# Real-Time Indoor Positioning Based on BLE Beacons and Pedestrian Dead Reckoning for Smartphones
## 4 Performance Evaluation
### Experimental Results
#### 4.2.2 Performance of Different Methods  
Figure 7 displays the trajectories obtained in the corridor of a campus building with different positioning methods. It can be seen that the volunteer walks along a right-angle corridor at a uniform speed. Figure 8 shows the average errors of these methods. In the following, we make a detailed analysis of these methods. 1. For pure PDR positioning, the error is mainly caused by inaccurate measurement of the heading angle and also by inaccurate step length estimation. Analyzed from the source, the error comes from the measurement errors of the magnetometer, the accelerometer, and the gyroscope, which is inevitable. Since the position of the current point is derived from the position of the previous one, a high correlation appears between adjacent points, and thus the error gradually accumulates over a period of time. For example, in Figure 7, the trajectory obtained with PDR positioning after the bend deviates from the ground truth farther and farther away. As shown in Figure 8, the average error increases from 0.5 m at the start to 2.2 m at the end. Therefore, it is concluded that PDR cannot be independently and continuously used for long-term indoor positioning unless supplementary means are adopted to reduce the cumulative error. 2. The performance of BLE-based positioning is unstable due to the influence of the environment. As shown in Figure 8, the average error obtained with BLE-based positioning is larger than that obtained by PDR in the first part of the trajectory, but the average error of PDR positioning becomes larger in the second part. Compared with PDR positioning, the advantage is that the error is not accumulating over time. It is consequently a good complement to PDR positioning. 3. The average error of our proposed fused positioning method is the smallest among all the methods. As shown in Figure 8, the average error is not as cumulative as with PDR, and the fluctuation is smaller than that of the BLE-positioning. It is also observed that the positioning errors are large at the start of the positioning process. This is because the initial positions of the particles are randomly generated and dependent on the results from BLE-based positioning. With the increase in the number of iterations and resampling steps, the particles' positions gradually converge, and the accuracy gradually improves. Figure 6: The estimated heading direction and the ground truth. Table 1 lists the maximum, minimum, and average errors of different methods. It is observed that our proposed fused positioning method has the smallest average error of 1.35 m, which is a reduction of 24.16% compared with PDR positioning and 10.60% compared with BLE-based positioning. Although PDR positioning has the smallest minimum error, its maximum error is the largest. These positioning results demonstrate that our proposed fused method can effectively improve the accuracy of indoor positioning. Figure 9 shows the cumulative distribution function (CDF) of the positioning errors with different methods. It is observed that for our proposed fused positioning method, about 95% of the positioning errors are smaller than 1.7 m, while the probability is 80% \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Positioning Methods** & **Maximum Error (m)** & **Minimum Error (m)** & **Average Error (m)** \\ \hline PDR positioning & 2.17 & 0.39 & 1.78 \\ BLE-based positioning & 2.05 & 0.7 & 1.51 \\ Fused positioning & 1.87 & 0.51 & 1.35 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Positioning errors of different methods. Figure 8: The average positioning errors of different methods. Figure 7: The trajectories obtained by different positioning methods and the ground truth. and 65% for PDR and BLE-based positioning, respectively. It is worth noting that PDR positioning has a higher confidence level with an error smaller than 1.2 m. However, due to the cumulative error, it cannot maintain the advantage and has a higher probability of incurring large errors.