On the determination of the effect of horizontal ionospheric gradients on ranging errors in GNSS positioning

An alternative approach to the traditionally employed method is proposed for treating the ionospheric range errors in transionospheric propagation such as for GNSS positioning or satellite-borne SAR. It enables the effects due to horizontal gradients of electron density (as well as vertical gradients) in the ionosphere to be explicitly accounted for. By contrast with many previous treatments, where the expansion of the solution for the phase advance is represented as the series in the inverse frequency powers and the main term of the expansion corresponds to the true line-of-sight distance from the transmitter to the receiver, in the alternative technique the zero-order term is the rigorous solution for a spherically layered ionosphere with any given vertical electron density profile. The first-order term represents the effects due to the horizontal gradients of the electron density of the ionosphere, and the second-order correction appears to be negligibly small for any reasonable parameters of the path of propagation and its geometry for VHF/UHF frequencies. Additionally, an “effective” spherically symmetric model of the ionosphere has been introduced, which accounts for the major contribution of the horizontal gradients of the ionosphere and provides very high accuracy in calculations of the phase advance.