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

Abstract A systematic analysis methodology for the precise seafloor positioning using the GNSS-A has been constructed and implemented into an open source software GARPOS. It introduced a linearized perturbation field model for the 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 constraint parameters non-linear to the observation equation. Even though such parameters can be optimized applying information criteria, it eliminates the information on the details of joint posterior probability, resulting in the estimation of conditional posterior. To overcome above limitations, we implemented the full-Bayes estimation using the Markov-Chain Monte Carlo (MCMC) algorithm. It can help not only evaluating the dependency of the existing hyperparameters on the seafloor position, but also discussing the effects of the additionally imposed constraints. We imposed the constraint assuming the situation where a temporally-variable gradient layer steadily lies on a certain depth in the observation scale (typically < 10 km x 10 km, < 1 day). This models the cases with large-scale structure such as the Kuroshio current or with the internal waves with long-wavelength. The constraint narrows the posterior of horizontal position and provided better solution in many datasets, especially in the Nankai Trough region. For the other datasets, the constraint emphasized the bias errors, which can also provide the information on the possibility of instrumental and modelling errors.