The problem of unknown input estimation and compensation is studied for actuated nonlinear systems with noisy measure-ments. The proposed solution is based on high order sliding-mode differentiation and discrete-time optimization technique. Accuracy of the proposed hybrid estimation scheme is evaluated and stability conditions of the compensating mechanism are established. It is shown that the fault detection delay as well as the smallest detectable fault magnitude can be estimated. Efficiency of the proposed approach is demonstrated through the oscillatory failure detection and compensation in aircraft surface servo loops.