Algebraic estimation in partial derivatives systems: parameters and differentiation problems

International audienceTwo goals are sought in this paper: namely, to provide a succinct overview on algebraic techniques for numerical differentiation and parameter estimation for linear systems and to present novel algebraic methods in the case of several variables. The state-of-art in the introduction is followed by a brief description of the methodology in the subsequent sections. Our new algebraic methods are illustrated by two examples in the multidimensional case. Some algebraic preliminaries are given in the appendix

A new method for estimating derivatives based on a distribution approach

International audienceIn many applications, the estimation of derivatives has to be done from noisy measured signal. In this paper, an original method based on a distribution approach is presented. Its interest is to report the derivatives on infinitely differentiable functions. Thus, the estimation of the derivatives is done only from the signal. Besides, this method gives some explicit formulae leading to fast calculus. For all these reasons, it is an efficient method in the case of noisy signals as it will be confirmed in several examples

A Numerical Algorithm for Filtering and State Observation

This paper deals with a numerical method for data fitting and estimation of continuous higher-order derivatives of a given signal from its non-exactsampled data. The proposed algorithm is a generalization of the algorithm proposed by Reinsch (1967). This algorithm is conceived as a key element in the structure of the numerical observer discussed in our recent papers. Satisfactory results are obtained which prove the efficiency of the proposed approach