## 3 3D Building Model Based Positioning Method  
The flowchart of the proposed 3D map-based pedestrian positioning method is shown in Figure 2.  
As shown in Figure 2, this method firstly implements a particle filter to distribute position candidates (particles) around the receiver estimated position, which is assumed to be within about 15 m of the ground truth. When a candidate position is given, the proposed method can evaluate whether each satellite is in LOS, multipath or NLOS, by applying the ray-tracing procedure with a 3D building model. According to the signal strength, namely carrier to noise ratio (C/N\({}_{0}\)), the satellite could be roughly classified into LOS, NLOS and multipath scenarios. The signal classification used in the proposed method is shown in Table 1[25]. The thresholds of the signal strength are set based on the empirical experience [25]. If the signal classifications are inconsistent between each other, the satellite will not be used for the candidate. If they are consistent, the simulated pseudorange of the satellite for the candidate will be calculated.  
Figure 2: Flowchart of the developed 3D building model based positioning method.  
In the LOS case, simulated pseudoranges can be estimated as the distance of the direct path between the satellite and the assumed position. In the multipath and NLOS cases, the simulated pseudoranges can be estimated as the distance of the reflected path between the satellite and the candidate position via the building surface. Ideally, if the position of a candidate is located at the true position, the difference between the simulated and measured pseudoranges should be zero. In other words, the simulated and measured pseudoranges should be identical. Therefore, the likelihood of each valid candidate is evaluated based on the pseudorange difference between the pseudorange measurement and the simulated pseudorange simulated by 3D building models and ray tracing. Finally, the expectation of all the candidates is the estimated positioning of the proposed map method. The proposed method is able to find the optimum position through a dedicated optimization algorithm of the above assumptions and evaluations. The detail algorithm of the particle filter using 3D city building models can be found in [23, 24, 25]. However, this particle filter still suffers from the effect of multiple reflected NLOS in the process of generating simulated pseudorange. In the developed method, a double reflected NLOS signal is devastating because of the assumption of single reflection. In a deep urban canyon environment, namely high buildings located on both sides of a street, the single reflection assumption is not always correct. If a double reflected NLOS is received, the developed method will estimate the user location at wrong side of street due to single reflection limit as shown in Figure 3. The candidates become invalid in the correct side of the street due to the incorrect assumption. As a result, the developed method will estimate a fault positioning solution.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Signal Strength (C/N\({}_{\textbf{0}}\))** & **Ray-Tracing** & **Valid Satellite Type** \\ \hline LOS (\(>\)40 dB-Hz) & LOS & LOS \\ \hline NLOS (\(<\)30 dB-Hz) & NLOS & NLOS \\ \hline LOS (\(>\)40 dB-Hz) & NLOS & Invalid \\ \hline NLOS (\(<\)30 dB-Hz) & LOS & Invalid \\ \hline Unknown (30 dB-Hz \(<\) C/N\({}_{0}\)\(<\) 40 dB-Hz) & LOS & Multipath (LOS if no reflection path is found) \\ \hline Unknown (30 dB-Hz \(<\) C/N\({}_{0}\)\(<\) 40 dB-Hz) & NLOS & NLOS \\ \hline \hline \end{tabular}
\end{table}
Table 1: Rule of signal classification for a candidate based on signal strength and ray-tracing [25].  
Figure 3: Illustration of the devastated effect caused by double reflected non-line-of-sight (NLOS).