  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.
