## 4 Experimental Result of the Position Tracking System and Discussion
### Position Tracking Experiment in Anechoic Chamber  
For this experiment, four anchors were installed at a 5 m interval in the length, width, and height directions, as shown in Figure 8. The position was repeatedly measured by controlling the movement of tags in a cubical space, during which the tags were controlled by being installed on a triaxial Cartesian robot. The results of measuring the position of  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Reference Values**} & \multicolumn{3}{c}{**Reference 1**} & \multicolumn{3}{c}{**Reference 2**} & \multicolumn{3}{c}{**Reference 3**} & \multicolumn{3}{c}{**Reference 4**} \\ \cline{2-13}  & x & **y** & **z** & **x** & **y** & **z** & **x** & **y** & **z** & **x** & **Y** & **z** \\ \hline Ref. coordinates (mm) & 0 & 0 & 1800 & 0 & 5000 & 1800 & 5000 & 0 & 1800 & 5000 & 5000 & 1800 \\ Max. deviation & & & & & & & & & & & \\ measurement value (mm) & \(-\)43 & \(-\)58 & 1893 & 75 & 4943 & 1943 & 4947 & \(-\)62 & 1965 & 4948 & 4949 & 1624 \\ Measurement absolute error (mm) & 43 & 58 & 93 & 75 & 57 & 143 & 53 & 62 & 165 & 52 & 51 & 176 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Measurement error for an immovable target.  
Figure 7: Anechoic chamber test (a yellow circle represents a tag and red circles represent anchors).  
Therefore, a moving average (MA) filter, Kalman filter [7], and our extended Kalman filters (EXT) were applied to the positioning data for improving the accuracy of positioning coordinates. Specifically, the MA, Kalman filter, and extended Kalman filter were applied to the measurement data after placing the tag on the reference coordinate (2700, 2700) on the fixed z axis. The measurements were taken for approximately 380 times to obtain reliable data; the results are shown in Figure 10.  
The figure shows the results of applying the MA, Kalman filter [7], and our EKT to the measurement data of moving nodes in an indoor space where multiple anchors are installed, and it can be observed that the position measurement error is significantly reduced when both types of filters are applied. The statistical results of the 380 measurements, as shown in Figure 10, are presented in Table 4; From these results, we found that our ETK-based method had less errors of 7.6 mm and 13.3 mm on the x and y axes compared to the MA method and also had less errors of 4.2 mm and 7.8 mm on the x and y axes compared to the Kalman filter method [7]. According to the numerical data, the application of the extended Kalman filter produced a smaller positioning error, which also can be confirmed through the graphical data.  
### Position Tracking Experiment in Anechoic Chamber  
Lastly, an experiment was conducted to examine the positioning accuracy for a tool in the actual automobile assembly process at an automobile repair shop, which resembles the real automobile assembly site. The fixed anchors were installed on four posts of the lift, and the tags were attached to the tool to measure its moving path, as shown in Figure 11. For displaying the current position of the tool operating in an automobile model, an application was developed for operation monitoring to display the position of the tool, as shown in Figure 12.