A single-stage linear method is devised in this paper to simultaneously fit rotation and translation (pose) parameters given two sets of three-dimensional (3-D) point measurements. The necessary and sufficient conditions for the unique solution of the pose determination problem are stated. The computational complexity of the new algorithm is similar to the existing linear algorithms. However it offers a mechanism to incorporate the reliability of measurements and a procedure to implement the estimation recursively. Applications of the technique include localization of a robot in its environment and real-time estimation of object motion based on computer vision.