## 6 Summary and Concluding Remarks  
This contribution presents research on individual empirical stochastic models of Multi-GNSS measurements. Based on the theoretical analysis of the GNSS receiver tracking errors, which depend on the carrier-to-noise density ratio parameter, a variance model was proposed. The empirical parameters of the model were determined utilizing the measurement data from the zero-length and very short baselines. Comparing the nominal tracking errors for Septentrio receivers with those determined using the empirical model confirmed the high compliance of theoretical assumptions with the modeling results. Additionally, the zero-length baseline data time series analysis was used to determine the parameters of cross- and time-correlation of GNSS signals. Using the weekly solution for the empirical stochastic parameters, a fully populated variance-covariance matrix, individual for GNSS system, signal and satellite blocks, was created. The impact of empirical stochastic modeling on ambiguity resolution as well as on position accuracy was analyzed with respect to the standard elevation-dependent model for different positioning scenarios. Positioning models were derived using modified Kalman Filter in which time-correlation is taken into account. Based on the stochastic modeling and positioning results, we can conclude that:  
* the C/N\({}_{0}\)-dependent stochastic model allows to consider the factors influencing the signal tracking errors and thus precisely modeling observation noise;
* the realistic empirical stochastic model increases the accuracy and reliability of positioning solution, in particular the effectiveness of ambiguity resolution, while including the correlation parameters increases this efficiency;
* the highest efficiency of applying the empirical model is noticeable for Multi-GNSS solutions, for which the adoption of uniform stochastic parameters for all systems leads to significantly lower reliability of the solution;
* the optimal solution in the context of AR, positioning accuracy and maximum errors was obtained for a four-system GNSS solution using a fully populated empirical model individual for satellite blocks.  
It should be noted that the determined stochastic parameters, apart from the signal properties, are also closely related to the tested receivers and may differ depending on the equipment used. However, the presented methodology for creating empirical stochastic models and including them in the positioning model is comprehensive and can be used for all types of GNSS receivers and measurements. On the other hand, the bottleneck of the presented methodology may be the fact that the C/N\({}_{0}\) parameter varies due to multipath, which in such a case may unreliably describe the precision of observations estimated based on triple-differences. In the case of strong multipath, the determined stochastic model should additionally consider the impact of this phenomenon.  
[PERSON], [PERSON] and [PERSON] jointly conceived and designed the research as well as carried out the filed experiment; [PERSON] developed software, processed raw data and created a research methodology; [PERSON] made data analysis and validated the experiment results. [PERSON] and [PERSON] wrote the first draft of the manuscript, reviewed the text and made edits. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the National Science Centre, Poland: Project No. 2016/23/D/ST10/00498.  
Not applicable.  
The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.