A numerical algorithm for filtering and state observation

This paper is dealing with a numerical method for data-fitting and estimation of the continuous higher derivatives of a given signal from its non-exact sampled data. The proposed algorithm is a generalization of the algorithm proposed by C.H. Reinsch (1967). This algorithm is conceived as being a key element in the structure of the numerical observer discussed in our last papers. The presented algorithm seems to be flexible because of the introduction of equivalent conditions of smoothness derived from finite difference methods. Detailed steps of the computational method are given to evaluate the continuous approximates of higher derivatives of a signal given by its noisy discrete values together with the filtered continuous signal. Satisfactory results have been obtained showing the efficiency of such an algorithm