Filter interpretation of regularized impulse response modeling

Kernel-based regularization techniques are constantly gaining attention in the identification world, due to their success in modeling the impulse response of linear systems. In this work, the same problem is considered from a different perspective. Instead of including prior knowledge in the definition of the covariance matrix of the parameters, here the focus is on the cost function level. The key idea is to define the regularization matrix as a filtering operation on the parameters, which allows for a more intuitive formulation of the problem from an engineering viewpoint. Moreover, this results in an effective user-friendly method to model a wide range of systems, including low-pass, band-pass and high-pass systems. The effectiveness of the proposed approach is illustrated by means of Monte Carlo simulations on five linear modeling examples, where the filter-based regularization outperforms the existing method based on the TC and DC kernels.