A method has been proposed to estimate the fundamental matrix of a positing and monitoring binocular vision system with a long working distance and a large field of view. Because of the long working distance and large field of view, images grabbed by this system are seriously blurred, leading to a lack of local features. The edge points are acquired using the Canny algorithm firstly, then the pre-matched points are obtained by the GMM-based points sets registration algorithm, and eventually the fundamental matrix are estimated using the RANSAC algorithm. In actual application, two cameras are 2km away from the object, the fundamental matrix are figured out, and the distance between each point and the corresponding epipolar line is less than 0.8 pixel. Repeated experiments indicate that the average distances between the points and the corresponding epipolar lines are all within 0.3 pixel and the deviations of the distances are all within 0.3 pixel too. This method takes full advantage of the edges in the environment and does not need extra control points, whats more, it can work well in low SNR images.