This paper presents a novel method for the dynamic positioning of an unmanned underwater vehicle (UUV) with unknown trajectories based on an autonomous tracking buoy (PUVV-ATB) that indirectly positions the UUV using ultra-short baseline measurements. The method employs a spatial location geometric model and divides the positioning process into four steps, including data preprocessing to detect geometric errors and apply mean filtering, direction capture, position tracking, and position synchronization. To achieve these steps, a new adaptive tracking control algorithm is proposed that does not require trajectory prediction and is applied to the last three steps. The algorithm is deployed to the buoy for tracking simulation and sea trial experiments, and the results are compared with those of a model predictive control algorithm. The autonomous tracking buoy based on the adaptive tracking control algorithm runs more stably and can better complete the precise tracking task for the UUV with a positioning error of less than 10 cm. This method breaks the premise of trajectory prediction based on traditional tracking control algorithms, providing a new direction for further research on UUV localization. Furthermore, the conclusion of this paper has important reference value for other research and application fields related to UUV.