Path length of curved RF trajectories through vertically stratified and isotropic ionospheres

Global navigation satellite systems (GNSS) require the removal of ionospheric-induced range errors for high geolocation accuracy. At the GHz frequencies used by GNSS, ionospheric correction is calculated by perturbative expansion in plasma frequency assuming a vertically stratified or isotropic ionosphere. Currently, these techniques are limited by formal analytic difficulties in calculating ionospheric dispersion along a curved ray path. Building on the earlier work of Roussel-Dupre et al., we have developed a new perturbation scheme that overcomes the current difficulties associated with refractive ray bending. In this short paper, we present exact perturbative expressions for excess path length in vertically stratified and isotropic ionospheres, accurate to 6th order in the ratio of plasma frequency to wave frequency.