© 2015, Springer-Verlag Berlin Heidelberg.This paper presents a fast and accurate algorithm for high-frequency trans-ionospheric path length determination. The algorithm is merely based on the solution of the Eikonal equation that is solved using the conformal theory of refraction. The main advantages of the algorithm are summarized as follows. First, the algorithm can determine the optical path length without iteratively adjusting both elevation and azimuth angles and, hence, the computational time can be reduced. Second, for the same elevation and azimuth angles, the algorithm can simultaneously determine the phase and group of both ordinary and extra-ordinary optical path lengths for different frequencies. Results from numerical simulations show that the computational time required by the proposed algorithm to accurately determine 8 different optical path lengths is almost 17 times faster than that required by a 3D ionospheric ray-tracing algorithm. It is found that the computational time to determine multiple optical path lengths is the same with that for determining a single optical path length. It is also found that the proposed algorithm is capable of determining the optical path lengths with millimeter level of accuracies, if the magnitude of the squared ratio of the plasma frequency to the transmitted frequency is less than $$1.33\times 10^{-3}$$1.33×10-3, and hence the proposed algorithm is applicable for geodetic applications.

Geometrical optics,Ionospheric propagation effects,Ray tracing,Space geodesy,Trans-ionospheric signals

https://doi.org/10.1007/s00190-015-0843-z