# A Real-Time BLE/PDR Integrated System by Using an Improved Robust Filter for Indoor Position
## 4 Experiments and Analysis
### BLE/PDR Integrated System Position Experiment  
The BLE/PDR integrated system position experiment was carried out in the C7 test site. The BLE AP routers and the smartphone used in the experiment are the same as in the experiment of Section 3.1. The new trajectory was planned and was shown in Figure 13.  
In Figure 13, the red star and blue cycle refer to the start point endpoint of the trajectory, respectively. The green dotted line represents the reference trajectory and the arrow represents the direction. During the experiment, the data sampling frequency of  
Figure 12: Comparison of Motion state and heading estimation. Figure 13: The trajectory of BLE/PDR integrated system position experiments in the C7 test site. PDR was set as 50 Hz and the smartphone scanned the BLE APs per second. The pedestrian started from the start point and reached the endpoint at a constant speed. The pedestrian held the smartphone level and walked 107 steps in total during the experiment. Another integrated system position experiment was conducted at the 331 test site. The comparison results of the different methods were shown in Figure 16.  
To validate the efficiency of the robust filter method, another two methods, the BLE fingerprint method and the EKF method, were also utilized for the experiment. Position errors of the three methods were computed concerning the reference points for evaluation. Figure 14a showed the time series of the position errors and (b) showed the corresponding cumulative distribution errors. In the above figure, the blue line refers to the BLE fingerprint method. The red line and green line represent the EKF and robust filter methods, respectively. From the value and distribution of the position error, the robust filter method denoted by the green line performs best. The cumulative distribution of the robust filter indicates that it has a higher confidence level than the other two methods. About 74% of the position error of points are lower than 1 m and about 86% of the position error of points are lower than 2 m. Compared with the common EKF, these two indicators are increased by 38% and 18%, respectively. Then, Table 2 shows the detail of the mean error and RMSE of the three methods. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Method** & **Min** & **Max** & **Mean** & **RMSE** \\ \hline BLE fingerprint method & 0.165 & 13.033 & 2.647 & 2.727 \\ Extend Kalman filter method & 0 & 7.122 & 1.960 & 1.727 \\ Robust filter base on EKF & 0 & 2.641 & 0.844 & 0.745 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Position error comparison/(m). Figure 14: Comparison of Position errors and cumulative errors of three methods. (**a**) Time series of position errors, (**b**) cumulative errors of three methods. As shown in Table 2. The mean position accuracy and the RMSE of the robust filter method are 0.844 m and 0.745 m respectively. Comparing with the EKF and BLE fingerprint methods, the position accuracies were reduced by 1.116 m and 1.803 m, and the RMSEs were decreased by 1.982 m and 0.982 m. From the perspective of max value, the max value of the robust filter is 2.641 m which is also significantly reduced. The figure and table mentioned above show that the proposed robust filter can not only reduce the position error but also improve the stability. Figure 15 shows the  
Figure 15: _Cont._  
The blue line, red line, green line, and dark green line represent the trajectory of BLE fingerprint, EKF, robust filter methods, and reference trajectory, respectively. In Figure 15a, some jump points, which mean the gross error surrounded by the red circle, appear in the BLE fingerprint method or the EKF method. The robust filter can improve the observation matrix based on detecting the gross errors and get a smooth trajectory without jump points. We can see that the proposed robust filter performs better than the other two methods in (b). (c) and (d) are the results of different hybrid positioning methods under two trajectories.