The invention relates to an apparatus for cleaning an immersed surface, comprising a hollow body, guiding and driving members, a filtration chamber which is provided in the hollow body and which has at least one liquid inlet, at least one liquid outlet and a hydraulic circuit for circulation of liquid through a filtering device. An accelerometer device is fixedly joined to the hollow body and which is adapted to provide instantaneous measurements of at least one acceleration component of the terrestrial gravity in at least one fixed direction which is fixed relative to the hollow body, and a processing unit for processing the acceleration measurements supplied by the accelerometer device.