This aircraft navigation assistance system comprises an inertial navigation module adapted for providing first positional information from accelerometric and gyrometric measurements, and a module adapted for determining second positional information from satellite positioning data. The system is characterized in that it comprises means for estimating a first localization of the aircraft at a time of estimation on the basis of first positional information determined from accelerometric and gyrometric measurements at said time of estimation and second positional information determined from positioning data received prior to said time of estimation, said first localization being determined independently from any positioning data received in a time interval preceding said time of estimation, advantageously equal to a time to alert.