The invention relates to a navigation system for aircraft comprising inertial sensors, a GNSS receiver and potentially a baro-altimeter. The measurements from the inertial sensors are hybridized with the code and phase measurements from the receiver within a main Kalman filter and, possibly, secondary filters. The said measurements are corrected for several types of errors, notably those due to the passage of the satellite signals through the ionospheric layers. The precision of the determination of the position of the aircraft is greatly improved, both in the horizontal plane and in the vertical direction. This is also the case for the corresponding protection radii, which allows margins to be created in order to satisfy the integrity constraints for the navigation solution.