# A Combined Elevation Angle and C/N0 Weighting Method for GNSS PPP on Xiaomi MI8 Smartphones
## 2 Correlation of CMN, Elevation Angle and C/N0  
To analyze the correlation of the CMN with the elevation angle and C/N0, a Xiaomi MI8 smartphone equipped with a BCM47755 GNSS chip and a linearly polarized antenna is used as the experimental device. The Xiaomi MI8 smartphone is the first-released dual-frequency Android smartphone. Figure 1 shows the GNSS observation on the roof of the Mining Building at Central South University, China on 15 November 2020. The smartphone application of GEO++ RINEX Logger 2.1.3 is used for the data collection [14]. The observation lasts about 5 h from GPS Time 9:00 to 14:00 with a sampling rate of 1 HZ. The Xiaomi MI8 smartphone can receive dual-frequency GPS L1/L5 signals and Galileo E1/E5a signals, as well as single-frequency GLONASS G1 and BDS B1 signals. Figure 1: Smartphone data collection in an open sky area on 15 November 2020. The CMN is a major error source on smartphones due to the built-in linear polarization antenna [3; 4]. The multipath effect at an epoch (\(M_{i}\)) can be estimated using the multipath combination below [15; 16]:  
\[M_{i}=P_{i}-\frac{f_{i}^{2}+f_{j}^{2}}{f_{i}^{2}-f_{j}^{2}}\varphi_{i}\lambda_{i }+\frac{2f_{j}^{2}}{f_{i}^{2}-f_{j}^{2}}\varphi_{j}\lambda_{j} \tag{1}\]  
where \(i\) and \(j\) (\(i\
eq j\)) denote two different frequencies. \(P\) is the pseudorange observation. \(\varphi\) is the carrier phase observation. \(\lambda\) is the wavelength at the corresponding frequency, \(f\). \(M_{i}\) contains multipath effect, code noise, ambiguity term and hardware delay biases. The latter two items are stable and thus can be obtained by calculating the mean value of \(M_{i}\) at a certain number of epochs free of cycle slips [17], which is denoted as \(\overline{M}_{i}\). Therefore, the CMN can be derived as:  
\[CMN_{i}=M_{i}-\overline{M}_{i} \tag{2}\]  
The correlation of the CMN to the satellite elevation angle and C/N0 was examined; Figure 2 shows the time series of the CMN, elevation angle and C/N0 for the GPS G26 and Galileo E27 satellites at both the L1/E1 and L5/E5a frequencies. In terms of the CMN amplitudes, the G26 satellite has a stronger CMN than the E27 satellite, and both satellites at the L1/E1 frequencies have a stronger CMN than the L5/E5a frequencies. These results are in line with the conclusions drawn by [3], which indicate that the Galileo satellites have a better CMN suppression ability than the GPS satellites and that the L5/E5a signals have a stronger CMN suppression ability than the L1/E1 signals. In addition, the CMN has a strong negative correlation with the C/N0 at both the L1/E1 and L5/E5a frequencies. When the CMN dramatically changes, the corresponding C/N0 vastly varies by over 10 dB-Hz. In contrast, the correlation with the elevation angle is relatively poor at the L1/E1 frequencies. In spite of this, their correlation is still obvious. When the elevation angle decreases, the CMN increases. However, at the L5/E5a frequencies, no obvious correlation is found between the CMN and the elevation angle, which might be caused by the irregular gain pattern of smartphones [18]. Figure 2: Time series of the code multipath and noise (CMN), carrier-to-noise ratio (C/N0) and elevation angle for G26 satellite at L1/L5 frequencies and E27 satellite at E1/E5a frequencies. In order to further analyze the correlation of the CMN to the satellite elevation angle and C/N0 at the L1/E1 frequencies, the CMN for all dual-frequency GPS and Galileo satellites is plotted against the elevation angle and the C/N0, respectively, as shown in Figure 3. A second-order polynomial fitting curve is also plotted to reflect the variation trend in panels (a) and (b). The fitting curves illustrate that the CMNs have a negative correlation with the elevation angle and the C/N0. Their correlation coefficients are \(-0.20\) and \(-0.37\), respectively. Figure 4 shows the CMN mean value statistics against the elevation angle per five degrees and against the C/N0 per 2 dB-Hz.