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An adaptive estimation method is developed to generate real-time estimates of the position and orientation of the end-effector of an industrial robot and estimates of the root mean squared errors in these estimates, using real-time measurements of the position of a point on the end-effector, in addition to the usual measurements of the joint positions. To compensate for the lack of real-time measurements of the orientation of the end-effector, a Kalman filter is used to update a lookup table model of the kinematics of the robot that most affect the orientation of the end-effector. Measurements of the positions of a point on the end-effector collected during a short sequence of motions of the last axis of the robot are used by the Kalman filter to update this lookup table model. The updated lookup table model, together with real-time measurements of the position of a point on the end-effector and real-time measurements of the joint positions, is used by the estimator to compensate for the effects of geometric errors in the robot's structure and temperature variations on the position and orientation of the end-effector. In an application to a six-axis industrial robot, the adaptive estimation method is shown to substantially outperform the direct forward kinematics method whereby the position and orientation of the end-effector are estimated based upon joint position measurements alone.