# Statistical Multipath Model Based on Experimental GNSS Data in Static Urban Canyon Environment
## 3 Description of the Research Campaign  
We chose Lujiazui, Shanghai, which is one of the most populated skyscraper areas in China, as the target urban canyon environment to study. This experiment area is located around 31 deg14'19.09'' N, 121 deg29'58.77'' E and covers approximately 1.7 square kilometers. We divided this area into 16 even cells, each of which covered approximately 0.1 square kilometers. On-field data collection occurred 26 times, all of which were marked on the Google map shown in Figure 4. Each cell area had an average of 1.6 spots of on-field data collection. For each on-field collection activity, more than 30 min of raw IF data for both GPS L1 and BDS B1 signals were recorded. All of these data were processed by the software receiver. More than 20,000 multipath signals were found from both constellations, which was large enough to build statistical models. The detailed number is shown in the Appendix A.  
Among all the multipath detected, it was necessary to design a principle to separate different types of multipath signals before conducting a statistical analysis. We used two different sets of separation criteria for the GEO and non-geosynchronous orbit (NGEO) satellites because their motion status and multipath characteristics differed.  
Figure 5 shows the raw multipath characteristic parameters of both GEO and NGEO signal. The top three panels are the GEO characteristics derived from the BDS PRN4 satellite, and the bottom three panels are the NGEO characteristics derived from the GPS PRN2 satellite. Referring to (1), each subplot gives a multipath delay \(\tau_{k}\), power attenuation \(20\log\alpha_{k}\), and carrier phase difference \(\Phi_{k}(t)\) separately. The multipath fading frequency \(d\Phi_{k}(t)/dt\) is the gradient of the carrier phase difference. It can be found that the characteristics of these two orbit satellites have significant differences.  
The principle of separating a multipath signal refers to time delay, power attenuation, and fading frequency simultaneously. First, the multipath is segmented into different sections when any characteristic changed significantly, so many sections are obtained for the whole period. Then, some sections are combined and considered one multipath if the mean value of all three parameters is similar. The multipath characteristics of the NGEO satellite fluctuate more heavily than the GEO multipath, so the methods of separating the multipath are slightly different between GEO and NGEO satellites. The boundary parameters of segmenting and combining sections are shown as follows,  
1. The difference of code delay is larger than 0.1 chip;
2. The difference of power attenuation is larger than 3 dB;
3. The difference of multipath fading frequency is larger than 1 \(\times\) 10\({}^{-4}\) Hz (for GEO)/1 \(\times\) 10\({}^{-2}\) Hz (for NGEO).
4. The interruption time is more than 1 min (only for NGEO).  
In Figure 5, four multipath signals are detected for the GEO satellite, and both multipath 1 and multipath 2 contain two sections. The two sections are combined into one multipath because all of the  
Figure 4: Satellite imagery of navigation signal collection spots and collecting live photos.  
characteristic parameters of the two sections are similar. However, for the NGEO satellite, multipath \(i\) and multipath \(j\) are considered two multipath signals, even though all of their feature parameters are similar.  
In addition, if only non-line-of-sight (NLOS) signals can be received, this satellite signals will be excluded from the data set. For the NLOS signal, the pseudorange error is usually very large and the signal power is much lower. Thus, it can be easily detected by the signal power and residual value of pseudorange especially in the static case [24; 25].