Provided are apparatus and methods for tracking a volume of interest in threedimensionsin real time, using fewer than 6 DOF tracking information together with anexternal 6 DOFcoordinate system. The apparatus and methods described herein provide moreaccurate, smaller,and less expensive tracking systems than prior approaches based on full 6 DOFtrackingcomprising translation and full orientation information. Embodiments may beused inapplications such as surgical navigation, gaming, robotics, motion capture,and training.