# Real-Time Indoor Positioning Approach Using iBeacons and Smartphone Sensors
## 5 Discussions  
In this paper, we focus on the accuracy of real-time positioning, especially for the cases with sharp turns. The accuracy of location estimate of our trilateration method is bound to fluctuating RSS values. Figure 15 presents the RSSI distribution of two BLE beacons at the same location. The most-frequent RSSI of the two beacons are \(-71\) dBm, but the absolute difference between RSS values can exceed 10 dBm (e.g., \(-84\) dBm). Supposing the most-frequent RSSI relates to the distance \(\bar{d}\), and the error can  
Figure 14: Trajectory of Route 2 when the heading was randomly swayed. (**a**) PDR locations; (**b**) PDR locations after orientation filtering; and (**c**) the path derived from the fusion workflow. \begin{table}
\begin{tabular}{l c c c c c} \hline \hline \multirow{2}{*}{**Case**} & \multirow{2}{*}{**RMSE XY (m)**} & \multirow{2}{*}{**RMSE X (m)**} & \multirow{2}{*}{**RMSE Y (m)**} & \multicolumn{1}{c}{**Mean**} & \multicolumn{1}{c}{**Mean**} \\  & & & & & **Error X (m)** & **Error Y (m)** \\ \hline Route 1 – inaccurate start & 2.39 & 2.27 & 0.77 & 1.82 & 0.64 \\ Route 1 – disturbed orientation & 3.48 & 3.34 & 0.98 & 2.58 & 0.80 \\ Route 2 – inaccurate start & 2.22 & 2.13 & 0.60 & 1.71 & 0.48 \\ Route 2 – disturbed orientation & 3.66 & 3.54 & 0.92 & 2.74 & 0.70 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Positioning accuracy of the four cases of Routes 1 and 2.  
exceed 20 m when \(\widetilde{d}\) reaches 10 m (see Equation (5)), this ranging error has to be alleviated for indoor positioning. Our solution is to fuse the trilateration result with RSSI fingerprints to compensate this error, which leads us to compute BLE-based locations in a relatively high accuracy. To prevent location estimates 'jump' dramatically, we average the RSSI values in each interval (e.g., 1 s) and run the trilateration algorithm iteratively (Equations (7) and (8)) to get reasonable estimates. The fusion of trilateration and fingerprinting effectively curbs the divergence of location error (see Equation (12)). The BLE-based method provides the baseline accuracy for the whole fusion positioning approach. According to a related study [12] comparing the positioning accuracy of iBeacons and WiFi APs, WiFi APs outperform iBeacons on fingerprinting positioning accuracy. This study has pointed out the accuracy of WiFi positioning is 5 m 90% of the time but that of iBeacon is 5 m less than 70% of the time (Figure 16a). We generated the cumulative distribution function (CDF) of our BLE-based positioning method (Figure 16b). It shows that the positioning accuracy can reach 4.50 m 90% of the time. This result indicates our BLE-based method boosts the positioning accuracy of iBeacon. This accuracy can be compared with that of WiFi positioning. We also provide CDF graphs for the four cases (Figure 4). The CDF values of 90% are listed in Table 4. In 90% of the time, the CDF of inaccurate initial position are 3.78 and 3.54 m, respectively. They are better than the BLE-based method (4.50 m) when the smartphone is held steadily. The error brought by an initial position can be promptly corrected, and the entire trajectory's accuracy is stable (see Figures 11c, 13c, and 17). The influence of the turns are limited as well. The accuracy of real-time tracking is competitive with the fingerprinting methods of iBeacon or WiFi APs in literature [11]. For the case of disturbed orientations, swaying the phone certainly enlarges the positioning error of PDR. Such errors have also been alleviated, and the RMSE of the both routes are 5.84 and 5.88 m, respectively (see Figure 17). The real-time tracking results are still not far away from the actual motions  
Figure 16: Comparison of CDF between a previous study and this paper: (**a**) CDF of positioning accuracy of iBeacons and WiFi APs [12]; and (**b**) CDF of our BLE-based method. Figure 15: RSSI Histogram of two BLE beacons: (**a**) Beacon ’AC:23:3F:20:8D:67’; and (**b**) Beacon ’AC:23:3F:20:8D:69’. (see Figures 12c and 14c).