Filter-based regularisation for impulse response modelling

Anna Marconato, Maarten Schoukens, Joannes Schoukens

Research output: Contribution to journalArticle

14 Citations (Scopus)

Abstract

In the last years, the success of kernel-based regularisation techniques in solving impulse response modelling tasks has revived the interest on linear system identification. In this work, an alternative perspective on the same problem is introduced. Instead of relying on a Bayesian framework to include assumptions about the system in the definition of the covariance matrix of the parameters, here the prior knowledge is injected at the cost function level. The key idea is to define the regularisation matrix as a filtering operation on the parameters, which allows for a more intuitive formulation of the problem from an engineering point of view. Moreover, this results in a unified framework to model low-pass, band-pass and high-pass systems, and systems with one or more resonances. The proposed filter-based approach outperforms the existing regularisation method based on the TC and DC kernels, as illustrated by means of Monte Carlo simulations on several linear modelling examples.
Original languageEnglish
Pages (from-to)194 – 204
Number of pages11
JournalIET Control Theory and Applications
Volume11
Issue number2
DOIs
Publication statusPublished - 20 Jan 2017

Keywords

  • high-pass filters
  • band-pass filters
  • Monte Carlo methods
  • covariance matrices
  • linear systems
  • transient response
  • identification
  • low-pass filters
  • linear system identification
  • kernel-based regularisation techniques
  • regularisation matrix
  • linear systems
  • cost function level
  • DC kernels
  • filter-based regularisation
  • low-pass system
  • high-pass systems
  • TC kernels
  • Monte Carlo simulations
  • parameter covariance matrix
  • filter-based approach
  • band-pass system
  • filtering operation
  • impulse response modelling

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