Full-Bayes GNSS-A solutions for precise seafloor positioning with single uniform sound speed gradient layer assumption

Abstract

A systematic analysis methodology for precise seafloor positioning using the GNSS-A has been constructed and implemented in the open-source software GARPOS. It introduces a linearized perturbation field model for extraction of the 4-dimensional sound speed variation, and solves the perturbation parameters simultaneously with the seafloor position based on the empirical Bayes approach. Although it can provide the solutions stably and almost analytically, it has less expandability when imposing additional nonlinear constraint parameters in the observation equation. Even though such parameters can be optimized by applying some information criteria, information on the details of the joint posterior probability would be lost and only the conditional posterior can be estimated. To overcome the above limitations, we implemented full-Bayes estimation using the Markov-Chain Monte Carlo algorithm. This approach can not only help evaluate the dependency of the existing constraint parameters on the seafloor position, but also let us discuss the effects of the additionally imposed constraints. We imposed a constraint under the assumption that a temporally-variable gradient layer steadily lies at a certain depth in the observation scale (typically < 10 km × 10 km, < 1 day). This models the cases with temperature gradients due to a large-scale structure such as the Kuroshio current or internal waves with long-wavelength. The constraint narrows the posterior of the horizontal position and provides a better solution for many datasets, especially in the Nankai Trough region. For the other datasets, the constraint emphasized bias errors, which can also provide information on the possibility of instrumental and modelling errors.