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The ionosphere and atmosphere may have significant impacts on the high-stable navigational signals of the Global Positioning System (GPS) in the communication link satellite to satellite. The classification of the different types of the ionospheric impact on the phase and amplitude of the GPS signals at altitudes of 40-90 km is introduced using the CHAllenging Minisatellite Payload (CHAMP) radio occultation (RO) data. An analytical model is elaborated for the description of the radio wave propagation in the stratified ionosphere and atmosphere. The propagation medium consists of sectors having the spherically symmetric distributions of refractivity. The newly developed model presents analytical expressions for the phase path and refractive attenuation of radio waves. The model explains significant amplitude and phase variations at altitudes of 40-90 km of the RO ray perigee associated with the influence of the inclined ionospheric layers. An innovative eikonal acceleration technique is described and applied to the identification and location of the inclined ionospheric layers using the comparative analysis of the amplitude and phase variations of the RO signals.