Ionospheric effects on Earth-satellite paths using MQP modelling and Nelder-Mead optimisation

The problem is considered of determining the radio propagation path(s) from a particular satellite location at a particular time to an Earth-based or low altitude satellite receiver, or vice-versa, taking into account the effect of the ionosphere on the ray path and thus also determining the phase and group delay introduced by the ionosphere. Both initial elevation and azimuth are automatically adjusted to find the path that arrives exactly at the receiver. The method can be used for any 3D ionospheric model to find precise ray paths or the group delay difference between rays of different frequency employed on the same Earth-satellite link, e.g. GPS. The method either uses an analytical ray-trace method based on an MQP (multiquasi-parabolic) model fit to the entire ionosphere (bottomside and topside) or, to also include full account of the geomagnetic field and the bending of the ray path resulting from horizontal as well as vertical gradients of electron density, a numerical 3D ray-tracing model. The latter can be expanded to include protonospheric contributions to the group path and can then enable accurate ionospheric and protonospheric correction for single frequency satellite navigation systems.