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 similar to 5 cm (1 sigma) using this method, an improvement on the precision of similar to 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.