## 3 Experiments and Results
### Verification of the UWB/IMU/Encoder Fusion Position Estimation
#### 3.2.2 Verification of the Proposed Direction Angle Estimation Algorithm  
Since the single UWB sensor-based direction angle estimation algorithm proposed in this study shows strong errors due to data distortion from obstacles and radio wave reception strength, a method of supplementing it using a complementary filter on the yaw-axis direction data of the IMU sensor was proposed. As shown in Figure 8, an experiment was conducted to measure the direction data through in-place rotation from 90\({}^{\circ}\) to -90\({}^{\circ}\). The in-place rotation was rotated by 3\({}^{\circ}\) per second, and the experiment confirmed that the weight \(\beta=0.03\) in Equation (6), a complementary filter formula, was ideal, and the data were updated every 15 Hz cycle. For quantitative comparison of the experiment, the measurement was performed by mounting a camera at the bottom of the wheelchair scaffold and comparing it with the reference position drawn every 30\({}^{\circ}\). The graph of the angle estimation experiment results is shown in Figure 12, and through this, it is possible to confirm that the direction angle algorithm fused with the UWB/IMU sensors is closer to the actual value after applying a complementary filter than the direction angle estimated only with the UWB sensor. Table 2 shows the comparison before and after the  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & & \multicolumn{3}{c}{**Raw Data**} & \multicolumn{3}{c}{**Filtered Data**} \\ \hline  & **MAX** & **MIN** & **PP** & **SD** & **MAX** & **MIN** & **PP** & **SD** \\ \hline
1 m & 1.28 & 0.90 & 0.38 & 0.044 & 1.07 & 0.96 & 0.11 & 0.015 \\
2 m & 2.28 & 1.96 & 0.32 & 0.032 & 2.07 & 2.02 & 0.04 & 0.007 \\
3 m & 3.31 & 3.01 & 0.30 & 0.029 & 3.09 & 3.04 & 0.04 & 0.006 \\
4 m & 4.30 & 3.95 & 0.34 & 0.033 & 4.07 & 4.02 & 0.05 & 0.008 \\
5 m & 5.340 & 4.92 & 0.41 & 0.041 & 5.08 & 4.99 & 0.08 & 0.015 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Comparison of data before and after pre-processing.  
Figure 11: Comparison data before and after UWB data pre-processing. (**a**) 1 m distance measurement graph; (**b**) 2 m distance measurement graph; (**c**) 3 m distance measurement graph; (**d**) 4 m distance measurement graph; (**e**) 5 m distance measurement graph.  
complementary filter is applied, and in the case of direction estimation based on a single UWB sensor, an average error of 6.18\({}^{\circ}\) and an error of up to 28.37\({}^{\circ}\) were verified, and an average error of up to 15.30\({}^{\circ}\) was confirmed through the UWB/IMU sensor-based fusion. It was verified that this showed an error of about 18% less than the direction estimation through only a single UWB sensor, and the maximum error decreased by 53%. It verified that the proposed complementary filter-based sensor fusion direction estimation algorithm showed less error than the single UWB sensor-based direction estimation and confirmed that the driving assistance system could be determined as a designable level because it was updated in real time.  
and maximum errors was possible compared to the value estimated only with the UWB sensor. In the case of the sensor fusion position estimation using EKF, it was confirmed that it was possible to estimate the position stably compared to the existing raw UWB sensor data, and there was no drift error, unlike the position estimated based on the encoder sensor. Therefore, the position and direction estimation system proposed in this study verified that the position estimation algorithm proposed by improving the shortcomings and accuracy of a single UWB sensor showed a level of accuracy capable of implementing an active driving assistance system.