The present paper proposes a successful application of differential evolution (DE) optimized fuzzy logic supervisors (FLS) to improve the quality of solutions that extended Kalman filters (EKFs) can offer to solve simultaneous localization and mapping (SLAM) problems for mobile robots and autonomous vehicles. The utility of the proposed system can be readily appreciated in those situations where an incorrect knowledge of Q and R matrices of EKF can significantly degrade the SLAM performance. A fuzzy supervisor has been implemented to adapt the R matrix of the EKF online, in order to improve its performance. The free parameters of the fuzzy supervisor are suitably optimized by employing the DE algorithm, a comparatively recent method, popularly employed now-a-days for high-dimensional parallel direct search problems. The utility of the proposed system is aptly demonstrated by solving the SLAM problem for a mobile robot with several landmarks and with wrong knowledge of sensor statistics. The system could successfully demonstrate enhanced performance in comparison with usual EKF-based solutions for identical environment situations.