Eliminating diffraction effects during multi-frequency correction in global navigation satellite systems

Abstract

In the geometrical optics approximation, the ionospheric part of error in measuring phase and code delays of the satellite signal may be represented as a rapidly decreasing series in inverse power of frequency. Such a simple frequency dependence allows us to use multi-frequency measurements for eliminating the error in such multi-frequency Global Navigation Satellite Systems as GPS, GLONASS, BeiDou, and Galileo. However, the elimination of errors is handicapped by diffraction effects during signal propagation through turbulent ionospheric plasma. The numerical simulation has shown that when using the spatial processing in the form of Fresnel inversion the transition from dual-frequency to triple-frequency measurements reduces the average error of measurement. Yet fluctuations of the error diminish only if the inner scale exceeds the Fresnel radius. In the opposite case of excess of the Fresnel radius over the inner scale, the random component of the residual error is growing during the transition to triple-frequency measurements. The numerical simulation results also suggest that the Fresnel spatial processing in dual-frequency measurements at the optimal distance to the virtual screen can reduce the average error from centimeter to submillimeter level, which renders the transition to triple-frequency measurements unnecessary. The study of the residual error dependence on the distance from the virtual screen to the observer has revealed that the optimum value of this distance may be found from the minimum condition of amplitude scintillation index of the processed signal. The signal thus processed may be utilized both in geodetic precise measurements and in diagnostics of the lower atmosphere.