# Noises in Double-Differenced GNSS Observations
## 5 Discussion and Conclusions  
This contribution presents research on the noise characteristics of double-differenced GNSS measurements. Based on weekly observations from a zero-length baseline, a detailed analysis of the noise type was performed for the code and carrier phase measurements for the GPS, GLONASS, and Galileo systems. The use of the autocorrelation function, spectral  
Figure 15: Averaged MDEV for each system along with the types of noise fitted to them.  
analysis using the L-S method, and a modified Allan deviation indicator made it possible to determine the type of noise and its parameters for individual systems and signals.  
For the tested signals, significant differentiation of the noise level is visible: the GPS C5Q and Galileo C7Q and C8Q signals are characterized by the highest accuracy among the code observations, with the standard deviation not exceeding \(\pm\)10 cm; the lowest accuracy was obtained for the GLONASS C1C and C2C observations, for which the standard deviations were \(\pm\)90 cm and \(\pm\)45 cm, respectively. The noise level for the carrier phase observations was very similar for all of the signal types and is in the range of \(\pm\)1.5-3.5 mm.  
The ACF analysis showed significant differences in the characteristics of the analyzed signals. Code signals, particularly GPS C2W and C5Q signals, are characterized by a significant temporal correlation, unlike carrier phase signals. The presented results lead to the conclusion that the double-differenced GNSS observation time series for a 1 Hz measurement rate can only be treated not being related to time for carrier phase observations. For code observations, such an assumption can be made for observations with an interval of more than 20 s.  
Depending on the kind of observations and their type, one should notice that the signals and the corresponding noise types have different stabilities. In the case of code observations, all signals of the are consistent with each other and can be characterized depending on the averaging time as either flicker PM or white PM. In the case of the GPS and Galileo phase observations, they are all uniquely characterized by white PM. In the case of the GLONASS satellites--similar to the code observations--white PM or flicker PM are possible depending on the integration step.  
It should be noted that as the presented research does not include analyses of the dependence of the noise level on the SNR, C/N0, satellite elevation, or receiver type, they could be the subject of further study.  
Conceptualization, D.P., J.K. and K.M.; methodology, D.P., J.K. and K.M.; software, D.P., J.K. and K.M.; validation, D.P., J.K. and K.M.; formal analysis, D.P., J.K. and K.M.; investigation, D.P., J.K. and K.M.; resources, D.P., J.K. and K.M.; data curation, D.P., J.K. and K.M.; writing--original draft preparation, D.P., J.K. and K.M.; writing--review and editing, D.P., J.K. and K.M.; visualization, D.P., J.K. and K.M.; supervision, D.P., J.K. and K.M.; project administration, D.P., J.K. and K.M.; funding acquisition, D.P., J.K. and K.M. Authors contribution: D.P. 40%, J.K. 30%, K.M. 30%. All authors have read and agreed to the published version of the manuscript.  
This work was funded by the National Science Centre, Poland: Project No. 2016/23/D/ST10/00498 and by the _Initiative for Excellence-Research University_ grant at AGH University of Science and Technology; and under scientific research 16.16.150.545.  
Not applicable.  
The authors declare no conflict of interest.