  The presented paper tackles the problem of modeling an unknown function, and
its first $r-1$ derivatives, out of scattered and poor-quality data. The
considered setting embraces a large number of use cases addressed in the
literature and fits especially well in the context of control barrier
functions, where high-order derivatives of the safe set are required to
preserve the safety of the controlled system. The approach builds on a cascade
of high-gain observers and a set of Gaussian process regressors trained on the
observers' data. The proposed structure allows for high robustness against
measurement noise and flexibility with respect to the employed sampling law.
Unlike previous approaches in the field, where a large number of samples are
required to fit correctly the unknown function derivatives, here we suppose to
have access only to a small window of samples, sliding in time. The paper
presents performance bounds on the attained regression error and numerical
simulations showing how the proposed method outperforms previous approaches.
