Underwater navigation is a challenging topic in the field of underwater exploration. Accurate and effective underwater navigation is necessary in applications such as 3D seafloor topography scanning, cable laying, deep-sea resource survey and wreck salvage. However, underwater navigation becomes difficult due to the variability and complexity of underwater environment. In the deep-sea environment, the ultra-short baseline positioning system (USBL) is very unstable, and the flying abnormal points and signal loss often occur. To solve these problems, this paper proposes a two-step filtering scheme combined with doppler velocity log (DVL). The first step is to construct a rough Monte Carlo particle filter (MPF) model for the autonomous underwater vehicle (AUV) position, and then select candidate particles with the strategy of minimizing the local backward dead reckoning (DR) errors. In the second step, the results of the first step are further smoothed and optimized using the weighted extended Kalman filter (WEKF). Finally, the robustness and practicability of the proposed method are verified by the multiple data obtained from several sea trials in the South-West Indian Ocean. The results also show that the integrated navigation framework is superior to single navigation method and other traditional filtering methods. The best balance between accuracy and computational cost is achieved.