Linear and bilinear approximations of sound speed profiles in GPS/Acoustic seafloor geodesy

Abstract

To reduce the effect of sound speed variation on the precision of GPS/Acoustic positioning, we present two synthetic models, the linear and bilinear profiles, for the approximation of a sound speed profile so that the acoustic travel times with the approximate and the exact profiles are negligibly different. The linear profile is assumed that the sound speed varies linearly as a function of depth, in which the surface sound speed and the gradient of sound speed over the whole depth are the design variables. In the bilinear model, the surface sound speed and the break depth are regarded as known constants, while the two piecewise gradients of the bilinear function are variables needing to be estimated to approximate a sound speed profile. The performance of the two synthetic models are numerically evaluated for the approximation of three types of sound speed profiles which were derived from CTD casts taken at 300, 1000, and 2000 m water depths, respectively. In the bilinear approximation, varying the break depth results in different best fit to a sound speed profile. Therefore, this study investigates the change in error of the best fit due to the change in break depth for the bilinear approximation of the three types of sound speed profiles. The performance of the linear and bilinear approximations to sound speed profiles are further evaluated by the data collected from a field GPS/Acoustic survey. The results demonstrate that the linear and bilinear approximations of sound speed profiles can effectively reduce the effect of sound speed variation on GPS/Acoustic positioning.