A motion controller for the autonomous mobile vehicle commands the robot's drive mechanism to keep the robot near its desired path at all times. In order for the controller to behave properly, the controller must know the robot's position at any given time. The controller uses the information provided by the optical encoders attached to the wheels to determine vehicle position. The author analyzes the effect of measurement errors, wheel slippage, and noise on the accuracy of the estimated vehicle position obtained in this manner. Specifically the location estimator and its uncertainty covariance matrix are derived.>