An approach for fuzzy Kalman filter modeling based on evolving clustering of experimental data

A methodology to systems identification based on Evolving Fuzzy Kalman Filter, is proposed in this paper. The mathematical formulation using an evolving Takagi-Sugeno (TS) structure, is presented: the offline Gustafson Kessel (GK) algorithm is used for initial parametrization of antecedent of the fuzzy Kalman filter inference system, considering an initial data set; and an evolving version of the GK algorithm is developed for online parametrization of antecedent of the fuzzy Kalman filter inference system. A fuzzy recursive version of OKID (Observer/Kalman Filter Identification) algorithm is proposed for parametrizing the matrices A, B, C, D and K (state matrix, input influence matrix, output influence matrix, direct transmission matrix, and Kalman gain matrix, respectively), in the consequent of the fuzzy Kalman filter inference system. Computational and experimental results from the estimation of the states and outputs of a dynamic system and a two-degree-of-freedom (2DoF) Helicopter, respectively, show the efficiency and applicability of the proposed methodology.