Robust Skew-t Kalman Filter for USBL Tightly Integrated Positioning System Under Measurement Uncertainties

Underwater ultrashort baseline (USBL) positioning systems suffer from significant estimation errors due to complex noise characteristics. Our analysis indicates that these errors manifest distinct skewed and heavy-tailed statistical characteristics, primarily attributed to system biases, time delays, and multipath effects. To effectively mitigate these issues, we propose a novel Kalman filter (KF) approach utilizing a skew-t-based Kalman filter (SKF). The SKF employs a hierarchical variational Bayesian (VB) approach to resolve linearization challenges caused by distribution asymmetry, using a structured likelihood representation of measurement errors. Simulations and field tests demonstrated that the SKF method improved accuracy by more than 56% in the USBL positioning system.