# Statistical Multipath Model Based on Experimental GNSS Data in Static Urban Canyon Environment
## 4 Statistical Model Analysis
### Model Comparison  
To give deeper insight into the statistical models developed in this paper, we compared our models with the models developed by the DLR group. The DLR group studied multipath models in several types of carriers and environments, and we chose the one obtained from the urban environment for comparison. The left three plots of Figure 16 show the distribution of horizontal reflector coordinates, mean of power and echo Doppler of the DLR models cited from ITU-R P.2145-1 [13], and the right three plots are our corresponding distributions. It has to be mentioned that the reflector horizontal coordinates distribution instead of the multipath delay distribution is obtained in DLR model because of different experiment instruments used in their research. The \(X\) and \(Y\) coordinates are the horizontal position of reflection points with respect to the receiver. Although longer distance from reflector to receiver does not necessarily produce larger multipath delay, it has large possibility that further reflector corresponds to large delay. Thus, it is reasonable to compare the overall trend of these two distributions. To compare the models in only one dimension for the time delay and mean power, we choose the DLR model with the coordinate interval \((x=0,\ y>0)\) which are shown in the white rectangular box. The middle three plots are the rectangular part of origin models which are zoomed in.  
We present the delay distribution and the power attenuation distribution from our research in a thermodynamic chart (shown in the right three plots of Figure 16) to compare the two sets of models in the same perspective. Since both the delay and the power attenuation have a one-dimensional distribution in our model, only the \(Y\) axis has physical meanings that corresponded to the delays, and the \(X\) axis do not contain any information about the distribution. The distributions are supposed to form a line in the two-dimensional thermodynamic charts. In order to make thermodynamic charts more readable, we use strips to replace the supposed lines.  
According to the time delay models (top three plots), the possibility of very short delays (or very near reflectors) from the antenna is quite low (dark blue shown in the charts). Then, the possibility increases as the delay increases (or the distance of reflector increases), but after a certain peak, the possibility decreases as the delay increased further. It can be seen that this trend occurs to the models of both the DLR and this paper. When we look at the power attenuation distribution (middle three plots), it can be found that both the models of the DLR and this paper follows decreasing trend as the delay increase. For fading frequency model (bottom three plots), since the DLR models  
Figure 16: Comparison between our models and the German Aerospace Center (DLR) models for the characteristics of time delay, mean power and fading frequency.  
are developed based on a moving carrier but the models in this paper focused on the static platform, the Doppler (or the multipath fading) distributions cannot be compared. However, we still determine that both models regarding the multipath Doppler are symmetrical around the zero axis.  
Overall, although the raw data are collected in different types of environment and different cities, the multipath delay and power attenuation derived in this paper are consistent with the distribution trend found by other research groups. Thus, in other types of environment, it can be believed that the distribution functions are also suitable for the multipath characteristics, but different parameters are needed.