I. Introduction
Autonomous underwater vehicle (AUV) has been widely used for underwater topographic survey, target detection, and underwater resource exploitation [1], [2]. In order to ensure that AUV can successfully complete underwater related tasks, the long term, autonomous and high-precision navigation, and positioning technology is needed. At present, among the existing positioning technologies, strap-down inertial navigation system (SINS) is widely used in underwater vehicles because of its highly concealment and autonomy [3], [4]. Although inertial navigation technology has become more and more mature, the fundamental characteristic that inertial navigation system positioning error needs to be readjusted regularly with time to ensure a certain accuracy cannot be changed. Due to the particularity of underwater environment, traditional positioning methods, such as satellite navigation, other traditional radio navigation, and visual navigation, are limited in underwater application. The navigation method based on acoustic information has become one of the effective ways of underwater high-precision positioning, such as long baseline (LBL), short baseline (SBL), and ultra-SBL (USBL) [5]–[7]. Lee et al. [8] proposed an auxiliary positioning algorithm for pseudo USBL system. Only two receivers are installed on the AUV. The distance between the seabed transponder and each receiver is measured by using the ranging ability, and the distance difference model is established with the position information of SINS. At the same time, the information observation of acoustic wave exit angle is added to construct the integrated navigation system of SINS, Doppler velocity log (DVL), and USBL. The pool experiment results show that the information provided by the acoustic system can effectively correct the position error of SINS.