Automatica, Vol.41, No.2, 197-208, 2005
Regularization aspects in continuous-time model identification
This paper presents an analysis of some regularization aspects in continuous-time model identification. The study particulary focuses on linear filter methods and shows that filtering the data before estimating their derivatives corresponds to a regularized signal derivative estimation by minimizing a compound criterion whose expression is given explicitly. A new structure based on a null phase filter corresponding to a true regularization filter is proposed and allows to discuss the filter phase effects on parameter estimation by comparing its performances with those of the Poisson filter-based methods. Based on this analysis, a formulation of continuous-time model identification as a joint system input-output signal and model parameter estimation is suggested. In this framework, two linear filter methods are interpreted and a compound criterion is proposed in which the regularization is ensured by a model fitting measure, resulting in a new regularization filter structure for signal estimation. (C) 2004 Elsevier Ltd. All rights reserved.