q Calculus Formalism for Non extensive Particle Filter
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.