An approach to using basic three-element arrays in tetrahedral-based USBL systems

This article describes an approach to designing the ultra-short baseline (USBL) system with a four-element three-dimensional receiving USBL array. In particular, the receiving array based on a four-element tetrahedron is considered. The four-element tetrahedral USBL array is considered as a set of the elemental skew three-element USBL arrays. The coordinates of the object are determined by utilizing the basic three-element USBL system of this set with the subsequent averaging of the obtained coordinates. In the article the Cartesian coordinates of the object are determined in the reference coordinate system bounded up with the USBL system's carrier. It is assumed that the receiving tetrahedral array is oriented as an inverted pyramid and mounted rigidly on the lower part of the carrier hull. It is assumed that the receiving USBL array can have an inclination, which is controlled by the measurement of the array's pitch and roll angles. The paper focused on exploiting the latent resources of the tetrahedral receiving USBL array for accurate coordinate determination in conditions when the receiving antenna can have significant inclination and the location of the object in the lower hemisphere is arbitrary.