Global Navigation Satellite System–Acoustic ranging combined seafloor geodetic technique (GNSS-A) has extended the geodetic observation network into the ocean. The key issue for analyzing the GNSS-A data is how to correct the effect of sound speed variation in the seawater. We constructed a generalized observation equation and developed a method to directly extract the gradient sound speed structure by introducing appropriate statistical properties in the observation equation, especially the data correlation term. In the proposed scheme, we calculate the posterior probability based on the empirical Bayes approach using the Akaike’s Bayesian Information Criterion for model selection. This approach enabled us to suppress the overfitting of sound speed variables and thus to extract simpler sound speed field and stable seafloor positions from the GNSS-A dataset. The proposed procedure is implemented in the Python-based software “GARPOS” (GNSS-Acoustic Ranging combined POsitioning Solver).

全球导航卫星系统–测距组合海底大地测量技术（GNSS-A）已将大地观测网络扩展到海洋中。分析GNSS-A数据的关键问题是如何纠正海水中声速变化的影响。我们构造了一个广义的观测方程，并开发了一种通过在观测方程中引入适当的统计特性（尤其是数据相关项）来直接提取梯度声速结构的方法。在提出的方案中，我们基于经验贝叶斯方法，使用Akaike的贝叶斯信息准则进行模型选择，计算后验概率。这种方法使我们能够抑制声速变量的过拟合，从而从GNSS-A数据集中提取更简单的声速场和稳定的海底位置。所建议的过程在基于Python的软件“ GARPOS”（GNSS-声学测距组合定位定位求解器）中实现。