# GNSS Multipath Detection Using Continuous Time-Series C/N0
## 2 Features of Measured C/N\({}_{0}\) in Dense Urban Areas
### Estimation of Pseudo-Range Errors  
This section describes the method used to estimate the errors between the measured and predicted geometrical ranges. The estimated accurate errors were significant in evaluating whether our proposed method using C/N\({}_{0}\) was valid for detecting multipath-contaminated satellites. Pseudo-range measurements include error sources from the receiver clock, satellite clock, ephemeris, ionosphere, troposphere, and multipath + noise. In this study, the predicted geometrical range was already set as the distance between the accurate positions of the antenna and the satellite. All above error sources, with the exception of the receiver clock and multipath + noise, can be modeled within several meters in total. Hence, a method for estimating the receiver clock error was required. In challenging areas, receiver clock errors, which are similar to multipath errors, occasionally jump and deviate over tens of meters. When the receiver clock error is determined within several meters, each residual can be precisely predicted, and these residuals are almost equivalent to multipath errors. In this study, we could track a good signal from the Japanese QZSS even near high-rise buildings in Tokyo as at least one QZSS remained at a very high elevation angle over 80\({}^{\circ}\). In reality, the accuracy of the pseudo-range of the highest QZSS was within 1.0 m. The summary and flow of the above method are presented in Figure 6, including equations. Note that it is important to estimate the bias between the GPS and other satellite systems, which can be achieved at the base station.  
According to the flow presented in Figure 6, we estimated the receiver clock error using a satellite, which was the highest elevation. At this time, QZSS 03 was the satellite with the highest elevation. These estimated receiver clock errors were applied for the other satellites, thereby generating an estimate of the errors for each satellite within several meters. This connotes that, if satellites are selected within a certain threshold of these errors, the accuracy of the DGNSS will be improved from tens of meters to several meters. To confirm the accuracy of the above estimated errors, the accuracy of the DGNSS was evaluated at the same location, with 30 min of data analyzed. The base station is on the rooftop of our laboratory, and the baseline length is 2.6 km. As the accuracy of the deduced pseudo-range error was approximately several meters, the threshold for selecting the satellites was set to 10 m. If the estimated pseudo-range error for each satellite was more than 10 m, the satellite was not used for DGNSS. Therefore, the horizontal standard deviation of the DGNSS was 2.8 m, and  
Figure 5: Temporal C/N\({}_{0}\) mainly receiving non-line-of-sight (NLOS) signals.  
the average horizontal position was only 0.9 m when using the selected satellites. However, in the case of the normal DGNSS, the horizontal standard deviation was 16.7 m and the average horizontal position was 40.3 m without the information of the selected satellites. The above result indicates that the proposed residual estimation is clearly effective for distinguishing large multipath errors such as those of more than 10 m in dense urban areas.