# GNSS Multipath Detection Using Continuous Time-Series C/N0
## 3 Proposed Strong Multipath Detection Using C/N\({}_{0}\) Information
### Method to Determine the Threshold and Period  
We explain how to set both the threshold and period properly. Regarding the threshold, we consider that the elevation-dependent C/N\({}_{0}\) for each GNSS obtained in the open sky conditions is suitable because C/N\({}_{0}\) generally changes according to the elevation angle. For most GNSS satellites, the C/N\({}_{0}\) is low at a low elevation angle and high at a medium or high elevation angle. The difference between the lowest and highest C/N\({}_{0}\) for each GNSS is more than 10 dB-Hz, except for the case of the geostationary satellite (GEO). Figure 8 presents the test results of C/N\({}_{0}\) for GPS L1-C/A according to the elevation angle obtained for 24 h in the open sky condition. The receiver used in this test was the u-blox F9P, as in the test described in Section 2.1. The mask angle for the elevation was set to 15\({}^{\circ}\). All observed C/N\({}_{0}\) values are indicated by black plots. The average C/N\({}_{0}\) depending on the elevation angle is depicted by the gray line. The minimum C/N\({}_{0}\) obtained in this test was 32 dB-Hz when the elevation angle was less than 20\({}^{\circ}\). The maximum C/N\({}_{0}\) obtained was 50 dB-Hz when the elevation angle was more than 50\({}^{\circ}\). The gray line indicates the average signal strength according to the elevation angle for GPS L1-C/A. If C/N\({}_{0}\) of the satellite decreased by more than approximately 10 dB-Hz from this average C/N\({}_{0}\), the satellites were clearly considered to exhibit diffraction or reflection received by the antenna based on the previous test results presented in Table 1. The black dotted line indicates our proposed threshold of C/N\({}_{0}\), which was set to 10 dB-Hz lower than the average C/N\({}_{0}\) depending on the elevation angle. Figure 8 depicts the case of GPS L1-C/A. We prepared each threshold for the other GNSS in the same manner. The method of deciding the suitable threshold is discussed as follows. As can be seen in Figure 8, if we set 5-6 dB-Hz below from the average line, we might remove a favorable satellite by mistake although it has a very small multipath error within 1 m, which should not be done. This is based on measurement but can be applied in any case. Conversely, if we set 14-15 dB-Hz below from the average line, we sometimes cannot detect the NLOS signal under challenging areas. Considering at the temporal C/N\({}_{0}\) of GPS 22 and GLONASS 02 shown in Figure 5, we cannot detect these satellites of NLOS for a long time. Although this fact is based on the measurement, this threshold of 14-15 dB-Hz is not suitable for our proposed method. Therefore, we set the threshold from approximately 6-14 dB-Hz. Even with the empirical data, we can decide the range of the threshold although we cannot decide the best threshold. In addition, regarding the several types of GNSS receivers, we investigated the consistency of C/N\({}_{0}\) under open sky conditions using 24-h data, and the difference between receivers was very small within 1-2 dB-Hz as long as we used the antenna and cable recommended by manufacturers. Furthermore, we showed the test results at three different locations showing how the threshold choice influences the test results in Section 5. For the setting of the period that should not be used for positioning, we investigated all satellites with large pseudo-range errors, as indicated in Table 1. In particular, satellites with pseudo-range errors over 15 m in the 90 th percentile of all errors were selected for investigation. If the C/N\({}_{0}\) was continuously over the threshold determined above, we counted the number of seconds. Table 2 summarizes the longest period, second longest period, and third longest period for each selected satellite. It also includes information regarding the 90 th percentile of all errors and the percentage of this time to the total time that C/N\({}_{0}\) was more than 40 dB-Hz. For Galileo 31, the pseudo-range error was small for most of the time over 80% of the total.