An estimation system includes a module for measuring a current angle of attack and current flight parameters of the aircraft, a module for estimating a current lift coefficient of the aircraft from the current flight parameters and from a mass of the aircraft, a module for estimating an angle of attack for a zero lift from the current angle of attack, from the current lift coefficient and from a slope of an affine part of at least one theoretical curve describing a lift coefficient of the aircraft as a function of an angle of attack, a module for estimating the current position of the flaps of the aircraft from the angle of attack for a zero lift and a module for sending the current position of the flaps to a user device.