In active noise control (ANC) systems, the traditional filtered-x least mean square (FxLMS) algorithm has poor control effect on impulsive noise. To overcome this drawback, a robust cost function was designed in this paper by embedding the cost function of the FxLMS algorithm into the framework of hyperbolic tangent function; this paper thus proposes a robust filtered-x least hyperbolic tangent (FxLHT) algorithm in ANC systems. Moreover, the value of λ in the FxLHT algorithm greatly affects the robustness and convergence performance of the algorithm. Therefore, a variable λ-parameter was proposed to enhance the performance of the FxLHT algorithm. Simulation results show that in the active control of impulsive noise, compared with the FxLMS algorithm and other robust ANC algorithms, the proposed FxLHT algorithm and variable λ-parameter FxLHT algorithm not only exhibit good robustness and noise reduction performance but also have a better tracking ability.

Due to the influence of the complex underwater environment, the initial alignment method for Doppler velocity log (DVL)-aided strap-down inertial navigation systems (SINS) often suffer from performance degradation, especially when DVL measurements are contaminated by outliers. In this paper, an outlier-resistant Initial Alignment method with interference suppression for SINS/DVL integrated navigation system is proposed, by which, by constructing an improved Mahalanobis distance anomalous detection criterion, the anomaly of the residual vector composed of observation vectors is judged, and an adaptive weighting factor is introduced into the observation matrix to suppress the abnormal interference in the alignment process. Simulation and experimental results show that, compared with existing initial alignment methods, the proposed method achieves higher alignment accuracy in the presence of outliers, which is more suitable for the SINS/DVL integrated navigation system.

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 $53.39\mathrm{m}$, compared with $878.75\mathrm{m}$, $58.84\mathrm{m}$, and $56.49\mathrm{m}$ 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.