Impulse Response Estimation of Linear Time-Invariant Systems Using Convolved Gaussian Processes and Laguerre Functions

Cristian Guarnizo, Mauricio A. Álvarez

Abstract: This paper presents a novel method to estimate the impulse response function of Linear Time-Invariant systems from input-output data by means of Laguerre functions and Convolved Gaussian Processes. We define a new non-stationary covariance function that encodes the convolution between the Laguerre functions and the input. The input (excitation) is modelled by a Gaussian Process prior. Thus, we are able to estimate the system’s impulse response by performing maximum likelihood estimation over the model hyperparameters. Besides, the proposed model performs well in missing and noisy data scenarios.