In the conventional integrated navigation system, the statistical information of the process and measurement noises is considered constant. However, due to the changing dynamic environment and imperfect knowledge of the filter statistical information, the process and measurement covariance matrices are unknown and time-varying. In this paper, a multirate adaptive Kalman filter is proposed to improve the performance of the Error State Kalman Filter (ESKF) for a marine navigation system. The designed navigation system is composed of a strapdown inertial navigation system along with Doppler velocity log and inclinometer with different sampling rates. In the proposed filter, the conventional adaptive Kalman filter is modified by adaptively tuning the measurement covariance matrix of the auxiliary sensors that have varying sampling grates based on the innovation sequence. The performance of the proposed filter is evaluated using real measurements. Experimental results show that the average root mean square error of the position estimated by the proposed filter can be decreased by approximately 60% when compared to that of the ESKF.