GARPOS: Analysis Software for the GNSS‐A Seafloor Positioning With Simultaneous Estimation of Sound Speed Structure

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).

The Rapid Uncertainty Prediction of the Ocean-Acoustic Coupled Model

<p>Focusing on the rapid prediction of acoustic field uncertainty in environment with temporal and spatial sound speed perturbation, evolvement of sound speed structure over time is predicted based on the ocean-acoustic coupled model to obtain the uncertainty distribution of the vertical structure of sound speed. Further, a method combining  the arbitrary polynomial chaos expansion with the empirical orthogonal function is proposed to reduce the dimensionality of uncertain parameters and to obtain the uncertainty distribution of the acoustic field. Simulations have shown that the computational complexity can be reduced by 2 orders of magnitude compared to the conventional polynomial chaos expansion while ensures the same precision. Moreover, the computational complexity is not influenced by the complexity of the sound speed profile. The acoustic field and uncertainty predicted in uncertain environment by proposed method also have been tested with the experimental data.</p>

Development of a kinematic GNSS-Acoustic positioning method based on a state-space model

GNSS-A (combination of Global Navigation Satellite System and Acoustic ranging) observations have provided important geophysical results, typically based on static GNSS-Acoustic positioning methods. Recently, continuous GNSS-Acoustic observations using a moored buoy have been attempted. Precise kinematic GNSS-Acoustic positioning is essential for these approaches. In this study, we developed a new kinematic GNSS-A positioning method using the extended Kalman filter (EKF). As for the observation model, parameters expressing underwater sound speed structure [nadir total delay (NTD) and underwater delay gradients] are defined in a similar manner to the satellite geodetic positioning. We then investigated the performance of the new method using both the synthetic and observational data. We also investigated the utility of a GNSS-Acoustic array geometry composed of multi-angled transponders for detection of vertical displacements. The synthetic tests successfully demonstrated that (1) the EKF-based GNSS-Acoustic positioning method can resolve the GNSS-Acoustic array displacements, as well as NTDs and underwater delay gradients, more precisely than those estimated by the conventional kinematic positioning methods and (2) precise detection of vertical displacements can be achieved using multi-angled transponders and EKF-based GNSS-Acoustic positioning. Analyses of the observational data also demonstrated superior performance of the EKF-based GNSS-Acoustic positioning method, when assuming a laterally stratified sound speed structure. Further, we found three superior aspects to the EKF-based array positioning method when using observational data: (1) robustness of the solutions when some transponders fail to respond, (2) precise detection for an abrupt vertical displacement, and (3) applicability to real-time positioning when sampling interval of the acoustic ranging is shorter than 30 min. The precision of the detection of abrupt steps, such as those caused by coseismic slips, is ~ 5 cm (1σ) using this method, an improvement on the precision of ~ 10 cm of conventional methods. Using the observational data, the underwater delay gradients and the horizontal array displacements could not be accurately solved even using the new method. This suggests that short-wavelength spatial heterogeneity exists in the actual ocean sound speed structure, which cannot be approximated using a simple horizontally graded sound speed structure.