Soft-Gating Mixture Robust Kalman Filter for SINS/DVL Integrated Navigation Under DVL Outlier Interference

Aiming at the problem that complex underwater environments induce outliers in Doppler Velocity Log (DVL) measurements, which degrade the navigation accuracy of the Strapdown Inertial Navigation System (SINS)/DVL integrated system, this paper proposes a soft-gating Gaussian–Student’s t mixture robust Kalman filter (MRKF). Firstly, the measurement noise is modeled as a mixture of Gaussian and Student’s t distributions to adapt to normal stationary noise and abrupt outliers, respectively. Secondly, a logistic soft-gating weight is constructed based on the innovation Mahalanobis distance to adaptively balance the output contributions of the standard Kalman Filter (KF) and the variational Bayesian Student’s t filter. Finally, moment matching is adopted to realize the weighted fusion of two-branch posterior distributions, and an equivalent Gaussian posterior estimation is obtained. Simulation results under the considered SINS/DVL integrated navigation scenarios show that the proposed MRKF maintains estimation accuracy close to the standard KF under nominal Gaussian measurement noise. In the designed DVL outlier-injection scenario, the proposed MRKF achieves a position RMSE of 53.39m, compared with 878.75m, 58.84m, and 56.49m for the nominal KF, Huber KF (HKF), and Student’s-t variational Bayesian KF (STVBKF), respectively. These results indicate that the proposed MRKF can improve robustness against DVL outliers while maintaining competitive estimation accuracy under the simulated conditions.