# Evaluation of Multi-Sensor Fusion Methods for Ultrasonic Indoor Positioning
Furthermore, a 3D positioning system presented in [16] was composed of a single mobile emitter and a set of six fixed and coplanar receivers at known positions; it proposed a linear ultrasonic chirp and the phase correlation approach to calculate the corresponding TOAs, additionally with a spherical trilateration technique to obtain the estimated positions. The LOCATE-US positioning system developed by the GEINTRA group from the University of Alcala presents suitable accuracy in the centimetre range [17,18]. For 3D positioning systems, a sensor network is utilized, based on several beacon units installed in particular orientations to cover as much of the environment as possible and achieve homogeneous ultrasonic coverage, which is a key parameter for stable accuracy. The final position estimates are obtained by fusing data from the available beacon units at each time point. That is why several fusion methods have been studied and applied (e.g., maximum likelihood estimation MLE [19]), with the goal of achieving suitable accuracy over time in all the covered volume. In general terms, the accuracy of ultrasonic systems in 3D positioning is in the centimetre and decimetre ranges even for large coverage areas. When the results obtained from a single unit or arrangement of beacons are poor (bad results in one particular coordinate or too many outliers), and several units are present in the environment, a fusion of data coming from the different deployed beacons can be applied. Its purpose is to merge complementary information accessible from different sensors to generate a more accurate result [20,21]. There are fusion techniques for all abstraction levels of sensor data, which depend on the desired application and resources [22,23]. This work proposes the use of fusion methods to merge position estimates coming from different beacons existing in the environment. In order to achieve a large coverage volume with enough accuracy in the three coordinates, several ultrasonic LPSs are deployed on different planes. This fact implies that several TDOA measurements or position estimates can be obtained for a single receiver's position, being necessary to merge all of them in an efficient way to obtain suitable accuracy. In this way, the main contribution of this work is in applying and evaluating tightly and loosely coupled methods for that purpose, not only in simulations, but also in experimental tests. A linear Kalman filter (LKF) and an adaptive Kalman filter (AKF) are considered as loosely coupled methods, whereas an extended Kalman filter (EKF) is the alternative as a tightly coupled method. The rest of the manuscript is organized as follows. Section 2 provides an overview of the proposed 3D ultrasonic positioning system, with a general description of the ultrasonic emitters and their 3D configuration, the ultrasonic receiver, and the low-level processing of the positioning algorithm. Section 3 presents the proposed fusion methods, thus including the loosely coupled approach applying the LKF and the AKF, and the tightly coupled approach using the EKF. Simulations and experimental results are detailed in Sections 4 and 5, respectively. Finally, conclusions are presented in Section 6.