## 2 GNSS Measurement Noise
Based on the presented values, it can be concluded that the nominal signal quality differs significantly between systems, reaching the lowest values for GPS 2L, 2W and BeiDou signals, which may considerably affect the GNSS receiver performance. The SNR parameter describes the relative magnitude of the measurement noise and is therefore directly related to the precision of the code and carrier-phase observations. The nominal precision of GNSS receiver performance due to thermal noise can be calculated \begin{table}
\begin{tabular}{l r} \hline \hline
**Component** & **Value** \\ \hline Transmitted signal power: & \(14.3\,\mathrm{d}\mathrm{B}\mathrm{W}\) \\ Minimum signal power & \(14.3\,\mathrm{d}\mathrm{B}\mathrm{W}\) \\ \hline Received signal power: & \(-141.0\,\mathrm{d}\mathrm{B}\mathrm{W}\) \\ Path loss & \(-204.0\,\mathrm{d}\mathrm{B}\mathrm{W}/\mathrm{Hz}\) \\ Satellite antenna gain & \(20.0\,\mathrm{d}\mathrm{B}\mathrm{W}/\mathrm{Hz}\) \\ Atmospheric attenuation & \(-20.8\,\mathrm{d}\mathrm{B}\mathrm{W}\) \\ Receiver antenna gain & \(-27.4\,\mathrm{d}\mathrm{B}\mathrm{W}\) \\ Received signal power & \(-161.8\,\mathrm{d}\mathrm{B}\mathrm{W}\) \\ \hline Noise power: & \(-141.0\,\mathrm{d}\mathrm{B}\mathrm{W}\) \\ Noise power density (\(N_{0}\)) & \(-204.0\,\mathrm{d}\mathrm{B}\mathrm{W}/\mathrm{Hz}\) \\ \hline Signal quality: & \(-20.8\,\mathrm{d}\mathrm{B}\) \\ Signal-to-noise ratio (SNR) & \(42.2\,\mathrm{d}\mathrm{B}\mathrm{W}\) \\ Carrier-to-noise density ratio (\(\mathrm{C}/\mathrm{N}_{0}\)) & \(42.2\,\mathrm{d}\mathrm{B}\mathrm{W}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Signal power budget of GPS C/ A for \(e=5^{\circ}\)[7; 79; 80]. Figure 1: Nominal \(\mathrm{C}/\mathrm{N}_{0}\) for minimum received signal power for GNSS signals. as tracking error in Delay Lock Loop (DLL) for code and in Phase Lock Loop (PLL) for carrier-phase measurements, given by [79]:  
\[\sigma_{\rm C}^{2} =\frac{B_{\rm DLL}d}{2{\rm C}/{\rm N}_{0}}\bigg{(}1+\frac{1}{t_{\rm DLL }{\rm C}/{\rm N}_{0}}\bigg{)}\quad[{\rm PRN\ chip}^{2}] \tag{2}\] \[\sigma_{\rm L}^{2} =\frac{B_{\rm PLL}}{{\rm C}/{\rm N}_{0}}\bigg{(}1+\frac{1}{2t_{\rm PLL }{\rm C}/{\rm N}_{0}}\bigg{)}\quad[{\rm rad}^{2}] \tag{3}\]  
where: \(\sigma_{\rm C}^{2}\) and \(\sigma_{\rm L}^{2}\) are tracking error variance for code and carrier-phase respectively, \(B_{\rm DLL}\) and \(B_{\rm PLL}\) are code and phase tracking loop bandwidth in Hz, \(t_{\rm DLL}\) and \(t_{\rm PLL}\) are DLL and PLL predetection integration intervals in seconds and \(d\) is the dimensionless correlator spacing normalized with respect to one Pseudorandom Noise (PRN) code chip. The C/N\({}_{0}\) in these equations must be expressed in units of ratio-Hz. Based on the above formulas, assuming the C/N\({}_{0}\) determined for the minimum received signal power and the characteristics of the tracking loops for the Sepentrito PolaRx5 receiver, which was used in the measurement experiment (\(B_{\rm DLL}=0.25\) Hz, \(B_{\rm PLL}=15\) Hz, \(t_{\rm DLL}=0.10\) s, \(t_{\rm PLL}=0.01\) s, \(d=0.1\)), the nominal errors of GNSS measurements were determined. Figures 2 and 3 show theoretical tracking errors for code and phase observations, respectively, for signals corresponding to those shown in Figure 1. The carrier phase observation errors accurately reflect the variability of C/N\({}_{0}\)--the lower the value, the greater the error. For code observations, high error values of GPS 2L and GLONASS 1C and 2C signals are distinguished. This is mainly caused by the narrow nominal bandwidth of these signals, which is generally smaller than the actual transmission bandwidth [81]. Based on the results in Figures 1-3, it can be concluded that the nominal measurement noise of individual observations varies significantly, and, assuming the same observation accuracy for different systems and signals, may cause significant inaccuracies of the realistic noise characteristics in the stochastic model. Figure 3: Nominal carrier-phase tracking errors for GNSS signals for receiver Sepentrito PolaRx5.