Estimating the speed of an aircraft estimates three components of the speed vector (TAS, AOA, SSA) of an aircraft relative to the surrounding air. The static pressure is estimated on the basis of measurements of geographical altitude. A first intermediate variation of a linear combination of the three components of the speed vector of the aircraft relative to the surrounding air is estimated using explicitly the fact that the pressure measured by the static probe is falsified by a known quantity under the effect of the three components of this speed vector of the aircraft relative to the surrounding air. The process then estimates the three components of the speed vector of the aircraft relative to the air by likening the latter to the speed vector of the aircraft relative to an inertial reference frame and by using inertial measurements. The various estimates are fused to provide a final result.