They are based on the assumption that residual observation errors not included in the functional model can be equivalently captured by the fully populated VC matrix [47]. These models, mainly dedicated to kinematic positioning, use a priori values of individual errors [48, 49, 50], the residual observations from previous epochs [51,52] or the atmospheric correction errors estimation determined from the network of reference stations [53]. Stochastic models for GPS and GLONASS measurements have been analyzed from the very beginning of their use [1,54, 55, 56, 57, 58]. The authors of these analyses, apart from developingthe observation variance empirical models, pointed to the lack of cross-correlation between code and phase observations and the existence of significant correlations between the same type of observations at two frequencies (e.g., [56; 59]). The conducted analyses also show significant time-correlations for the codes C1, P1 and P2 [18]. Apart from the numerous works related to the refinement of stochastic models for GPS and GLONASS observations, research on stochastic models of state-of-the-art Galileo and BeiDou systems has also been conducted in the recent years. These studies include analyses of single systems (e.g., variance of dual-frequency BeiDou B1/B2 code and phase observations [60], variance-covariance components as well as cross- and time-correlation parameters for dual-frequency [61] and triple-frequency BeiDou signals [4], a combination of BeiDou-2 and BeiDou-3 stochastic modeling [62], noise characteristic for five Galileo signals [63]), combined dual systems: GPS/Galileo [22], GPS/BeiDou [64], GPS/IRNSS [65] and triple systems GPS/Galileo/BeiDou [66; 67; 68] solutions as well as Multi-GNSS system solutions (e.g., [69; 70]). The analysis of the influence of various stochastic models on the results of the positioning model solution leads to the conclusion that their improvement (e.g., by changing the variance function or the diagonal VC matrix to the fully populated) affects: (a) the accuracy of the unknowns estimation--improvement in the accuracy of the horizontal baseline components at mm-level and height component up to a few centimeters [71; 72]; (b) carrier-phase integer ambiguity resolution--improvement of AR success rate in GPS L1/L2 geometry-based relative positioning model up to 25% [30], improving the efficiency of the AR validation test up to 10% in the case of false alarm probability using ratio test [4; 19]; (c) overestimation of the precision--neglecting the cross-correlation leads to a too optimistic estimate of the baseline solution precision [32; 37; 73]. All the above-mentioned scientific works and research results lead to the conclusion that the stochastic model is one of the crucial elements in the GNSS observations processing, and its correct definition has a significant impact on the quality of the obtained results. The previous analyses for multi-system solutions did not cover all aspects of stochastic modeling (determination of variance, cross- and time-correlation specific to a particular system/signal/satellite block) for each systems and its impact on the model solution (ambiguity resolution and positioning accuracy). The lack of uniform parameters for all GNSS systems results that one of the approaches taken in multi-system positioning is making the approximate assumptions for stochastic observation parameters or adapting parameters from the GPS system [74; 75; 76]. The aim of this work was to develop an individual, empirical stochastic model of all Mutli-GNSS code and carrier-phase observations in the form of a fully populated VC matrix that takes into account the physical correlations between measurements. The primary contributions of this paper are summarized as follows:  
* The empirical stochastic model was determined individually for the GPS, GLONASS, Galileo and BeiDou systems for each signal and individual blocks of satellites using a 4 th-degree Carrier-to-Noise density Ratio-dependent model.