In the overall position error determined by the satellite navigation systems, the atmosphere participates with errors caused by the ionosphere and troposphere layers. The troposphere is considered to be a neutral medium due to the same effect on the carrier phase and information signal phase. The position error caused by tropospheric effect (commonly called tropospheric delay) must be assessed while determining the position or subsequently determined using external tropospheric corrections. The most important elements that cause tropospheric delay are atmospheric gases, pressure, temperature and the amount of water in the atmosphere. The effect of tropospheric delay is observed separately in the zenith direction and in the slant direction of the incoming satellite navigation signal. Additionally, tropospheric delay can also be observed with regard to atmospheric causes, with hydrostatic (dry) and non-hydrostatic (wet) causes being observed separately. The movement of tropospheric delays shows daily, seasonal and annual regularities. Based on these findings, a number of tropospheric delay models of different approaches have been developed in the zenith direction only for dry and / or wet causes, a separate mapping function for slant directions for dry and / or wet causes, or a common overall model. In the dissertation, a model based on the Saastamoinen model of zenith tropospheric delay has been proposed. The model was developed based on the position records of the GLONASS satellite navigation system and appropriate meteorological input records within one year with three locations. The proposed model defines the tropospheric deviation separately for each position coordinate. The results show that the statistical equilibrium of positional GLONASS deviations in a function of the zenith component of the tropospheric delay has been achieved by the proposed model. The verification carried out (at three locations in the Republic of Croatia within a two-year period) shows that the proposed model reduces the zenith component of the tropospheric delay and thus improves the accuracy of the position. This confirmed the suitability of using the proposed model in the observed area and in wider areas of similar climate profile. The evaluation of the proposed model has been approached in the view of the initial limitations, the obtained accuracy results and the realized knowledge about the tropospheric dynamics of the observed area. The potential of practical and scientific application of the overall research results has been pointed out. The adaptability of the proposed model while reducing initial restrictions represents the basis for future tropospheric delay researches.