Numerically Efficient and Stable Algorithms for Kernel-Based Regularized System Identification Using Givens-Vector Representation

TL;DR

This paper introduces a Givens-vector based algorithm for kernel regularized system identification that improves numerical stability and accuracy while maintaining computational efficiency.

Contribution

It proposes an alternative Givens-vector representation for kernel matrices, enhancing numerical stability over existing generator-based methods.

Findings

Algorithms are more accurate than existing methods.

Maintains the same computational complexity as state-of-the-art.

Demonstrated effectiveness through Monte Carlo simulations.

Abstract

Numerically efficient and stable algorithms are essential for kernel-based regularized system identification. The state of art algorithms exploit the semiseparable structure of the kernel and are based on the generator representation of the kernel matrix. However, as will be shown from both the theory and the practice, the algorithms based on the generator representation are sometimes numerically unstable, which limits their application in practice. This paper aims to address this issue by deriving and exploiting an alternative Givens-vector representation of some widely used kernel matrices. Based on the Givens-vector representation, we derive algorithms that yield more accurate results than existing algorithms without sacrificing efficiency. We demonstrate their usage for the kernel-based regularized system identification. Monte Carlo simulations show that the proposed algorithms admit the same order of computational complexity as the state-of-the-art ones based on generator representation, but without issues with numerical stability.