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q-Calculus Formalism for Non-extensive Particle Filter

In: Integral Methods in Science and Engineering

Author

Listed:
  • Amarisio S. Araújo

    (Federal University of Viçosa (UFV))

  • Helaine C. M. Furtado

    (Federal University of West Pará (UFOPA))

  • Haroldo F. de Campos Velho

    (National Institute for Space Research (INPE))

Abstract

A class of sequential Monte Carlo estimation is frequently called particle filter. This filter belongs to the Bayesian strategy for estimation, where a non-linear and non-Gaussian assumptions can be applied. Here, the Tsallis’ distribution, from the non-extensive thermo-statistics, is used to design the best likelihood operator. Therefore, no previous likelihood operator is assumed. The new filter formulation will be named as non-extensive particle filter (NEx-PF). The distribution estimated by the NEx-PF can compute the standard form of the central limit theorem, as well as the Levy-Gnedenko central limit theorem. The q-calculus formalism is employed to generalize some definitions and properties.

Suggested Citation

  • Amarisio S. Araújo & Helaine C. M. Furtado & Haroldo F. de Campos Velho, 2019. "q-Calculus Formalism for Non-extensive Particle Filter," Springer Books, in: Christian Constanda & Paul Harris (ed.), Integral Methods in Science and Engineering, chapter 0, pages 25-35, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-16077-7_3
    DOI: 10.1007/978-3-030-16077-7_3
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