Real-time SSP inversion combining in-situ SSPs with GNSS-A observations

In seafloor geodesy, spatiotemporal variations of sound speed field (SSF) have great impact on positioning accuracy of Global Navigation Satellite System-Acoustic (GNSS-A) techniques. In-situ sound speed profile (SSP) observations can provide high vertical resolution of sound speed structure but have a limitation in temporal resolution due to the constraints of operational cost, making it difficult to fully capture time-varying characteristics of sound speed. In contrast, GNSS-A observations can continuously retrieve SSP-related information, yet have limited capability in representing vertical structure of sound speed. However, existing SSP parameterization approaches generally require stronger prior constraints or denser SSP observations to achieve stable inversion of time-varying sound-speed structures. To address this limitation, this study proposes a real-time SSP inversion method that combines in-situ SSPs with GNSS-A observations. First, empirical orthogonal function (EOF) spatial modes are constructed from in-situ SSPs to serve as a spatial basis function for constraining the vertical structure of sound speed perturbations. Then, principal component (PC) temporal model is established, and periodic grid-search strategy combined with Fourier series representation is adopted to determine optimal period combination. Finally, PC coefficients, delay parameters, and seafloor transponder coordinates are jointly incorporated into GNSS-A equations, enabling simultaneous real-time SSP inversion and positioning. Experimental results demonstrate proposed method can stably reconstruct time-varying vertical structure of sound speed under limited in-situ SSP conditions, achieving an RMSE of 0.499 m/s over the depth. Compared with fixed-profile strategy, the standard deviation of GNSS-A residuals is reduced by 66%-80% across three trajectories, and the improvement in positioning error reaches 44.7%. In addition, the Euclidean distance among independent trajectory solutions decreases, indicating improved consistency of positioning solutions across trajectories. Overall, the proposed method effectively characterizes time-varying sound speed under sparse in-situ SSP conditions, mitigates sound speed-induced positioning errors, and provides robust solution for high-precision GNSS-A seafloor geodesy.