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In the conventional integrated navigation systems, such as direct Kalman filter, the statistical information of the process and measurement noises is considered constant. In real applications, due to the variation of vehicle dynamics, the environmental conditions and imperfect knowledge of the filter statistical information, the process and measurement covariance matrices are unknown and time dependent. To improve performance of the direct Kalman filter algorithm, this paper presents an asynchronous adaptive direct Kalman filter (AADKF) algorithm for underwater integrated navigation system. The designed navigation system is composed of a high-rate strapdown inertial navigation system along with low-rate auxiliary sensors with different sampling rates. The auxiliary sensors consist of a global positioning system (GPS), a Doppler velocity log (DVL), a depthmeter, and an inclinometer. Performance of the proposed …