## 4 Results Analysis
### Flight Test Case
It is seen that the noise process of L1 carrier phase observations from different systems resembles largely white phase noise (WPM) for up to \(\tau=500\) [s]. Moreover, receiver combinations with different clock configurations does not have a large impact on the quality of the observations. Also, the higher noise level of the GLONASS L1 observation is clearly visible compared to GPS and Galileo L1. Figure 13: DDs of L1 carrier phase observations from all satellites for different receiver combinations with respect to the flight experiment time. GPS, GLONASS and Galileo noise levels are shown in blue, green and red colours, respectively. Black dashed vertical lines indicate different flight phases, which are explained in Table 3.  
The stochastic behaviour of GNSS L1 carrier phase DDs is analysed in connection with satellites elevation angles and the received C/N\({}_{0}\) of the corresponding signals. Figure 15 shows the DDs for GPS, GLONASS and Galileo L1 carrier phases with regards to the satellite elevation angles. All the sudden spikes observed in computed GNSS DD at elevation angles greater than about 10\({}^{\circ}\) are due to recorded data from an ascending satellite or just before the loss of visibility of a satellite already in view. An elevation dependency is observed for all the computed DDs. The standard deviation of the phase range dependent on the elevation angle \(h\) can be approximated using the following exponential function [13]:  
\[\sigma(h)=a_{0}+a_{1}\cdot\exp\left(\frac{-h}{h_{0}}\right) \tag{6}\]  
where \(a_{0}\), \(a_{1}\) are constant terms; \(h_{0}\) represents the scaling factor for the elevation angle. The values listed in Table 6 are derived empirically to model all the estimated L1 carrier phase system specific DDs with all the receiver combinations. As examples, decreasing exponential functions for two different receiver combinations evaluated using the parameters in Table 6 can be seen in all plots of Figure 15. The corresponding increasing exponential function seen in Figure 15 is equivalent to a change in the sign of decreasing exponential function. From Figure 15, an elevation dependent weighting scheme modelled as an exponential function is justified for aerial navigation applications requiring higher accuracy and precision. The DDs for GPS, GLONASS and Galileo L1 carrier phases in relation to the received signal's C/N\({}_{0}\) from different satellites are shown in Figure 16. It is observed that the behaviour of GPS L1 DDs is similar for both the receiver combinations. In the case of GLONASS, the DDs varies largely randomly with the C/N\({}_{0}\) and no correlation is observed for both receiver combinations. A C/N\({}_{0}\) dependency is visible for GPS and Galileo, wherein large C/N\({}_{0}\) leads to smaller noise levels in most cases and vice versa. As explained in the elevation dependency scenario, few outliers seen at large \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Observation Type** & **a\({}_{0}\) [mm]** & **a\({}_{1}\) [mm]** & **h\({}_{0}\) [\({}^{\circ}\)]** \\ \hline GL1C & 1.1 & 3.2 & 15 \\ RL1C & 3.2 & 5.5 & 20 \\ EL1X & 1.2 & 3 & 15 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Empirical values of the exponential function parameters—JVD Delta receivers. Figure 14: Modified ADEV’s of the L1 carrier phase DDs for one satellite pair of each GNSS system with two different receiver combinations in (**a**), corresponding elevation angles of the satellites in (**b**). Solid and dash-dot lines represent reference and the other satellite in (**b**), respectively. C/N\({}_{0}\) are due to the addition of a new visible satellite or loss of visibility of a satellite during the experimental campaign. Based on the analysis, a C/N\({}_{0}\) dependent weighting scheme is also suitable for GPS and Galileo L1 phase observations in aerial applications. Figure 16: DDs of L1 carrier phase observations for different receiver combinations with respect to the received C/N\({}_{0}\) from all the satellites.