  Extended Kalman Filter (EKF) has been a popular approach to localization a
mobile robot. However, the performance of the EKF and the quality of the
estimation depends on the correct a priori knowledge of process and measurement
noise covariance matrices (Qk and Rk, respectively). Imprecise knowledge of
these statistics can cause significant degradation in performance. This paper
proposed the development of an Adaptive Neuro- Fuzzy Extended Kalman Filtering
(ANFEKF) for localization of robot. The Adaptive Neuro-Fuzzy attempts to
estimate the elements of Qk and Rk matrices of the EKF algorithm, at each
sampling instant when measurement update step is carried out. The ANFIS
supervises the performance of the EKF with the aim of reducing the mismatch
between the theoretical and actual covariance of the innovation sequences. The
free parameters of ANFIS are trained using the steepest gradient descent (SD)
to minimize the differences of the actual value of the covariance of the
residual with its theoretical value as much possible. The simulation results
show the effectiveness of the proposed algorithm.
