Geopositioning and tracking a moving boat at sea is a very challenging problem, requiring boat detection, matching and estimating its GPS location from imagery with no common features. The problem can be stated as follows: given imagery from a camera mounted on a moving platform with known GPS location as the only valid sensor, we predict the geoposition of a target boat visible in images. Our solution uses recent ML algorithms, the camera-scene geometry and Bayesian filtering. The proposed pipeline first detects and tracks the target boats location in the image with the strategy of tracking by detection. This image location is then converted to geoposition to the local sea coordinates referenced to the camera GPS location using plane projective geometry. Finally, target boat local coordinates are transformed to global GPS coordinates to estimate the geoposition. To achieve a smooth geotrajectory, we apply unscented Kalman filter (UKF) which implicitly overcomes small detection errors in the early stages of the pipeline. We tested the performance of our approach using GPS ground truth and show the accuracy and speed of the estimated geopositions. Our code is publicly available at https://github.com/JianliWei1995/AI-Track-at-Sea.