## 5 Experimental Results and Discussion
### Middle Urban Canyon  
Figure 7 shows the dynamic pedestrian positioning results of the proposed 3D map in the middle canyon. The yellow and red dots indicate the position solutions of the 3D map method before and after using the RAIM satellite selection method, respectively. As can be seen in Figure 7, it is difficult to find which side of the street the pedestrian is walking on by the yellow dots at many different points. On the contrary, the red ball, the result of applying RAIM, is much closer to each side of the street. In the intersection, the reflection path is more complicated than that in the link. The 3D map method could sometimes estimate the incorrect NLOS reflection path, which resulted in inaccurate positioning result. The proposed RAIM method can also reduce this defect because the satellite that inconsistent between  
Figure 6: Constructed 3D building models in the middle and deep urban canyons. The cyan lines indicate the pedestrian walking trajectories in the dynamic experiments. pseudorange measurement and simulated pseudorange will be excluded. The statistic of Figure 7 is listed in Table 3. Comparing the two, the positioning error is about 3.97 and 2.96 m before and after using the RAIM, respectively. The improvement by RAIM not only can be found in terms of mean but also standard deviation. This improvement indicates the proposed RAIM makes the 3D map method more accurate and precise. The conventional positioning methods cannot achieve a similar performance even if it only uses the LOS satellite measurements. To demonstrate the performance improved by the RAIM, we select two typical points in this dynamic data, point 264,038 and 264,239. To observe the left side of Figure 7 (point 264,239), the positioning result before and after applying RAIM is very different. The red ball is much closer to the ground truth than yellow ball. The position solution of the 3D map method is calculated by:  
\[x=\frac{\sum_{i}\alpha^{(i)}P^{(i)}}{\sum_{i}\alpha^{(i)}} \tag{8}\]  
where \(x\) denotes the position estimated, \(\alpha\) denotes the weighting of a particle and \(P\) denotes the position of a particle. Hence, the weighting of the particles is very essential for the proposed method. Figure 8 \begin{table}
\begin{tabular}{c c c c} \hline
**Methods** & **Mean (m)** & **Std (m)** & **Availability** \\ \hline Conventional positioning method (WLS) & 24.28 & 28.61 & 97.23\% \\ WLS using only LOS & 12.57 & 13.38 & 53.36\% \\
3D map method & 3.97 & 3.97 & 100\% \\
3D map method with RAIM FDE & 2.96 & 2.44 & 100\% \\ \hline \end{tabular}
\end{table} 
Table 3: Lateral positioning performance of the conventional method and the proposed 3D map method before and after using the RAIM method in the middle urban canyon. Figure 7: Results of the proposed 3D map positioning method before and after using the RAIM satellite selection method in a middle urban canyon. shows the weighting of the particle of point 264,239 before and after applying the RAIM. It is obvious that the weighting of the particle behaviors are very different in Figure 8a,b. All of the particles in the left side of Figure 8a are invalid; on the contrary, most of particles in the left side of Figure 8b are valid. Figure 9a,b shows the skylpot and ray-tracing result of point 264,239, respectively. Before applying RAIM technique, the GPS PRN 11 is used in all the particles in the left side. Its simulated pseudorange is assumed to be the single reflection (green line in Figure 9b). However, its pseudorange measurement indicates it is a double reflected NLOS (red line in Figure 9b). Figure 8: Weighting of all the particles of the point 264,239 before (**a**) and after RAIM (**b**). The color of the particle indicates the weighting of each particle. Red and blue indicates the highest and lowest weighting, respectively. Figure 9: **(a)** Skyplot of point 264,239, and the dark grey color indicates the view blocked by surrounding buildings; **(b)** Ray-tracing result of point 264,239 based on the ground truth position.