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Student-t Process Quadratures for Filtering of Non-Linear Systems with Heavy-Tailed Noise

Abstract · Mar 15, 2017 14:47 ·

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Arxiv Abstract

  • Jakub Prüher
  • Filip Tronarp
  • Toni Karvonen
  • Simo Särkkä
  • Ondřej Straka

The aim of this article is to design a moment transformation for Student- t distributed random variables, which is able to account for the error in the numerically computed mean. We employ Student-t process quadrature, an instance of Bayesian quadrature, which allows us to treat the integral itself as a random variable whose variance provides information about the incurred integration error. Advantage of the Student- t process quadrature over the traditional Gaussian process quadrature, is that the integral variance depends also on the function values, allowing for a more robust modelling of the integration error. The moment transform is applied in nonlinear sigma-point filtering and evaluated on two numerical examples, where it is shown to outperform the state-of-the-art moment transforms.

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