Adaptive Unscented Kalman Filtering and Signal-Sending Time Estimation for Calibration of SINS/USBL Navigation System

Ultra-Short Baseline (USBL) systems are susceptible to installation errors that necessitate accurate calibration before deployment. In this paper, we propose an innovative calibration method that does not require time synchronization, enhancing calibration accuracy and mitigating the effects of acoustic array motion. First, we construct a novel installation error model based on the slant range difference to estimate signal sending time. Then, we designed an improved filtering algorithm—variational Bayesian unscented Kalman filter-range (VBUKF-r). In VBUKFr, to address challenges related to unknown and time-varying measurement noise covariance matrix (MNCM), we integrate variational Bayesian methods with the unscented Kalman filter (UKF) and enhance the accuracy of MNCM estimation by analyzing the relationship between ranging noise and distance. Furthermore, we utilize matrix diagonalization instead of Cholesky decomposition to resolve computational issues associated with non-positive definite state covariance matrixs. Finally, we propose a K-means clustering iterative optimization strategy for VBUKF-r to mitigate the influence of initial measurement vectors on parameter estimation. Simulation analysis and sea trials demonstrate that our algorithm significantly outperforms existing methods.