Nonlinear System Identification With Gaussian Processes Using Laguerre and Kautz Filters

System identification can be used to determine data-driven mathematical models of dynamic processes. For nonlinear processes, model architectures that are as flexible as possible are required. One possibility is to utilize Gaussian processes (GPs) as a universal approximator with an external dynamics realization, leading to highly flexible models. Novel Laguerre and Kautz filter-based dynamics realizations in GP models are proposed. The Laguerre/ Kautz pole(s) are treated as hyperparameters with the GPs’ standard hyperparameter for the squared exponential kernel with automatic relevance determination (SE-ARD) kernel. The two novel dynamics realizations in GP models are compared to different state-of-the-art dynamics realizations such as finite impulse response (FIR) or autoregressive with exogenous input (ARX). The big data case is handled via support points. Using Laguerre and Kautz regressor spaces allows both the dimensionality of the regressor space to be kept small and achieve superior performance. This is demonstrated through numerical examples and measured benchmark data of a Wiener–Hammerstein process. Copyright © 2025 by ASME.