An autonomous underwater vehicle (AUV) requires a precise navigational system for localization, positioning, path tracking, guidance and control. The main navigational device for an AUV is an inertial navigation system (INS) because highprecision navigational devices such as the Global Positioning System have a limited usage in the underwater environment. In this study, based on the dynamic mathematical model of AUV, we develop two types of low-cost integrated navigational system for AUVs based on error models of INS and its aiding devices such as Doppler velocity logs, compasses and pressure depth sensors. Nine-and 15-state INS error models and corresponding measurement models of aiding devices are derived for the Kalman filter (KF). We compare the performance of those two integrated navigation systems. The simulation results confirm that low-cost inertial measurement unit sensors produce a notable amount of noisy measurements, but KF-based integrated navigation system models for AUV can effectively mitigate those drawbacks.