In a mobile robotic system, complexities in positioning arise due to the motion. An adaptive position estimation scheme has been developed for an automated guide vehicle (AGV) to overcome these complexities. The scheme's purpose is to minimize the position error--the difference between the estimated position and the actual position. The method to achieve this is to adapt the system model by incorporating a parameter vector and using a maximum likelihood algorithm to estimate the parameters after an accurate position determination is made. A simulation of the vehicle's guidance system was developed and the estimator tested on an oval-shaped path. Upon injecting biases into the system, initial position errors were 10 centimeters or more. After the estimator converged, the maximum final errors were on the order of 1 to 2 centimeters (prior to measurement update). After each measurement update, after the estimator had converged, errors were on the order of 1 to 2 millimeters.