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 enabler for ensuring system performance. Existing calibration methods suffer from insufficient real-time capability during 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 the 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, real-time first-order bilinear interpolation is performed online to circumvent complex iterative computations of ray tracing, thereby 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 by information reconstruction, ensuring the dynamic update of acoustic measurements. Finally, the sound speed error correction method and the residual time-delay model are incorporated into a state estimation framework. Through joint closed-loop estimation of multi-source errors, the joint calibration of USBL range distortion and installation misalignment angles is realized. Simulation and experimental results demonstrate that the proposed method can effectively suppress deep-sea sound speed fluctuation errors and mitigate the negative impact of measurement latency. Compared with traditional methods without considering deep-sea errors, the proposed calibration approach improves the positioning accuracy by approximately 90.1%.