Positioning accuracy in a specific area using a satellite navigation system is based on satellite signal propagation. The troposphere, as the atmospheric layer closest to the Earth's surface, causes a tropospheric delay of the satellite signal due to its inhomogeneous physical properties. The tropospheric delay occurs as an influential quantity in measuring pseudoranges, and determines positioning accuracy of the satellite navigation system. Descriptive statistical analysis identified meteorological features and established the statistical nature of tropospheric effects on the total horizontal positioning error. These findings were used to develop candidate models for estimating the tropospheric contribution to total satellite positioning errors. The above candidate models were analyzed based on predetermined performance criteria. A prognostic model obtained using the linear regression method was chosen as the best candidate model. Furthermore, the dissertation proposes a new approach to describing and predicting satellite positioning errors based on the known current state of the troposphere in the immediate vicinity of the satellite navigation receiver, and expressed using descriptive variables: temperature, air pressure and humidity. The dissertation analyzes existing error correction models in measuring pseudoranges based on tropospheric delays of satellite signals, occurring as indirect causes of degradation in positioning accuracy using the satellite navigation system, and discusses associated shortcomings and limitations. The position estimation process is also analyzed in the dissertation. Based on theoretical considerations, the dissertation identifies the essential difference between measurements of pseudo-distance errors and position determination errors, and subsequently proposing a new model for mathematical transformation (transition) of pseudo-distance measurement errors into position determination errors. The dissertation proposes a new model, based on supervised statistical learning, which directly connects the tropospheric delay of a satellite signal in determining position along with the accuracy requirements in determining the position of individual basic navigation tasks in marine surface navigation. Moreover, a new model for classifying navigation tasks in marine surface navigation based on position accuracy requirements is proposed. Finally, the dissertation proposes a model for the mathematical transformation of the tropospheric delay of a satellite positioning signal into a satellite-based positioning error caused by tropospheric effects. These models are the scientific contributions of the dissertation. The proposed models were evaluated using the example of long-term experimental observations. Their potential limitations in application (accuracy, comprehensiveness, applicability of computer performance, etc.) were considered in a critical manner, thus highlighting potential topics for future research. Finally, the results have been considered in terms of various applications in maritime surface navigation, especially in navigation procedures for the requirements of the navy.