A hyper-parameter estimation algorithm in kernel based regularization approach for system identification using Kautz kernels

A Bayesian approach for system identification using kernel functions is a popular method. The kernel functions are considered as certain prior knowledge about a target system, so selecting proper kernels is required. Recent studies show that it is successful to use OBF-s(orthonormal basis function)-based kernels as the kernel functions, but estimating hyper-parameters of the kernel functions is a difficult problem. We propose a suitable algorithm to estimate hyperparameter in the empirical Bayesian framework when Kautz kernels, one of the OBF-s kernels, are used and show the efficiency of the algorithm by a numerical simulation.