Online Joint Calibration Method for SINS/USBL Integrating Sound Speed Correction and Time-Delay Estimation

The integration of the strapdown inertial navigation system(SINS) and the ultra-short baseline(USBL) acoustic positioning system has become the mainstream solution for deep-sea navigation. High-precision sensor calibration is the core prerequisite for ensuring the performance of the integrated navigation system. Existing calibration methods lack sufficient real-time performance for deep-sea acoustic ray-bending correction. Moreover, traditional methods often ignore the strong coupling characteristics between random acoustic measurement time-delay jitter and spatial errors. This limitation restricts calibration accuracy, which in turn limits the operational precision and adaptability of the navigation system in deep-sea scenarios. To address these issues, this paper proposes an online joint calibration method that integrates an effective sound speed table with time-delay estimation. First, a refined mapping table among the transponder depth, the initial grazing angle, and the effective sound speed is established offline. During the calibration process, first-order bilinear interpolation is performed online to circumvent the complex iterative computations of ray tracing, thus achieving real-time correction of sound speed errors. Furthermore, the system calculates historical position and attitude matrices through time-delay backtracking. The residual time delay is modeled as a first-order Markov process to compensate for the time jitter introduced during information reconstruction, thus enabling dynamic updates of acoustic measurements. Finally, the sound speed error correction method and the residual time-delay model are incorporated into a state estimation framework. Through closed-loop joint estimation of multiple error sources, USBL range distortion and installation misalignment angles are jointly corrected. Simulation and sea trial results demonstrate that the proposed method can effectively suppress deep-sea sound speed disturbance errors and mitigate the negative impact of measurement latency. Compared with calibration methods without deep-sea multi-source error compensation, the proposed method improves navigation positioning accuracy by approximately 90.1%.