Kernel Regularization for Low-Frequency Decay Systems

This paper discusses a kernel regularization method in the frequency domain. In particular, this paper proposes a new kernel which encodes prior knowledge on the rate of low frequency decay. Since the proposed kernel is designed for frequency response rather than impulse response, it becomes possible to estimate unstable systems. A numerical example with unstable system is shown to demonstrate the effectiveness of the proposed method.

I. INTRODUCTION

A classical approach of system identification for complex dynamic systems is to use the least squares method and model selection (e.g., Akaike Information Criteria, AIC) [1]. However, most of the model selection methods tune the model complexity in a discrete manner, i.e., tune the number of model parameters. More flexible approach which employs regularized least squares method with finite impulse response model is introduced in 2010s [2], [3]. This approach, which is called kernel regularization, tunes the model complexity by a real parameter, thus allowing for more flexibility compared to the classical approach [4], [5]. From the above background, many works on kernel regularization have been reported; e.g., kernel design [6], [7], kernel properties [8]–[10], hyperparameter tuning [11]–[13], input design [14]–[16], and so on.