Sound speed profile-free GNSS-acoustic positioning using extended cubic spline function

Acoustic range error is the dominant error affecting the positioning accuracy of GNSS-Acoustics (GNSS-A). To reduce the impact, the sound speed profile (SSP) measurement data are typically used. However, the SSP measurement data may not be obtained when an unmanned observation platform is used for positioning GNSS-A. To address the issue of lacking SSP measurements, a new method that does not require SSP has been proposed. The method uses an extended cubic spline function to model the temporal variation of sound speed, employs cubic polynomials to model the spatial variation of sound speed, utilizes a squared function to model sound ray bending error, and uses least squares estimation to determine the coordinates of seafloor transponder. The observations of seafloor stations TOS2 and MYGI from 2011 to 2019 were used to test the method. The results were compared with the coordinates of the seafloor transponder provided by the GARPOS software. The results show that (1) the average root mean square (RMS) of the GNSS-A positioning residuals for TOS2 and MYGI are 6.84 cm and 8.59 cm, respectively, with the residuals exhibiting a normal distribution; (2) the centimeter-level positioning of the seafloor transponder can be realized by using the method of SSP-free GNSS-A positioning. (3) the approach using the extended cubic spline function improves the position accuracy by approximately 9.25% for TOS2 and 24.94% for MYGI, compared to the method using the cubic spline function; (4) the average difference between the baselines obtained from GARPOS software and those calculated by the method using the extended cubic spline function is 0.23 cm for TOS2 and 0.03 cm for MYGI; (5) the accuracy of the baseline derived from the method using the extended cubic spline function improves by about 17.05% for TOS2 and 13.53% for MYGI when compared to the GARPOS software results. Since no sound speed profile observation is required, the SSP-free GNSS-A positioning method is particularly suitable for unmanned GNSS-A observation systems where in-field SSP measurements are difficult to conduct. However, the SSP-free GNSS-A positioning method with the extended cubic spline function is only applicable for the positioning of seafloor stations equipped with multiple transponders within a limited sea area.