1. A method for detecting a failure of at least one sensor on board an aircraft comprising: measuring a vertical acceleration; measuring a pressure altitude; implementing a baro-inertial loop in a computer, the loop including: obtaining a computed vertical speed, then a short-term baro-inertial altitude, based on a double integration of the measured vertical acceleration; developing at least one intermediate loop parameter based on a deviation between the short-term baro-inertial altitude and the pressure altitude; and looping on the measured vertical acceleration before integration and/or on the vertical speed computed after integration, based on the value of at least one intermediate parameter; observing at least one failure detection parameter obtained from the at least one intermediate parameter of the baro-inertial loop; determining the presence of a failure on the at least one sensor of the aircraft based on a value of the observed failure detection parameter.