## 6 Conclusions  
The observation weighting and the realistic stochastic model estimation is still a challenging problem in GNSS processing. To deal with this problem, the LS-VCE method was applied to real GNSS data sets collected by three multi-GNSS receivers (Trimble NETR9, SEPT POLARX5, and LEICA GR30) to estimate different variances and covariances for each GNSS observation type as well as the correlation between various observations. Considering these values and the observables' satellite elevation dependence weighting, a realistic stochastic model for GNSS observables can be estimated and ultimately achieve the best linear unbiased estimators in high precision GNSS positioning. To repeat the LS-VCE scenario several times and reduce the processing time, the data were divided into 288 groups containing ten epochs of observations.  
The results showed the estimated (co)variance values for Trimble NETR9 and SEPT POLARX5 are compatible. The Trimble NETR9 has the lowest and highest variances for Galileo and GLONASS code observations of all, respectively. On the SEPT POLARX5 receiver, GLONASS has the highest standard deviation for code observations, and GALILEO has the lowest for phase observations. The phase observations from the LEICA GR30 have the highest standard deviation, while those from the SEPT POLARX5 have the lowest. In most cases, the correlations between the phase observations are significantly larger than those between the code observations. Moreover, the correlation values for the SEPT POLARX5 are the lowest, while they are the highest for the Trimble NETR9. BeiDoN has the lowest correlation values for Trimble NETR9 and LEICA GR30, among other systems.  
In summary, the preliminary numerical results show that the stochastic model determination of the observables is highly dependent on the type of receiver used and the signal quality. This is because each receiver measures the code pseudorange and carrier phase measurements using its recovery method. Therefore, the overall design of the receiver and its antenna can affect the noise structure and hence the stochastic model. As a result, it is preferable to do the VCE before processing to obtain the BLUE of unknown parameters. This could be seen as a kind of calibration for the measurements of a specific GNSS receiver.  
As previously mentioned, a realistic stochastic model affects the IAR success rate. The SR was compared in two cases, once with the nominal and once with the realistic (co)variance matrix used in the stochastic model. The results emphasized that using a more realistic stochastic model would increase IAR success rates in single and multi-GNSS cases. Affecting the IAR, using a realistic stochastic model based on LS-VCE, can shorten the TTF, which is a challenge for real-time positioning techniques.  
Another criterion may be the impact of the realistic stochastic model on the estimated baseline components values and standard deviations, which are influenced by the observables' weight matrix. In this way, the reported precision of the solution is realistic, neither too optimistic nor too pessimistic. The findings show that introducing the realistic stochastic model improves the baseline components' standard deviation and accuracy and make them reliable. Considering all of the positive effects of utilizing a realistic stochastic model, we may evaluate the values of VCE for observations of each receiver and use the values in other upcoming processing.  
[PERSON] proposed the initial idea. [PERSON], [PERSON] and [PERSON] designed the algorithm and experiment. [PERSON] developed the software and wrote the manuscript. A.A.-S. All coauthors analyzed the results and reviewed and edited the manuscript. All authors have read and agreed to the published version of the manuscript.  
This research was funded by Delft University of Technology.  
The authors declare no conflict of interest.