A numerical algorithm for filtering and state observation

We explore the regularization techniques to construct both numerical observers and smooth filters. Assuming that the observation data are given at equally spaced instants and verify certain statistical properties, we develop a new discrete smoothing algorithm that permits the estimation of not only the continuous signal but also the continuous higher derivatives of this signal. The paper focuses on the computational steps of the algorithm conceived to be a key element in the structure of the numerical observer discussed in the author's previous paper (1997). The presented algorithm seems to be flexible because of the introduction of equivalent conditions of smoothness derived from finite difference methods. Satisfactory results have been obtained showing the efficiency of such an algorithm.