# Investigation into the Effect of Atmospheric
## 3 Methodology of Investigation and Experimental Data Description  
Since the receiver clock offset of a GNSS receiver is not a constant, we cannot compare GNSS pseudorange and carrier-phase measurements collected in high and low PM periods directly. Moreover, relative positioning techniques cannot be used to detect the impact of particulate matter on GNSS signal propagation because the assumption of different residuals due to particulate matter in different atmospheric paths cannot be justified. An empirical method is used to investigate any impact of particulate matter on GNSS signal propagation, and the detail is described as follows. The empirical method is to compare the CNR data in the unit of dBHz in two consecutive sidereal days with similar and very different PM indices; it is called the CNR method, see below. Owing to the unique condition of repeatable satellite geometry in about one sidereal day at continuous static antennas, the same multipath errors repeat at the same sidereal time of the next day [13] and so as the CNR if there are no abnormal ionospheric and tropospheric activities such as ionospheric scintillation. The method of calculating sidereal days used in this paper can be found in [23]. Six GPS data sets collected at a GNSS reference station (with a Leica GR25 receiver and AT20 antenna) on the roof of the Science and Engineering Building (SEB) at the University of Nottingham Ningbo China (UNNC) are used in this investigation, and PM\({}_{10}\), PM\({}_{2.5}\) and Air Quality Index (AQI) data was collected at a national air quality monitoring station located at the Ningbo Wanli University, which is about 1.5 km from UNNC and the altitudes of the two stations are similar (about 20 m). Details of PM\({}_{10}\), PM\({}_{2.5}\), AQI indices and their conversion to concentration of pollutant in \(\mu\)g/m\({}^{3}\) can be found in [24]; for example, PM\({}_{2.5}\) AQI 50 = 12 \(\mu\)g/m\({}^{3}\), PM\({}_{2.5}\) AQI 200 = 150.4 \(\mu\)g/m\({}^{3}\), PM\({}_{2.5}\) AQI 300 = 250.4 \(\mu\)g/m\({}^{3}\), PM\({}_{10}\) AQI 50 = 54 \(\mu\)g/m\({}^{3}\), PM\({}_{10}\) AQI 200 = 354 \(\mu\)g/m\({}^{3}\), PM\({}_{10}\) AQI 300 = 424 \(\mu\)g/m\({}^{3}\). The UNNC GNSS reference stations on the roof are shown in Figure 3. Two selected data sets were collected in November 2014 and four data sets were collected in December 2015, the values of PM\({}_{10}\), PM\({}_{2.5}\) and AQI indices of the six data sets are shown in Tables 1-4. Periods of high (\(>\)200) and low (\(<\)50) PM indices are selected for this investigation, ratios of PM\({}_{10}\), PM\({}_{2.5}\) and AQI indices between the same time periods of the first day and second day are also shown in the tables. Data set 1 has great differences in PM\({}_{10}\), PM\({}_{2.5}\) and AQI indices between the two sidereal days (6-8 November 2014), and the ratios of the indices are in the range of about 3 to 12 as shown in the last three columns of Table 1. On the other hand, the differences in PM\({}_{10}\), PM\({}_{2.5}\) and AQI indices between the two sidereal days (7-9 November 2014) in Data set 2 are small, the ratios of the indices are in the range of about 0.6 to 1.8 (mainly around 1) as shown in the last three columns of Table 2. Data sets 3-5 are the data sets with large differences in PM\({}_{10}\), PM\({}_{2.5}\) and AQI indices in two sidereal days (15-17, 23-25, 23-24 in December 2015), the ratios are about 4 as shown in Tables 3-5. Data set 6 has small differences in PM\({}_{10}\), PM\({}_{2.5}\) and AQI indices in the two sidereal days in 27-29 December 2015, and the ratios are close to 1 as shown in Table 6. If there is an impact of particulate matter and its concentration on GNSS signal propagation such as refraction, the CNR should be different when the ratios of PM\({}_{10}\), PM\({}_{2.5}\) and AQI indices in two sidereal days are large. Data sets (i.e., Data sets 2 and 6) with low ratios (\(\sim\)1) of PM\({}_{10}\), PM\({}_{2.5}\) and AQI indices in two sidereal days are used to show the nominal differences in CNR.