Calibration algorithm for SINS/USBL installation misalignment errors based on Student’s T-distribution

In this paper, the reduced calibration accuracy of installation misalignment angles in underwater environments is addressed due to acoustic measurement uncertainties. A robust SINS/USBL calibration method is proposed based on a variational Bayesian framework. A geometric model for installation misalignment calibration is first established. State-space equations and nonlinear measurement equations are derived. The algorithm innovatively integrates Student’s T-distribution into the variational Bayesian filtering framework. To mitigate outlier interference in acoustic positioning, the heavy-tailed properties of Student’s T-distribution are adopted for noise modeling. The noise covariance matrix and auxiliary variables are dynamically co-estimated through variational Bayesian inference, effectively suppressing anomalous measurements during state updates. Variational iterative optimization ensures adaptive matching between noise models and state estimates while maintaining calibration accuracy. Simulations compare the proposed method with traditional Gaussian-based Kalman filter. The proposed method improves the installation angle estimation accuracy by 64.6% in outlier-contaminated simulation environments. Furthermore, field river experiments demonstrate enhanced positioning accuracy across all axes after calibration with the proposed algorithm. The enhanced robustness demonstrates significant potential for complex underwater calibration tasks.