Open AccessContinuous‐time linear time‐varying system identification with a frequency‐domain kernel‐based estimator
Author(s) -
Lataire John,
Pintelon Rik,
Piga Dario,
Tóth Roland
Publication year - 2017
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/iet-cta.2016.0385
Subject(s) - estimator , kernel (algebra) , mathematics , kernel regression , minimum variance unbiased estimator , ordinary differential equation , frequency domain , control theory (sociology) , mathematical optimization , computer science , differential equation , statistics , artificial intelligence , mathematical analysis , control (management) , combinatorics
A novel estimator for the identification of continuous‐time linear time‐varying systems is presented in this paper. The estimator uses kernel‐based regression to identify the time‐varying coefficients of a linear ordinary differential equation, based on noisy samples of the input and output signals. The estimator adopts a mixed time‐ and frequency‐domain formulation, which allows it to be formulated as the solution of a set of algebraic equations, without relying on finite differences to approximate the time derivatives. Since a kernel‐based approach is used, the model complexity selection of the time‐varying parameters is formulated as an optimisation problem with continuous variables. Variance and bias expressions of the estimate are derived and validated on a simulation example. Also, it is shown that, in highly noisy environments, the proposed kernel‐based estimator provides more reliable results than an ‘Oracle’‐based estimator which is deprived of regularisation.