A stereovision based methodology to estimate the position, speed and heading of a moving marine vehicle from a pursuing unmanned surface vehicle (USV) is considered, in support of enabling a USV to follow a target vehicle in motion. The methodology involves stereovision ranging, object detection and tracking, and minimization of tracking error due to image quantization limitations and pixel miscorrespondences in the stereo pixel-matching process. The method consists of combining a simple stereovision-matching algorithm, together with a predictive-corrective approach based on an extended Kalman filter (EKF), and use of suitable choices of probabilistic models representing the motion of the target vehicle and the stereovision measurements. Simple matching algorithms perform faster at the expense of potential errors in depth measurement. The approach considered aims to minimize the tracking errors related to such errors in stereovision measurements, thereby improving the accuracy of the state estimation of the vehicle. Results from simulations and a real-time implementation reveal the effectiveness of the system to compute accurate estimates of the state of the target vehicle over non-compliant trajectories subjected to a variety of motion conditions.