The stochastic model, together with the functional model, form the mathematical model of observation that enables the estimation of the unknown parameters. In Global Navigation Satellite Systems (GNSS), the stochastic model is an especially important element as it affects not only the accuracy of the positioning model solution, but also the reliability of the carrier-phase ambiguity resolution (AR). In this paper, we study in detail the stochastic modeling problem for Multi-GNSS positioning models, for which the standard approach used so far was to adopt stochastic parameters from the Global Positioning System (GPS). The aim of this work is to develop an individual, empirical stochastic model for each signal and each satellite block for GPS, GLONASS, Galileo and BeiDou systems. The realistic stochastic model is created in the form of a fully populated variance-covariance (VC) matrix that takes into account, in addition to the Carrier-to-Noise density Ratio (C/N${}_0$)-dependent variance function, also the cross- and time-correlations between the observations. The weekly measurements from a zero-length and very short baseline are utilized to derive stochastic parameters. The impact on the AR and solution accuracy is analyzed for different positioning scenarios using the modified Kalman Filter. Comparing the positioning results obtained for the created model with respect to the results for the standard elevation-dependent model allows to conclude that the individual empirical stochastic model increases the accuracy of positioning solution and the efficiency of AR. The optimal solution is achieved for four-system Multi-GNSS solution using fully populated empirical model individual for satellite blocks, which provides a 2% increase in the effectiveness of the AR (up to 100%), an increase in the number of solutions with errors below 5 mm by 37% and a reduction in the maximum error by 6 mm compared to the Multi-GNSS solution using the elevation-dependent model with neglected measurements correlations.

Continuously operating reference station (CORS) networks, as one of the fundamental segments of the precise global navigation satellite systems (GNSSs) positioning techniques, have been undergoing rapid development and growth in the last two decades. The existing and newly created CORS networks coincide with both the services provided and the covered area. This is the situation in Poland, where there are five nation-wide and local networks that have in total over 500 stations and provide access to similar GNSS data, real time kinematic (RTK), and network real time kinematic (NRTK) services. This paper presents one of the most comprehensive tests conducted to evaluate the quality of network-based GNSS positioning services performance provided by all CORS networks available in Poland. The test was performed in November 2017 and included the analysis of accuracy and reliability of positioning performance, time to first fix (TTFF), an average age of correction as well as the compliance of the reference frame realization. The test data were obtained from the field measurements of consecutive RTK/NRTK services and simultaneous continuous measurements carried out at 20 reference points of the first-order geodetic network, evenly distributed throughout Poland. Obtained results allowed to estimate the positioning performance accuracy and reliability for all tested streams and their mutual comparison of quality along with the analysis of the reference frame realization compliance implemented by all networks. In most cases, the results confirm the nominal accuracy of positioning (at 68% confidence level) based on tested streams of 1 cm for horizontal and 2 cm for vertical components. However, it was also found that for some networks and streams the obtained accuracy was twice lower (reaching up to 4 cm for the height component), and compliance with the vertical reference frame is lower.