q-Calculus Formalism for Non-extensive Particle Filter

Amarisio S. Araújo (), Helaine C. M. Furtado () and Haroldo F. de Campos Velho ()
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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)

Chapter Chapter 3 in Integral Methods in Science and Engineering, 2019, pp 25-35 from Springer

Abstract: 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.

Date: 2019
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DOI: 10.1007/978-3-030-16077-7_3

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