## 5 Experimental Results and Discussion
### Deep Urban Canyon  
Figure 12 shows the dynamic pedestrian positioning results of the proposed 3D map method in the deep canyon. As can be seen in Figure 12, it is difficult to understand the trajectory of the pedestrian using the 3D map method (yellow dots). The 3D map method even gives a result with the wrong side of the street at many points. After applying the RAIM FDE, the positioning results of the 3D map method became much closer to the ground truth. Table 4 lists the lateral positioning performance of the conventional and 3D map methods. Both the conventional methods cannot provide accurate positioning service. It is interesting to note the WLS using only LOS has low availability because of the insufficient number of LOS satellites. Comparing the 3D map method before and after applying the RAIM FDE, there are about 4.9 and 2.1 m of improvements in terms of positioning mean error and standard deviation, respectively. Figure 12 shows that the positioning results before applying RAIM have about 12 m of lateral positioning error at point 272,748. After applying the RAIM, the positioning error is reduced to about 2 m. The improvements are due to the exclusion of the double reflected NLOS and strong multipath effects, as previous demonstrated in Figures 8 and 10. The availability is also increased after applying the RAIM. Point 272,697 in Figure 12 is an example of the increase of the availability. The particle weighting distribution of the point 272,697 is shown in Figure 13.  
Figure 12: Results of the proposed 3D map positioning method before and after using the RAIM satellite selection method in the deep urban canyon. As can be seen in Figure 13a, there are no valid particles before applying the RAIM. The reason is the 3D map method cannot find a single reflected NLOS transmission length that is similar to that of the multiple reflected NLOS. If the NLOS satellite is excluded, the weighting of the particle is shown in Figure 13b. As a result, the positioning result becomes close to the ground truth. In Tables 3 and 4, we can see that the proposed RAIM abnormal satellite exclusion method can reduce lateral positioning error greatly in both middle and deep urban canyons. Histogram Study of the Lateral Positioning Error of the Proposed 3D Building Model Based Positioning Method  
This subsection focuses on the statistical comparison of the proposed 3D map method before and after using the RAIM satellite selection technique. The GNSS positioning solution is large in lateral direction, especially in urban canyon environments. It is essential to study the histogram of the lateral positioning error. This paper defines the bins of the histogram as the percentage of the road width, as shown in Figure 14. The experiments are conducted in both middle and deep urban canyon. The road widths of the experimental place are about 20 m. As can be seen, if the lateral positioning error is larger than 50% of the road width, namely larger than 10 m, the pedestrian is estimated on the wrong side of the road. The point with positioning error less than 3 m are classified as accurate solutions. In this experiment, the \begin{table}
\begin{tabular}{c c c c} \hline
**Methods** & **Mean (m)** & **Std (m)** & **Availability** \\ \hline Conventional positioning method (WLS) & 23.99 & 20.10 & 55.02\% \\ WLS using only LOS & 13.21 & 20.32 & 10.58\% \\
3D map method & 8.78 & 5.62 & 73.68\% \\
3D map method with RAIM FDE & 3.85 & 3.56 & 83.16\% \\ \hline \end{tabular}
\end{table} 
Table 4: Lateral positioning performance of the conventional method and the proposed 3D map method before and after using the RAIM method in the deep urban canyon. Figure 13: Weighting of all the particles of point 272,697 before (**a**) and after RAIM (**b**). pedestrian walks the street back and forth. The trajectory is as the red line in Figure 14. The lengths of the data used are about 20 min, which contains about 1200 epochs. The results in the middle and deep urban canyon are shown in Figures 15 and 16, respectively.