Estimation of Atmospheric Radio Refraction Errors for Ground Stations

In communications between ground stations and vehicles, including launch vehicles and satellites, radio waves are bent owing to the vertical gradient of atmospheric refractivity. The refraction errors of the ground stations can be estimated based on the true positions of the vehicles. This study proposes algorithms to estimate the refractive elevation angle error by utilizing a bisection search based on ray tracing, where the lower and upper bounds are derived from the true elevation angle and range. The refractive range and altitude errors are determined accordingly, and the radio refractivity is modeled to decay exponentially with altitude from surface weather observations. As a case study, the radar estimation results are presented for the flight of a launch vehicle whose altitude ranges from the ground to 700 kilometers (km). At the radar station, the surface refractivity at sea level and scale height are computed from weather observations as 369.2 N-units and 6.07 km, respectively, showing differences from the reference values of 315 N-units and 7.35 km. In the latter part of tracking, the mean deviation between the estimated and measured altitudes using the proposed scheme is several meters, while those obtained from the reference refractivity model and formulas in previous studies are around 2 km. The estimation of refraction errors can be improved by the proposed method, even when the meteorological conditions of ground stations differ significantly from the reference atmosphere or the altitudes of vehicles are low. Moreover, refractive error processing on radar data is investigated in the case of the remote control of antenna systems for ground stations.