An apparatus (10) for winding a screen (12) comprises a winding drum (14) for winding the screen (12) which can rotate about an axis of rotation (16) with respect to a fixed frame of reference over more than one revolution between at least one first end-of-travel position and a second end-of-travel position, a motor assembly (30) comprising a motor (32) equipped with a stator (32.1) intended to be fixed to a fixed support (23, 26) and a rotor (32.2) kinematically connected to the winding drum (14). A first measurement assembly (51) comprises a first encoder (46) secured to the rotor (32.2), a first sensor for reading the first encoder (46) and generating a first counting signal when the first encoder (46) turns. First processing means (50) generate, as a function of the first counting signal, a first signal indicative of the position of the screen, which signal is monotonous when the drum moves from the first end-of-travel position to the second end-of-travel position. A second measurement assembly (64) makes it possible to detect at least one indexed position of the drum (14) per revolution of the drum in the fixed frame of reference. A calibration memory (56) stores at least one first calibration value for the first signal indicative of the position of the screen in the indexed position of the drum and at least one first quantitative algebraic comparison between a current value of the first signal indicative of the position of the screen as measured on passing through the indexed position during an observation phase and the first calibration value is delivered.