Kernel-based system identification from noisy and incomplete input-output data

TL;DR

This paper introduces a kernel-based approach using Gaussian processes and an empirical Bayes method to identify linear systems from noisy, incomplete data, leveraging stable spline kernels and EM optimization.

Contribution

It presents a novel kernel-based system identification method that handles noisy and incomplete data using Gaussian process modeling and marginal likelihood maximization.

Findings

Effective in identifying systems from noisy, incomplete data

Uses stable spline kernel for impulse response modeling

Demonstrates success on benchmark datasets

Abstract

In this contribution, we propose a kernel-based method for the identification of linear systems from noisy and incomplete input-output datasets. We model the impulse response of the system as a Gaussian process whose covariance matrix is given by the recently introduced stable spline kernel. We adopt an empirical Bayes approach to estimate the posterior distribution of the impulse response given the data. The noiseless and missing data samples, together with the kernel hyperparameters, are estimated maximizing the joint marginal likelihood of the input and output measurements. To compute the marginal-likelihood maximizer, we build a solution scheme based on the Expectation-Maximization method. Simulations on a benchmark dataset show the effectiveness of the method.