Extended Kalman Filtering (EKF) is proposed for: (i) the extraction of a fuzzy model from numerical data; and (ii) the localization of an autonomous vehicle. In the first case, the EKF algorithm is compared to the Gauss-Newton nonlinear least-squares method and is shown to be faster. An analysis of the EKF convergence is given. In the second case, the EKF algorithm estimates the state vector of the autonomous vehicle by fusing data coming from odometric sensors and sonars. Simulation tests show that the accuracy of the EKF-based vehicle localization is satisfactory.

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NeuroFAST is an on-line fuzzy modeling learning algorithm, featuring high function approximation accuracy and fast convergence. It is based on a first-order Takagi-Sugeno-Kang (TSK) model, where the consequence part of each fuzzy rule is a linear equation. Structure identification is performed by a fuzzy adaptive resonance theory (ART)-like mechanism, assisted by fuzzy rule splitting and adding procedures. The well known delta rule continuously performs parameter identification on both premise and consequence parameters. Simulation results indicate the potential of the algorithm. It is worth noting that NeuroFAST achieves a remarkable performance in the Box and Jenkins gas furnace process, outperforming all previous approaches compared.