Tuning the hyperparameters of the filter-based regularization method for impulse response estimation

Abstract

This paper discusses the use of a filter-based method for regularized impulse response modeling for linear time-invariant systems. The proposed method is a reformulation of the Bayesian, kernel based impulse response modeling approaches. The filter interpretation of the regularization cost function allows one to develop an intuitive framework to model a wide range of systems with different properties in a flexible way. Two hyperparameter selection techniques, based on Cross Validation and on Marginal Likelihood Maximization are presented. The proposed methods are tested on Monte Carlo simulation examples and on a real robotics problem. The results are compared with the ones obtained with the kernel-based methods based on the DC and TC kernels.