Abstract: We propose a novel algorithm, based on nonlinear optimization, for calculating the position pose measurement of a rectangle with an unknown aspect ratio. With only four corresponding corner points of the rectangle, the proposed algorithm can effectively estimate its aspect ratio, the relative pose between the rectangle and the camera, and the relative position, as determined by the unit length of the side of the rectangle. By separating the calculation into two steps: the estimations of the relative position-pose and then the aspect ratio, we establish the cost function of the position pose matrix, which is represented by the theory of the Lie group. By optimizing the cost function, the position pose matrix is solved, and by using a binary search algorithm we obtain the best estimation of the aspect ratio. Our experimental results show that by using four corresponding image points we can estimate the aspect ratio with less than a 3% error rate. The proposed algorithm can also be run in real-time on a regular PC.