This paper describes a novel tracking filter, designed primarily for use in collision avoidance systems on autonomous surface vehicles (ASVs). The proposed methodology leverages real-time kinematic information broadcast via the Automatic Information System (AIS) messaging protocol, in order to estimate the position, speed, and heading of nearby cooperative targets. The state of each target is recursively estimated in geodetic coordinates using an unscented Kalman filter (UKF) with kinematic equations derived from the spherical law of cosines. This improves upon previous approaches, many of which employ the extended Kalman filter (EKF), and thus require the specification of a local planar coordinate frame, in order to describe the state kinematics in an easily differentiable form. The proposed geodetic UKF obviates the need for this local plane. This feature is particularly advantageous for long-range ASVs, which must otherwise periodically redefine a new local plane to curtail linearization error. In real-world operations, this recurring redefinition can introduce error and complicate mission planning. It is shown through both simulation and field testing that the proposed geodetic UKF performs as well as, or better than, the traditional plane-Cartesian EKF, both in terms of estimation error and stability.