Delay-aware robust adaptive SINS/USBL navigation based on VB-MMCUKF for long-duration mid-water AUV missions

Ultra-short baseline acoustic positioning (USBL) is an essential positioning aid for autonomous underwater vehicles (AUVs) operating in mid-water environments, where Doppler velocity log bottom lock may be unavailable and inertial navigation errors accumulate over time. In such missions, USBL observations are affected by acoustic propagation delays, outliers, non-Gaussian disturbances, and unknown or time-varying measurement-noise covariances. This paper proposes a delay-aware robust adaptive strap-down inertial navigation system (SINS)/USBL integrated navigation method based on variational Bayesian maximum mixture correntropy unscented Kalman filtering (VB-MMCUKF). A delay-aware USBL measurement model is established to reduce the temporal mismatch between acoustic observations and inertial navigation states. Maximum mixture correntropy is used to suppress outlier-contaminated residuals, while variational Bayesian estimation adaptively updates the measurement-noise covariance. The method is evaluated using simulation experiments and a sea trial involving a PX-600 AUV operating at a depth of 150 m for approximately 2.5 h. In the sea trial, the proposed method achieves the lowest normalized terminal position error among the compared filters and improves positioning accuracy by 12.80% relative to MMCUKF. These results indicate that the proposed method improves the accuracy and short-term stability of SINS/USBL navigation under delayed and outlier-contaminated acoustic measurements.