Positioning Accuracy Model of Sailing‐Circle GPS‐Acoustic Method.

Sailing‐circle GPS‐acoustic method, prevalently applied for measuring ocean floor crustal deformation, allows the precise positioning of an underwater transponder in a global frame. In the method, distance estimation requires prior information, such as transponder depth or incident angle. However, sometimes the prior information is inaccurate or absent. Under these circumstances, this study proposes two kinds of positioning methods that utilize an iteration composed of an inverse or direct ray tracing method and the least squares approach to constantly modify the initial data to obtain an accurate incident angle and coordinates of an underwater transponder. Even though an accurate incident angle can be got and there is no time delay or spatial‐temporal heterogeneities of SSP (sound speed profile), SSP density and geometric incident angle still influence ranging errors and PDOP (position dilution of precision) during distance intersection. In order to reduce the two kinds of impacts, this paper deduces a positioning error model based on the principle of sailing‐circle method. On the one hand, the proposed algorithms and model are verified by a simulated experiment for various SSP density, geometric incident angle, and transponder depth. On the other hand, in a practical experiment, average positioning accuracy of 0.025 m and vertical accuracy of −0.02 m are achieved, and the improved accuracy is about 85% higher than that of the ordinary sailing‐circle method. Plain Language Summary: GPS‐acoustic method is a kind of method that utilizes GPS, which is usually placed in our vehicle for navigation, and sonars, which can measure the distance between two points in water, for determining the position of a fixed point underwater. By continuously monitoring the location of this point, the position change is obtained and the change can help us predict earthquakes and study earthquakes. Among GPS‐acoustic methods, sailing‐circle method that the vessel equipped with GPS and sonars drives a circle centered on the underwater point can gain the best positioning accuracy. However, the method requires accurate prior information, such as transponder depth or incident angle. When the prior information is inaccurate or absent, accuracy will decrease and therefore, we propose two kinds of new sailing‐circle methods to deal with this situation. And it is noted that whether the prior information is accurate or not, there will be errors in the final positioning results caused by instruments, algorithms, and environments. Consequently, based on the principle of sailing‐circle method, we deduce the positioning error model to guide us design various parameters in a practical experiment, such as sailing radius, and improve the positioning accuracy. The ultimate goal of this paper is to improve the positioning accuracy of sailing‐circle method. To check the effectiveness of the two proposed methods and model, on the one hand, they are verified by a simulated experiment for various situations. On the other hand, in a practical experiment, positioning accuracy of the proposed method is about 85% higher than that of the ordinary method. Key Points: Two new sailing‐circle GPS‐acoustic methodsPositioning error model with respect to geometric incident angle (or sailing radius) and the density of sound speed profile is deducedGeometric incident angle should be controlled within 50° and the smaller the density of sound speed profile, the better [ABSTRACT FROM AUTHOR]