A new method for estimating derivatives based on a distribution approach

In 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.     

The HEATOX Project

HEATOX is the acronym for a European Union-funded project entitled Heat-Generated Food Toxicants: Identification, Characterization, and Risk Minimization. Acrylamide will be the main experimental focus, but identification of unknown toxicants in heated carbohydrate-rich foods will also be attempted. The project includes research on formation chemistry, food technology, analytical methods, hazard characterization, and exposure assessment. The results will finally be used in risk assessment and risk management advice.     

System Identifiability (Symbolic Computation) and Parameter Estimation (Numerical Computation)

A system identification based on physical laws often involves a parameter estimation. Before performing an estimation problem, it is necessary to investigate its identifiability. This investigation leads often to painful calculations. Generally, the numerical computation of the parameters does not use these calculus. In this contribution we propose least-squares methods to link identifiability approaches with numerical parameter estimation.