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This study considers an asynchronous multirate data integration problem in the linear state space model with unknown and time-varying statistical parameters of the measurement noises. To improve performance of the multirate adaptive Kalman filter algorithm, a multi-sensor adaptive Kalman filtering algorithm based on variational Bayesian approximations has been developed in an asynchronous multirate multi-sensor integrated navigation system. The proposed filtering algorithm estimates measurement noise variances of the sensors adaptively and also it is robust to anomalous measurements of sensors and however, multirate adaptive Kalman filter is required to use an appropriate algorithm for outlier rejection to achieve a reliable and optimal estimation of position, velocity, and orientation. A navigation system composed of a strapdown inertial navigation system along with Doppler velocity log, inclinometer …