Inter-Element Phase Error Compensated Calibration Method for USBL Arrays

This study addresses the critical limitation of existing Ultra-Short Baseline (USBL) calibration algorithms in handling transducer positional errors and inter-element phase errors. We propose a novel positioning-calibration model based on vector projection theorem. The model achieves two key innovations: it eliminates the influence of inter-element positional errors through its structural design, and, for the first time, incorporates inter-element phase errors from acoustic array measurements as observational parameters to establish joint estimation equations for system installation angle errors and inter-element phase errors. The estimation process is implemented using an unscented Kalman filter (UKF). Simulation results demonstrate that the UKF outperforms the Gauss–Newton method (GNM), achieving estimation errors for installation angles and phase errors within 0.05°. Comparative evaluations confirm the model’s superiority over conventional calibration methods in accurately estimating installation angles under transducer positional errors. Field experiments further validate the algorithm’s effectiveness in real-world marine environments, successfully estimating system installation angle errors and inter-element phase errors to enhance final target positioning accuracy. This approach provides a practical solution to persistent calibration challenges in USBL systems.