An adaptive self-aligning underwater navigation system based on data fusion from a set of multiple sensors including a MEMS-based inertial measurement unit (IMU), a Doppler Velocity Log (DVL), a 3-axis magnetic compass, and a pressure sensor for depth measurement is proposed. These sensors are typically included as part of the standard sensory complement in Autonomous Underwater Vehicle (AUV) platforms. A generic estimation framework is developed that addresses both estimation of the kinematic state of the vehicle (including position, velocity, and orientation angles) as well as sensor parameters (including bias/mis-alignment parameters of IMU accelerometer and gyros, compass, and DVL). Detailed noise models of all the considered sensors are addressed in the development of the navigation system. The performance of the proposed system is demonstrated through simulation studies.