Method and system for aircraft navigation

A system for aircraft navigation along a predetermined airway, including an on-board navigation system and including an electronic computing device including at least a processor and a memory unit, supplying a positioning integrity of the aircraft during flight relative to said airway respecting an expected position precision performance level, and at least one on-board radio receiver on the aircraft suitable for communicating with at least one land-based radio beacon suitable for supplying a distance of the aircraft relative to said radio beacon,

• the electronic computing device comprising the at least one processor in a navigation phase of the aircraft and configured to:
• obtain, from a current position of the aircraft, from data stored in said memory unit, a tuple of N radio beacons to be used,
• obtain, by at least one of said on-board receivers, a distance measurement of the aircraft relative to each of the N radio beacons of said tuple,
• a compute an integrity position, with a probabilistic protection radius around the computed integrity position, from distance measurements obtained using a predetermined computing method, and
• implement the computed integrity position as current integrity position.