Efficient and Stable Implementation of Algorithms for Kernel-based Regularized System Identification using Givens-vector Representation

Numerically efficient and stable implementation of algorithms is essential for the kernel-based regularized system identification in practice. The state of art algorithms explore 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, and thus limits its application in practice. In this paper, we aim to address this issue, and we consider the alternative Givens-vector representation of semiseparable kernels instead, which is numerically more stable but often much harder to derive. In particular, we derive the Givens-vector representation of some widely used kernel matrices. Then, we design algorithms based on the Givens-vector representation. 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 with more stable and accurate implementation.