An automatic piloting device utilizing a measurement of ground speed deduced from the measurements of acceleration originating from an AHRS attitude and heading platform which it readjusts by ground speed information provided by a T readjustment device: satellite-based positioning receiver or a Doppler radar exhibiting periods of unavailability. This automatic piloting device includes a preprocessing part with readjustment blocks based on estimator filters of the complementary type of second order with two branches one of the first order, the other of the second order which are momentarily transformed into first-order complementary filters, by action on their branch gains, with each return of availability of the readjustment device.