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

Guarnizo, Cristian; López, Mariano Jiménez

doi:10.1007/978-3-319-75193-1_34

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A High-dimensional Input Example1

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2018

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“…kernel with an EQ form, but it is also possible to use smoothing kernels that correspond to Green's function of dynamical systems. Automatically learning the smoothing kernel from data is also an alternative as for example in Guarnizo and Álvarez [2017].…”

Section: A High-dimensional Input Examplementioning

confidence: 99%

Non-linear process convolutions for multi-output Gaussian processes

Álvarez¹,

Ward²,

Guarnizo³

2018

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The paper introduces a non-linear version of the process convolution formalism for building covariance functions for multi-output Gaussian processes. The non-linearity is introduced via Volterra series, one series per each output. We provide closed-form expressions for the mean function and the covariance function of the approximated Gaussian process at the output of the Volterra series. The mean function and covariance function for the joint Gaussian process are derived using formulae for the product moments of Gaussian variables. We compare the performance of the non-linear model against the classical process convolution approach in one synthetic dataset and two real datasets.

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Section: A High-dimensional Input Examplementioning

confidence: 99%