This work addresses the problem of fault detection and diagnosis (FDD) for a quad-rotor mini aerial vehicle (MAV). Actuator faults are considered on this paper. The basic idea behind the proposed method is to estimate the faults signals using the extended state observers theory. To estimate the faults, a polynomial observer is presented by using the available measurements and know inputs of the system. In order to investigate the observability and diagnosability properties of the system, a differential algebra approach is proposed. Furthermore, an evaluation function depending on the system states is developed, in order to be used in a controller, which will compensate the failures. The effectiveness of the methodology is illustrated by means of numerical simulations and some experimental tests.