Extended Kalman filter (EKF) has been a popular choice to solve simultaneous localization and mapping (SLAM) problems for mobile robots or vehicles. However, the performance of the EKF depends on the correct a priori knowledge of process and sensor/measurement noise covariance matrices (Q and R, respectively). Imprecise knowledge of these statistics can cause significant degradation in performance. The present paper proposes the development of a new neurofuzzy based adaptive Kalman filtering algorithm for simultaneous localization and mapping of mobile robots or vehicles, which attempts to estimate the elements of the R matrix of the EKF algorithm, at each sampling instant when a ldquomeasurement updaterdquo step is carried out. The neuro-fuzzy based supervision for the EKF algorithm is carried out with the aim of reducing the mismatch between the theoretical and the actual covariance of the innovation sequences. The free parameters of the neuro-fuzzy system are learned offline, by employing particle swarm optimization in the training phase, which configures the training problem as a high-dimensional stochastic optimization problem. By employing a mobile robot to localize and simultaneously acquire the map of the environment, under several benchmark environment situations with varying landmarks and under several conditions of wrong knowledge of sensor statistics, the performance of the proposed scheme has been evaluated. It has been successfully demonstrated that in each case, the neuro-fuzzy assistance is able to improve highly unpredictable, degrading performance of the EKF and can provide robust and accurate solutions.