This study considers a multi-rate multi-sensor data integration problem in the linear state space model with time-varying and unknown measurement noise. 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, a Doppler velocity log, a depthmeter, and an inclinometer. Using sensors with different sampling rates requires the design of multi-rate integration algorithms. To improve the performance of multi-rate error state Kalman filter (MESKF) for marine navigation system, a multi-rate adaptive error state Kalman filter (MAESKF) and a variational Bayesian approximation based MAESKF (VB-MAESKF) are proposed. Performance of the proposed algorithm is investigated using real measurements. Results of two experimental tests show that the average relative root mean square error (RMSE) of the position estimated by VB-MAESKF can be decreased approximately 57% and 36% when compared to that of MESKF and MAESKF algorithms, respectively. Key Words Strapdown Inertial Navigation System, Multirate Integrated Navigation System, Adaptive Kalman Filter.
