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In this paper, non-linear observer-based trajectory tracking control for a wheeled mobile robot is proposed. The non-linear observer is designed for not only an unmeasurable orientation error but current position error. This full-order observer shows robustness to measurement noise. Besides, a controller which exponentially stabilizes the tracking error is used. The non-linear observer with the controller is asymptotically stable by means of persistently exciting (PE) condition and cascaded system theory. A proof of stability and simulation results are given.