Underwater positioning plays a crucial role in the operation of autonomous underwater vehicles (AUVs). When multiple AUVs collaborate for positioning, higher accuracy can typically be achieved. However, traditional cooperative positioning models often overlook the impact of hydroacoustic propagation delay on model mismatch, which can degrade positioning performance. To tackle this issue, this study proposes a master–slave AUV cooperative positioning framework that accounts for hydroacoustic propagation delay. Additionally, an adaptive unscented Kalman filter (AUKF) algorithm is introduced to address the problem. The effectiveness of the proposed method is evaluated through simulation experiments, where it is compared against the extended Kalman filter (EKF) and unscented Kalman filter (UKF). The results demonstrate that the new approach significantly enhances co-location accuracy compared to EKF and UKF.