Autonomous Underwater Vehicle (AUV) is an important carrier for studying the ocean. AUV's accurate navigation and positioning capabilities are most important in ocean exploration. Due to the limitation of communication, the limitation of cost, and the limitation of beacon use conditions, the navigation and positioning of AUV still rely on the sensor equipped with its own dead reckoning algorithm. In the deep sea, Extended Kalman Filtering(EKF), Unscented Kalman Filtering(UKF), and Adaptive Kalman Filtering(AKF) all produce error divergence in navigation and positioning. The article adopted the acoustic-based ranging and positioning method to analyze the error under different conditions, accurately compensate the error in the dead reckoning, and finally improve the navigation and positioning accuracy. Considering the controllability and observability of AUV during ranging positioning, the article proved the stability of AUV model. The article also explained the observability and selection of paths in the ranging and positioning methods to ensure the observability of AUV. The simulation results showed that compared with the dead reckoning method using Kalman filter, the method of introducing ranging location is effective and feasible. The article considered the direction and size of the actual current, and verifies the effectiveness of the method under different conditions. The article considered the divergence of the dead reckoning error and explores the optimal path size at different depths to better obtain the actual AUV motion position. The article also discussed the research that can be done in the future. In the practical application of underwater robots, the article proposed a solution to the inaccuracy of navigation and positioning in the case of large diving depth. The results of the article have practical application value.