This paper proposes a neural network controller using a new efficient optimisation algorithm for learning that is the Levenberg-Marquart Iterated Extended Kalman filter LM-IEKF. The trained neural network is applied to control a wheeled mobile robot for trajectory tracking problem. The proposed algorithm is compared to the standard extended Kalman filter and the back-propagation algorithms. Simulation and experimental results using MATLAB 7.1 and National Instrumentation mobile robot (starter kit 2.0) respectively show that in terms of mean squared errors, the proposed algorithm is superior to the extended Kalman filter and back-propagation. This indicates that LevenbergMarquart iterated extended Kalman filter based neural networks learning could be a good alternative in the artificial neural networks based applications for mobile robot trajectory tracking.

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