Positioning error components related to tropospheric and ionospheric delays are caused by the atmosphere in positioning determined by global navigation satellite systems (GNSS). Depending on the user’s requirements, the position error caused by tropospheric influences, which is commonly referred to as zenith tropospheric delay (ZTD), must be estimated during position determination or determined later by external tropospheric corrections. In this study, a new approach was adopted based on the reduction of residual tropospheric error (RTE), i.e., the unmodeled part of the tropospheric error that remains included in the total geodetic position error, along with other unmodeled systematic and random errors. The study was performed based on Global Navigation Satellite System (GLONASS) positioning solutions and accompanying meteorological parameters in a defined and harmonized temporal-spatial frame of three locations in the Republic of Croatia. A multidisciplinary approach-based analysis from a navigational science aspect was applied. The residual amount of satellite positioning signal tropospheric delay was quantitatively reduced by employing statistical analysis methods. The result of statistical regression is a model which correlates surface meteorological parameters with RTE. Considering the input data, the model has a regional character, and it is based on the Saastamoinen model of zenith tropospheric delay. The verification results show that the model reduces the RTE and thus increases the geodetic accuracy of the observed GNSS stations (with horizontal components of position accuracy of up to 3.8% and vertical components of position of up to 4.37%, respectively). To obtain these results, the Root Mean Square Error (RMSE) was used as the fundamental parameter for position accuracy evaluation. Although developed based on GLONASS data, the proposed model also shows a considerable degree of success in the verification of geodetic positions based on Global Positioning System (GPS). The purpose of the research, and one of its scientific contributions, is that the proposed method can be used to quantitatively monitor the dynamics of changes in deviations of X, Y, and Z coordinate values along coordinate axes. The results show that there is a distinct interdependence of the dynamics of Y and Z coordinate changes (with almost mirror symmetry), which has not been investigated and published so far. The resultant position of the coordinates is created by deviations of the coordinates along the Y and Z axes—in the vertical plane of space, the deviations of the coordinate X (horizontal plane) are mostly uniform and independent of deviations along the Y and Z axes. The proposed model shows the realized state of the statistical position equilibrium of the selected GNSS stations which were observed using RTE values. Although of regional character, the model is suitable for application in larger areas with similar climatological profiles and for users who do not require a maximum level of geodetic accuracy achieved by using Satellite-Based Augmentation Systems (SBAS) or other more advanced, time- consuming, and equipment-consuming positioning techniques.