On Kernel Design for Regularized Non-Causal System Identification

TL;DR

This paper develops systematic methods for designing kernels in regularized non-causal system identification, introducing the NCSI kernel and analyzing its properties to improve identification accuracy.

Contribution

It introduces the NCSI kernel for non-causal systems, extending the system theoretic framework and analyzing its structural properties for better kernel design.

Findings

NCSI kernel outperforms existing kernels in simulations

Structural properties like stability and semiseparability are established

Guidelines for kernel design in non-causal systems are provided

Abstract

Through one decade's development, the kernel-based regularization method (KRM) has become a complement to the classical maximum likelihood/prediction error method and an emerging new system identification paradigm. One recent example is its application in the non-causal system identification, and the key issue lies in the design and analysis of kernels for non-causal systems. In this paper, we develop systematic ways to deal with this issue. In particular, we first introduce the guidelines for kernel design and then extend the system theoretic framework to design the so-called non-causal simulation-induced (NCSI) kernel, and we also study its structural properties, including stability and semiseparability. Finally, we consider some special cases of the NCSI kernel and show their advantage over the existing kernels through numerical simulations.