# Noises in Double-Differenced GNSS Observations
## 4 Results
### Allan Variance  
Figures 12-14 show the MDEV calculated for each GPS, GLONASS, and Galileo satellite signal, respectively. The z-axis is the MDEV in seconds, the x-axis is averaging time (\(T\)) in seconds, and the y-axis represents the satellites used in the evaluation. To make figure interpretation easier for the reader, the z-axis scale is the same for all of the images.  
Figure 11: Spectral index for double differences of observations.  
Figure 12 shows the MDEV of the whole GPS segment divided by the signal type. The first row has the code signals, and the second row has the phase signals. The magnitudes for C1C, C2L C2W, and C5Q are very similar and cover ranges between \(10^{0}\) s and \(10^{-7}\) s.  
Figure 14: MDEV of the analyzed observation type for Galileo satellites.  
Figure 12: MDEV of the analyzed observation type for GPS satellites.  
Figure 13: MDEV of the analyzed observation type for GLONASS satellites.  
In the case of the phase signals, the MDEV ranges for each signal are between the ranges from \(10^{-2}\) s to \(10^{-9}\) s, which is two orders of magnitude more accurate in relation to the code signals.  
Figure 13 shows the MDEV of the GLONASS signals divided by the type. The magnitudes for C1C and C2C are similar and cover ranges between \(10^{0}\) s to \(10^{-7}\) s, while for C1P and C2C, the ranges vary between \(10^{-1}\) s and \(10^{-6}\) s. In the case of the phase signals, the MDEV ranges for each signal are between \(10^{-2}\) s and \(10^{-8}\) s. The slope of the graphs also differs from one signal to another and is consistent for each satellite. Such analyses are presented later in the text.  
Unlike GPS and GLONASS, the Galileo code observations do not have the same range of data values (Figure 14). For the C1C, C5Q, and C7Q signals, the range is from \(10^{-1}\) s to \(10^{-9}\) s. In contrast, the C8Q signal is an order of magnitude more accurate and ranges from \(10^{-2}\) s to \(10^{-9}\) s, which corresponds to the accuracy of the phase observations of the GPS and GLONASS signals. In the case of the Galileo phase observations, the stability is similar for each type of signal and ranges from \(10^{-2}\) s to \(10^{-10}\) s, which is the most accurate among all of phase signals from the analyzed GNSS systems.  
Figure 15 shows the averaged MDEV values for each signal type and system. The first row comprises mean code values, and the second comprises the phase values. Moreover, properly matched noise was added to the data on the chart in each graph. In the case of the code signals for the GPS and Galileo signals, the shortest averaging times (\(\tau\leq 128\) s) are affected by the flicker PM (\(\tau^{-1}\)), while the l white PM (\(\tau^{-1.5}\)) is the noticed. The GLONASS code signals are also affected by the above two noise types, but the flicker PM characterizes the observations for \(\tau\leq 16\) s, and white PM characterizes the others.  
In the case of the phase observations for the GPS and Galileo systems, all of the observation types are very consistent with each other, which shows high-quality and perfect reproduction of the white PM noise (Figure 15, 2 nd row). In the case of the GLONASS system, the conclusions are the same as they are in the case of the code signals--for \(\tau<64\) s flicker PM, for the other, larger averaging times represents white PM. Additionally, none of the four types of GLONASS phase observations are consistent with each other--this is not reflected in any of the graphs.