in Section 4 for simulations. Table 9 shows the positioning errors for 90% of the cases, when the three ULPSs operated independently, with errors varying in the decimetre and meter ranges. With regard to the LKF in the loosely coupled fusion, Figure 12 plots the estimated positions after fusion, with their different plane projections at both heights. The LKF merged up to nine position estimates, as there were three ULPSs and three receivers in the experimental prototype. Additionally, a CDF error is plotted for both cases in Figure 12e,j, where the average error for all the points is 0.72 m at \(z_{1}\) and 0.34 m at \(z_{2}\). Table 10 shows the mean error and standard deviation for P1-P7. The height \(z_{2}\) was more accurate for the  
==WARNING: Truncated because of repetitions==
8 & 0.223 & 0.054 & 0.298 & 0.074 & 0.071 & 0.110 & 0.080 & 0.053 & 0.089 \\ P2 & 0.0
+++  
Figure 13: _Cont._  
Finally, some results from the EKF applied as a tightly coupled method are presented in Figure 14 with variance in the measurements of distances fixed at \(\sigma_{w}=0.2\) m. As was confirmed in simulations previously, the clouds of the seven positions were more concentrated around the ground-truth points, with low dispersions as well. The mean errors and standard deviations are listed in Table 12. It is worth mentioning that all the axis errors decreased for both heights, especially for \(z_{2}\), to less than 0.17 m at \(z_{1}\) and less than 0.13 m at \(z_{2}\). The CDF errors for 90% of the cases for the seven studied points were between 0.1  
In summary, the experimental results in Table 13 corroborated the positioning errors previous simulations listed in Table 8. It is possible to observe that the tightly coupled method applying an EKF presents more accurate estimated positions, where the mean  
Figure 14: Experimental results for the tested points P1–P7 for both heights, \(z_{1}\) = 1.35 m on the left (**a**–**e**) and \(z_{2}\) = 1.93 m on the right (**f**–**h**): successively, 3D representation of clouds of points; Y–X projections; Z–X projections; Z–Y projections; and experimental CDFs for each point after EKF fusion (\(\sigma\) = 0.2 m).