# Evaluation of Multi-Sensor Fusion Methods for Ultrasonic Indoor Positioning
## 5 Experimental Results
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Position**} & \multicolumn{6}{c}{\(z_{1}\)} & \multicolumn{6}{c}{\(z_{2}\)} \\ \cline{2-13}  & \multicolumn{3}{c}{**Mean Error (m)**} & \multicolumn{3}{c}{**Std Deviation (m)**} & \multicolumn{3}{c}{**Mean Error (m)**} & \multicolumn{3}{c}{**Std Deviation (m)**} \\ \cline{2-13}  & \(x\) & \(y\) & \(z\) & \(x\) & \(y\) & \(z\) & \(x\) & \(y\) & \(z\) & \(x\) & \(y\) & \(z\) \\ \hline P1 & 0.143 & 0.076 & 0.060 & 0.067 & 0.062 & 0.038 & 0.061 & 0.009 & 0.037 & 0.006 & 0.004 & 0.006 \\ P2 & 0.135 & 0.104 & 0.176 & 0.080 & 0.071 & 0.151 & 0.074 & 0.062 & 0.027 & 0.008 & 0.009 & 0.007 \\ P3 & 0.121 & 0.168 & 0.111 & 0.119 & 0.097 & 0.079 & 0.087 & 0.090 & 0.147 & 0.010 & 0.010 & 0.008 \\ P4 & 0.140 & 0.197 & 0.157 & 0.100 & 0.136 & 0.112 & 0.108 & 0.015 & 0.153 & 0.006 & 0.008 & 0.010 \\ P5 & 0.129 & 0.204 & 0.155 & 0.076 & 0.101 & 0.103 & 0.156 & 0.156 & 0.095 & 0.012 & 0.009 & 0.007 \\ P6 & 0.102 & 0.337 & 0.135 & 0.092 & 0.142 & 0.117 & 0.105 & 0.098 & 0.105 & 0.009 & 0.011 & 0.012 \\ P7 & 0.225 & 0.397 & 0.097 & 0.109 & 0.148 & 0.066 & 0.110 & 0.114 & 0.110 & 0.008 & 0.007 & 0.010 \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Mean errors and standard deviations for three ULPSs and a single EKF (\(\sigma_{w}\) = 0.2 m). error for the grid of positions is less than 0.3 m at \(z_{1}\) and about 0.15 m at \(z_{2}\). In addition, this method is capable of providing a valid estimate in all the realizations, thus implying high availability. A key comparison can be made with the results in Table 9, for the scenario when the ULPS are working independently. It is possible to observe that errors in Tables 10-12 are considerably reduced by merging the measurements from the three ULPS. The height \(z_{1}\) leads to higher errors, where each point P1-P7 is particularly complicated for a different independent ULPS, according to their position. On the other hand, the approaches based on measurement fusion allow these restrictions to be compensated, thus yielding more than four times smaller errors. With regard to previous works dealing with the design of ultrasonic positioning systems, a proposal based on a single ULPS was described in [18] for 2D positioning, with errors below 20 cm in 90% of the cases for a grid of points on the ground with a size of 4 \(\times\) 4 m\({}^{2}\). After the fusion process proposed here, errors were also below 20 cm for 90% of the cases involving the EFK approach (tightly coupled), but considering a 3D positioning, which was already a significant improvement. In [27], the ultrasonic measurements were merged with those coming from inertial measurement units (IMU), as well as with graphs defined and matched by maps from the navigation environments. In this case, the ultrasonic system was only used to correct the accumulative errors from the inertial sensors, applied to the guidance and monitoring of people in indoor environments. Another 3D positioning system based on ultrasound was presented in [3], where mean errors below 1 cm were reported. Nevertheless, it is worth noting that that proposal applied a sequential polling for every beacon, as well as a different ultrasonic signal processing approach with a higher computational load than the one described here. Finally, in [38], average errors in 3D ultrasonic positioning around 9.5 cm were reported, which was in the same range as the ones presented in Tables 7 and 12 for the EKF approach.