  Frequency response function (FRF) estimation is a classical subject in system
identification. In the past two decades, there have been remarkable advances in
developing local methods for this subject, e.g., the local polynomial method,
local rational method, and iterative local rational method. The recent
concentrations for local methods are two issues: the model order selection and
the identification of lightly damped systems. To address these two issues, we
propose a new local method called local Gaussian process regression (LGPR). We
show that the frequency response function locally is either analytic or
resonant, and this prior knowledge can be embedded into a kernel-based
regularized estimate through a dot-product kernel plus a resonance kernel
induced by a second-order resonant system. The LGPR provides a new route to
tackle the aforementioned issues. In the numerical simulations, the LGPR shows
the best FRF estimation accuracy compared with the existing local methods, and
moreover, the LGPR is more robust with respect to sample size and noise level.
