Improvement of Multi-GNSS Precision and Success Rate Using Realistic Stochastic Model of Observations  
[PERSON]  
1 Department of Geomatics Engineering, Faculty of Civil Engineering and Transportation, University of Isfahan, Isfahan 81746-73441, Iran; [PERSON]F.M. ); [PERSON]_ADDRESS] (J.A. ); [PERSON]_ADDRESS] (A.A.-S.)  
[PERSON]  
1 Department of Geomatics Engineering, Faculty of Civil Engineering and Transportation, University of Isfahan, Isfahan 81746-73441, Iran; [PERSON]F.M. ); [PERSON]_ADDRESS] (J.A. ); [PERSON]_ADDRESS] (A.A.-S.)  
[PERSON]  
2  
[PERSON]  
1 Department of Geomatics Engineering, Faculty of Civil Engineering and Transportation, University of Isfahan, Isfahan 81746-73441, Iran; [PERSON]F.M. ); [PERSON]_ADDRESS] (J.A. ); [PERSON]_ADDRESS] (A.A.-S.)  
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The estimated values for different receivers are shown in Tables 5-7. Figures 6-8, for example, show the groupwise estimated correlations between code observations for each system. +++  
Figure 7: Estimated correlation coefficients between the C1 and P2 observations (dashed line) with their average values in 10 epoch group windows (bold line) over a very short baseline. \begin{table}
\begin{tabular}{c c c c c c} \hline
**GNSS** &
\begin{tabular}{c} **Between** \\ **Observation** \\ **Types** \\ \end{tabular} & \(\hat{\sigma}_{i,j}\)**(mm2)** & \(\sigma_{\hat{\sigma}_{i,j}}\)**(mm2)** & \(\hat{\rho}_{i,j}\) & \(\sigma_{\hat{\rho}_{i,j}}\) \\ \hline \multirow{6}{*}{GPS} & C1-P2 & 116.85 & 0.24 & 0.026 & 1.31\(\times 10^{-3}\) \\  & C1-L1 & \(-\)0.91 & 2.87\(\times 10^{-5}\) & \(-\)0.018 & 1.44\(\times 10^{-3}\) \\  & C1-L2 & 1.82 & 2.87\(\times 10^{-5}\) & 0.038 & 1.44\(\times 10^{-3}\) \\  & P2-L1 & 0.05 & 9.79\(\times 10^{-6}\) & 0.003 & 1.44\(\times 10^{-4}\) \\  & P2-L2 & 0.90 & 9.88\(\times 10^{-6}\) & 0.035 & 1.40\(\times 10^{-3}\) \\  & L1-L2 & 0.10 & 1.31\(\times 10^{-9}\) & 0.368 & 1.95\(\times 10^{-3}\) \\  & C1-P2 & 2156.70 & 18.33 & 0.080 & 2.29\(\times 10^{-3}\) \\  & C1-L1 & 9.06 & 3.67\(\times 10^{-4}\) & 0.075 & 2.46\(\times 10^{-3}\) \\ \multirow{2}{*}{GLONASS} & C1-L2 & \(-\)0.74 & 5.08\(\times 10^{-4}\) & \(-\)0.007 & 2.43\(\times 10^{-4}\) \\  & P2-L1 & \(-\)0.74 & 9.98\(\times 10^{-5}\) & \(-\)0.004 & 2.51\(\times 10^{-4}\) \\  & P2-L2 & 1.13 & 1.52\(\times 10^{-4}\) & 0.018 & 2.51\(\times 10^{-3}\) \\  & L1-L2 & 0.03 & 3.02\(\times 10^{-9}\) & 0.080 & 2.82\(\times 10^{-3}\) \\  & C1-P2 & 565.10 & 0.68 & 0.076 & 2.82\(\times 10^{-3}\) \\ \multirow{2}{*}{Galileo} & C1-L1 & \(-\)0.71 & 1.97\(\times 10^{-5}\) & \(-\)0.025 & 1.92\(\times 10^{-3}\) \\  & C1-L2 & \(-\)0.048 & 2.11\(\times 10^{-5}\) & \(-\)0.005 & 1.2\(\times 10^{-4}\) \\  & P2-L1 & 0.07 & 3.50\(\times 10^{-5}\) & 0.003 & 1.88\(\times 10^{-4}\) \\  & P2-L2 & \(-\)6.36 & 4.05\(\times 10^{-5}\) & \(-\)0.141 & 1.95\(\times 10^{-3}\) \\  & L1-L2 & 0.02 & 1.26\(\times 10^{-9}\) & 0.095 & 2.19\(\times 10^{-3}\) \\ \multirow{2}{*}{BeiDou} & C1-P2 & \(-\)4488.63 & 9.056 & \(-\)0.149 & 1.32\(\times 10^{-3}\) \\  & C1-L1 & \(-\)1.07 & 1.02\(\times 10^{-4}\) & \(-\)0.012 & 1.29\(\times 10^{-3}\) \\ \multirow{2}{*}{BeiDou} & C1-L2 & 0.72 & 1.02\(\times 10^{-4}\) & 0.007 & 1.19\(\times 10^{-4}\) \\  & P2-L1 & \(-\)0.11 & 2.25\(\times 10^{-4}\) & -8.6\(\times 10^{-4}\) & 1.28\(\times 10^{-3}\) \\ \multirow{2}{*}{} & P2-L2 & 0.80 & 2.24\(\times 10^{-4}\) & 0.007 & 1.8\(\times 10^{-4}\) \\  & L1-L2 & 0.22 & 3.49\(\times 10^{-9}\) & 0.479 & 1.94\(\times 10^{-3}\) \\ \hline \end{tabular}
\end{table} 
Table 6: Covariances and correlation coefficient and their precision between the observation types for each system for SEPT POLARX5 receiver over a very short baseline. The tables show that the correlations between two code and two phase observations are significant in most cases. The correlation values for the SEPT POLARX5 are the lowest, while Trimble NETR9 is the highest. The correlations between the phase observations are