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

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10657)


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.


Convolved Gaussian Process Impulse response function Laguerre function 



Authors would like to thank Convocatoria 567 from the Administrative Department of Science, Technology and Innovation of Colombia (COLCIENCIAS) for the support and funding of this work.


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Engineering PhD ProgramUniversidad Tecnológica de PereiraPereiraColombia
  2. 2.Department of Computer ScienceThe University of SheffieldSheffieldUK

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