Filter-based regularisation for impulse response modelling

TL;DR

This paper introduces a filter-based regularisation approach for impulse response modelling, offering an intuitive and unified framework that outperforms existing kernel-based methods in linear system identification tasks.

Contribution

It presents a novel regularisation technique that injects prior knowledge through filtering operations at the cost function level, enhancing modeling flexibility and performance.

Findings

Outperforms TC and DC kernel-based methods in simulations

Unified framework for different system types

Effective for systems with multiple resonances

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.