# Noises in Double-Differenced GNSS Observations
## 4 Results
### Spectral Analysis  
Spectral analysis was performed for each satellite arc separately during the analyzed week. As an example of the results, the L-S periodograms for the GPS PRN09 (arc 3), GLONASS PRN21 (arc 14) and Galileo PRN19 (arc 5) satellites are presented in Figures 8-10. In our calculations, all of the available signals (Table 4) were analyzed separately for all of the satellites in the constellations. For all of the analyzed satellite signals, there is a noticeable change in the noise characteristic (power spectrum slope) around the frequency of 0.001 Hz, regardless of the GNSS system. For this reason, the spectral index k was calculated for the part of the spectrum that was in the range 0.001 Hz-0.5 Hz. The spectral index was determined by the linear regression of the L-S power spectrum after frequency and power logarithmization. The fitted line corresponding to the noise type is plotted in orange in Figures  
The spectral analysis examples presented in Figure 8 for GPS satellite PRN09 show that for all of the phase observations (L1C, L2L, L2W, and L5C), there is only white noise (k = 0) presented over the entire frequency range studied. The code observations C2L, C2W, and C5Q show a clear change in the nature of the noise--the slope of the L-S spectrum--for frequencies above 10\({}^{-2}\) Hz. For frequencies below 10\({}^{-2}\) Hz, the spectral index is k = 0 (white noise), above k = \(-\)1, which corresponds to flicker noise. On the other hand, in the C1C signal, fractional white noise is visible (\(-\)1 < k < 0).  
As shown in the example for the GLO PRN21 satellite (Figure 9), in the case of the GLONASS satellites, all of the code observations (C1C, C1P, C2C, C2P) are characterized by the presence of flicker noise in the entire range of the tested frequencies. In the phase observations, white noise is present at frequencies above 10\({}^{-3}\) Hz, similar to the GPS  
Figure 10: Lomb–Scargle periodograms for Galileo PRN19 satellite. Orange lines represent the line fitted in the part of the spectrum in the range of 0.001–0.5 Hz. The slope of the line represents the spectral index value.  
Figure 9: Lomb–Scargle periodograms for the GLONASS PRN21 satellite. Orange lines represent the line fitted in the part of the spectrum in the of range 0.001–0.5 Hz. The slope of the line represents the spectral index value.  
observations. However, for frequency components lower than \(10^{-3}\) Hz, the noise is closer to flicker noise.  
The code and phase observations of the Galileo system (the example of the GAL PRN19 satellite in Figure 10) exhibit the same type of noise as the GPS satellites. The code observations show flicker noise for frequencies above \(10^{-2}\) Hz, and the phase signals only show white noise.  
Figure 11 and Table 4 show a statistical summary of the spectral index \(k\) for the double differences of the code and phase observations for all of the GNSS signals analyzed. There is a clear similarity in the nature of the noise in the different types of observations.  
In the code observations, the noise has characteristics of flicker noise, except for the C1C observations for all of the GNSS systems and the C7Q signal of the Galileo system. In contrast, white noise is present in the double difference phase observations for all of the GNSS systems that were analyzed.