# GNSS Multipath Detection Using Continuous Time-Series C/N0
## 2 Features of Measured C/N\({}_{0}\) in Dense Urban Areas
### Relationship Between Pseudo-Range Errors and C/N\({}_{0}\)  
This section demonstrates the relationship between the pseudo-range error and C/N\({}_{0}\) for all satellites with an elevation angle over 15\({}^{\circ}\). Based on the above method for estimating the pseudo-range error, we analyzed the 30 min of GNSS data used previously. The results are presented in Table 1. For each satellite vehicle (SV), the condition of satellite, the maximum pseudo-range error, 90 th percentile of the pseudo-range error, 10 th percentile of the pseudo-range error, percentage of this time to the total time that C/N\({}_{0}\) was less than 30 dB-Hz, percentage of this time to the total time that C/N\({}_{0}\) was less than 40 dB-Hz and more than 30 dB-Hz, and percentage of this time to the total time that C/N\({}_{0}\) was more than 40 dB-Hz are shown in Table 1. As for the condition of each satellite, when the percentage of the LOS condition was 90% or more for 30 min, the satellite was regarded as LOS. When the percentage of NLOS condition was 90% or more for 30 min, the satellite was regarded as NLOS. When the percentage of LOS or NLOS condition was less than 90% for 30 min, the satellite was regarded as partial. The analysis conditions for each satellite were as follows: the elevation mask angle was 15\({}^{\circ}\), and both the pseudo-range and carrier phase measurements had to be generated. The cycle slip and half-cycle validation for the carrier phase measurement were not checked. Note that not all satellites were constantly output for 30 min because the signals of certain satellites were completely blocked by buildings. Therefore, the sum of the percentages for C/N\({}_{0}\) was not always 100%. When calculating the maximum error and percentile, the error was converted into the absolute error. The error for QZSS 03 was quite small because QZSS 03 was used as the reference satellite for estimating the receiver clock error. Important clarifications regarding LOS or NLOS for each satellite were obtained using a 3D map and precise antenna position, as previously mentioned in Section 2.1. Figure 6: Summary and flow of pseudo-range error estimation. The pseudo-range error of GPS 22 was over 50 m in more than 90% of the 30 min. The percentage of this time to the total time that C/N\({}_{0}\) was more than 40 dB-Hz was higher than 67%. The percentage of this time to the total time that C/N\({}_{0}\) was more than 30 dB-Hz was 95%. Even if the signal of GPS 22 was clearly affected by the NLOS signal, the C/N\({}_{0}\) of GPS 22 was maintained at a sufficiently high level to track the carrier phase measurements, as illustrated in Figure 5. This indicates that it is very difficult to detect satellites affected by strong NLOS signals by using the normal C/N\({}_{0}\) threshold. We usually set the minimum threshold for C/N\({}_{0}\) at approximately 30 to 35 dB-Hz. Even if we set 40 dB-Hz as a threshold in this case, GPS 22 with a large pseudo-range error was included in the positioning for 67% of the total duration. This is exactly the case we need to consider to improve the accuracy in dense urban areas. Similar trends to GPS 22 as described above could be observed for other satellites, such as GPS 03, GPS 08, GPS 27, Galileo 21, and GLONASS 02. However, the pseudo-range error of GPS 01 was less than 5 m for 30 min. The percentage of this time to the total time that C/N\({}_{0}\) was more than 40 dB-Hz was 100%. Similar trends to GPS 01 as described above could be seen for other satellites, such as GPS 03, GPS 11, QZSS 02, QZSS 03, QZSS 07, Galileo 01, BDS 07, BDS 08, BDS 25, and GLONASS 15. We noticed that the C/N\({}_{0}\) of these satellites did not decrease by 30 dB-Hz and C/N\({}_{0}\) did not fluctuate substantially. The C/N\({}_{0}\) values of the satellites receiving LOS signals fluctuated occasionally because of the reception of the reflected signals, as indicated in Figure 1. In such cases, the correlator-based multipath mitigation technique is very powerful for reducing multipath errors, as described in Section 1[13; 14].