An approximate travel time calculation and a robust GNSS-acoustic positioning method using an MCMC technique

Abstract

It is important to consider horizontal heterogeneity in an underwater sound speed structure to accurately estimate positions of GNSS-acoustic sites. Although large amounts of moving survey data (a sea-surface platform moves around when acoustic signals are transmitted) are required to accurately detect a sloping sound speed structure, the actual observational data do not necessarily include sufficient moving survey data due to sea conditions or observational time. To treat these insufficient data, it was assumed that a shallow sound speed gradient was continuously present up to a fixed water depth (gradient depth). However, the validity of this assumption has not been investigated, and the gradient depth has not been optimized. In this study, we developed a new GNSS-acoustic array positioning method that optimizes the gradient depth using an MCMC technique. To employ this technique, we also developed an approximate technique for rapidly calculating travel time, because the conventional travel time calculation requires high computational cost for integration into the MCMC technique. We assessed the performance of the approximate travel time calculation technique and demonstrated its sufficient accuracy and precision for estimating array positions. Then, we applied the new GNSS-acoustic array positioning method to the actual observational data collected by the Japan Coast Guard and Tohoku University. Using enough amounts of the moving survey data, our method demonstrated the results comparable with the conventional GNSS-acoustic positioning method estimating a sloping sound speed structure; thus, the assumption of the sound speed gradient with the fixed water depth was valid. Moreover, due to the physical restriction of this assumption, our method provided robust solutions even when the observational data contained small quantities of moving survey data with a simple sea-surface track. Although our method still cannot be used in the scenario, where no moving survey data are available, it can work robustly compared with the conventional methods.Graphical