author = "Ara{\'u}jo, Amar{\'{\i}}sio S. and Furtado, Helaine C. M. and 
                         Campos Velho, Haroldo Fraga de",
                title = "q-Calculus formalism for non-extensive particle filter",
            booktitle = "Integral methods in science and engineering",
            publisher = "Springer",
                 year = "2019",
               editor = "Constanda, Christian and Harris, Paul",
                pages = "25--35",
              address = "Brighton, UK",
             keywords = "q-Calculus, non-extensive entropy, particle filter.",
             abstract = "A class of sequential Monte Carlo estimation is frequently called 
                         particle filter. This filter belongs to the Bayesian strategy for 
                         estimation, where a no-linear and no-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 NEc-PF can compute the 
                         standard form of the central limit theorem, as weel as the 
                         Levy-Gnedenko central limit theorem. The q-calculus formalism is 
                         employed to generalize some definitions and properties.",
          affiliation = "{Universidade Federal de Vi{\c{c}}osa (UFV)} and {Universidade 
                         Federal do Oeste do Par{\'a} (UFOPA)} and {Instituto Nacional de 
                         Pesquisas Espaciais (INPE)}",
                 isbn = "978-3-030-16077-7",
             language = "en",
           targetfile = "araujo_calculus.pdf",
        urlaccessdate = "24 nov. 2020"