Fuzzy and Bayesian algorithms for nonlinear estimation problem

A problem of nonlinear estimation is considered. An approach to designing estimation algorithms based on fuzzy logic is offered. The approach suggested is compared with the well-known Bayesian approach. The conditions are determined such that the algorithms derived within these two approaches coincide. It is shown, in particular, that the fuzzy algorithm based on the Takagi-Sugeno inference that uses Gaussian membership functions and the defuzzification procedure as the centroid, will coincide with the point-mass algorithm that corresponds to the problem solution within the Bayesian approach with the Gaussian measurement errors and the vector to be estimated. The results derived are illustrated by an example.