# Evaluation of Multi-Sensor Fusion Methods for Ultrasonic Indoor Positioning
## 6 Conclusions  
This work presented a 3D ultrasonic positioning system, as well as developed positioning and fusion algorithms. This structure is composed of three ULPSs installed in three perpendicular walls with the aim of covering almost the whole space of a common room shape. Moreover, a 3D ultrasonic receiver prototype is used to acquire signals coming from different directions. Then, several fusion algorithms were tested based on two different approaches: the loosely coupled and tightly coupled one. Taking into account that two heights were studied for all considered algorithms, the height \(z_{2}\) had more accurate positions due to its specific location with respect to the three ULPSs, especially for ULPS-2 and ULPS-3 (the same height). Additionally, the tightly coupled approach presented lower errors in general terms at both heights \(z_{1}\) and \(z_{2}\). However, the AKF fusion also provided good accuracy for the loosely coupled approach at \(z_{2}\). Generally, the positioning error was in the decimetre range for the different studied configurations, which makes the proposal suitable for numerous indoor positioning applications, such as logistics in warehouses, tourist guidance in museums and historical buildings, or accurate positioning in independent living settings for the elderly.  
A last aspect to consider is the scalability of the proposal. The aforementioned LOCATE-US system can be extended to larger environments by suitably distributing the ULPSs to cover the desired area, or by increasing the number of installed ULPSs.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**CDF Error (m)**} & \multicolumn{4}{c}{\(z_{1}\)} & \multicolumn{4}{c}{\(z_{2}\)} & \multirow{2}{*}{**\% of Positions**} \\ \cline{2-3} \cline{5-8}  & & **Min** & **Max** & **Mean** & **Min** & **Max** & **Mean** \\ \hline \multirow{2}{*}{Loosely coupled} & LKF & 0.48 & 0.76 & 0.68 & 0.16 & 0.283 & 0.211 & 90\% \\  & AKF & 0.221 & 0.574 & 0.354 & 0.116 & 0.227 & 0.157 & 90\% \\ \hline Tightly coupled & EKF & 0.182 & 0.46 & 0.302 & 0.105 & 0.301 & 0.151 & 100\% \\ \hline \hline \end{tabular}
\end{table}
Table 13: Summary of the CDF errors for 90% of the estimated positions and the availability of estimates at z\({}_{1}\) and z\({}_{2}\).  
Furthermore, the ultrasonic beacons in every ULPS can be separated to better fit the requirements of a given environment (note that in this case an infrared link is used to synchronize simultaneous emissions from all the beacons).  
Conceptualization, J.U., K.M. and A.H.; methodology, J.U. and J.M.V.; software, K.M.; validation and formal analysis, J.U., M.M. and K.M.; investigation, J.U., K.M., A.H. and T.A.; writing--original draft preparation, K.M.; writing--review and editing, A.H. and J.M.V.; supervision, J.U.; funding acquisition, J.U. and J.M.V. All authors have read and agreed to the published version of the manuscript.  
This work has been supported by the Spanish Ministry of Science, Innovation and Universities (MICROCEBUS project, ref. RTI2018-095168-BC51, and POM project, ref. PID2019-105470 RA-C33), the Community of Madrid (PUILPOS project, ref. CM/JIN/2019-038, and CODEUS project, ref. CM/JIN/2019-043).  
Not applicable.