Mathematical Modeling of Atmospheric Effects on Distance Determination Accuracy in the VDES R-Mode System

This paper investigates the impact of atmospheric conditions on distance determination accuracy in the VDES R-Mode system, based on system development and long-term analytical work conducted within the ORMOBASS project. A dedicated VDES R-Mode transmitter and monitoring station were developed and deployed in Poland, in the Port of Gdynia and at the boatswain's office in the port of Jastarnia, respectively. Both stations were synchronized in time and frequency using a fiber-optic link and White Rabbit technology, ensuring high-precision and stable operation during long-term measurements. Based on a one-year stationary measurement campaign, a comprehensive dataset combining ranging results and meteorological observations was collected and analyzed. Statistical evaluation demonstrated that atmospheric conditions-particularly rainfall intensity and water vapor density-have a measurable impact on ranging accuracy. These findings motivated the development of a mathematical model describing the relationship between atmospheric conditions and distance measurement errors. The proposed logarithmic regression-based approach was validated using real measurement data; the authors also demonstrated its ability to reduce error variability during changing weather conditions, indicating its potential for future implementation in VDES R-Mode receivers.