Augmented reality requires the geometric registration of virtual or remote worlds with the visual stimulus of the user. This can be achieved by tracking the head pose of the user with respect to the reference coordinate system of virtual objects. If tracking is achieved with head-mounted cameras, registration is known in computer vision as pose estimation. Augmented reality is by definition a real-time problem, so we are interested only in bounded and short computational time. We propose a new linear algorithm for pose estimation. Our algorithm shows better performance than the linear algorithm of Quan and Lan [14] and is comparable to the non-predicted time iterative approach of Kumar and Hanson [8].