# Noises in Double-Differenced GNSS Observations
###### Abstract  
Precise data processing from the Global Navigation Satellite Systems (GNSS) reference station network is mainly based on a combination of double-differenced carrier phase and code observations. This approach allows most of the measurement errors to be removed or reduced and is characterized as the most accurate method. However, creating observation differences between two receivers and two satellites increases the measurement noise of the observations by a factor of 2. As a result, it increases the impact of the incorrect definition of the noise characteristic on the results of the estimation of the unknowns in the positioning model. This is especially important in Multi-GNSS solutions, which integrate measurements from different systems, for which the stochastic parameters of observation may differ significantly. In this paper, the authors prepared a complex analysis of the noise type in double-differenced GNSS (GPS, GLONASS and Galileo) observations, both carrier phase and code ones, with a 1 s sampling interval. The Autocorrelation Function (ACF) method, the Lomb-Scargle (L-S) periodogram method, and the Allan variance (AVAR) method were used. The results that were obtained for the weekly set of measurement data showed that, depending on the system and type of observation, the noise level and its type are significantly different. Among the code measurements, the lowest noise levels were obtained for the GPS C5Q and Galileo C7Q/C8Q observations, with the standard deviations not exceeding \(\pm\)10 cm, while the noisiest observations were for the GLONASS C1C and C2C signals, which had standard deviations of about \(\pm\)90 cm and \(\pm\)45 cm, respectively. For the carrier phase observations, each signal type was characterized by very similar noise levels of \(\pm\)1.5-3.5 mm. The ACF analysis showed that 1 Hz double-differenced GNSS data can only be treated as being not correlated to time for carrier phase observations; for code observations, an irrelevant autocorrelation may be considered for measurement intervals greater than 20 s. Depending on the GNSS signals, the spectral index k varies in a range from \(-\)1.3 to \(-\)0.2 for code data and k = 0.0 in the case of phase data. Using the modified Allan deviation (MDEV) allows for specific noise types for each signal and GNSS system to be determined. All of the code observations were characterized by either flicker PM or white PM. In the case of the phase observations, they were all uniquely characterized by white PM (GPS and Galileo or by white PM and flicker PM (GLONASS). GNSS; observations noise; double-difference; code; carrier phase +
Footnote †: journal: Physics Letters A  
0000-0002-0001-9800]D. [PERSON]  
0000-0002-00  
and diagonal variance-covariance (VC) matrix. For this type of noise, the signal power spectrum is equal in all frequency bands. Identifying the type of noise allows for the determination of the noise density coefficients that are characteristic of a given noise, which can be included in the mathematical model of the observation development through the stochastic model [2; 3]. Moreover, the noise is one of the coefficients that, in Kalman filtering for example, makes it possible to increase the accuracy of the position determination [4; 5]. Adopting the white noise assumption for GPS observations is not a strict approach. Analyses of code and carrier phase measurements have shown significant temporal correlation, mainly due to the atmospheric delay, multipath effect, and the receiver itself [6; 7; 8] as well as cross-correlations between different types of observation [9; 10; 11]. The obtained correlation parameters were dependent on the type of observation and the measurement set. Non-uniformity in observation noise parameters that is even more significant occurs when comparing Multi-GNSS measurements.