Method of estimation of the speed of an aircraft relative to the surrounding air, in a reference frame tied to the aircraft estimates an estimated static pressure on the basis of measurements of geographical altitude. The process then estimates a first intermediate variation of the speed of the aircraft relative to the surrounding air using explicitly the fact that the pressure measured by the static probe is falsified by a known quantity under the effect of the speed of the aircraft relative to the surrounding air. Finally, temporal integration of the first intermediate variation of the speed of the aircraft relative to the surrounding air provides an estimated speed of the aircraft relative to the surrounding air.