Spherical Harmonic Expansion Model for GNSS/Acoustic Precise Seafloor Positioning

The Global Navigation Satellite System (GNSS)-acoustic ranging technique has found application in the field of marine geodesy. However, the seafloor positioning accuracy is affected by the sound speed error and the multipath effect. To address these issues, the error sources in seafloor positioning are initially classified into two categories: one category pertains to the propagation path-related errors of an acoustic signal and the other category involves the propagation path-unrelated errors. Then, a novel GNSS/Acoustic precise seafloor positioning method is proposed, which addresses the signal propagation path-related errors using a spherical harmonic expansion. This expansion is based on the azimuth angle and the elevation angle between the shipborne transducer and the seafloor transponder. The solution to the ill-conditioning issue is mainly divided into two steps, first, the initial parameter values are obtained with a truncated singular value decomposition and then the parameters are iteratively estimated to correct characteristic values. The experiment utilized observational data collected on 15 March 2019, at the SAGA site (139.26°E, 34.96°N) established by Hydrographic and Oceanographic Department of Japan. The results show that the positioning precision of the seafloor transponder reaches centimeter level in the horizontal direction and approximately 10 cm in the vertical direction when expanding the spherical harmonic model to degree 9. The estimation of coordinates at different sites and points is also analyzed and discussed. The estimated transponder position is consistent with the estimated transponder position by GARPOS (GNSS-Acoustic Ranging combined Positioning Solver) package.