The Inertial Navigation System (INS) and Doppler Velocity Log (DVL) combination navigation system has been widely used in Autonomous Underwater Vehicles (AUVs) due to its independence, stealth, and high accuracy. Compared to the standalone INS or DVL, the integrated system provides continuous and accurate navigation information. However, the underwater environment is complex, and system noise and observation noise may not satisfy the condition of mutual independence. In addition, the DVL may produce abnormal measurement values during operation. In this study, an Event-Triggered Correlation Noise Filter (ETCNF) method was designed for fusing INS and DVL data. An auxiliary matrix was introduced to decouple the correlated noise, allowing novel state estimation. Moreover, the event-triggered mechanism detected and eliminated abnormal values in DVL measurements, which improved the positioning accuracy and robustness of the INS/DVL integrated system. Finally, simulation experiments were conducted to verify the effectiveness and superiority of the proposed algorithm.