Designing a USBL system based on a square pyramid array with a complete set of three-element arrays

This paper describes an approach to designing an ultra-short baseline (USBL) system with a three-dimensional receiving USBL array. In particular, a five-element USBL receiving array based on a five-vertex convex polyhedron (square pyramid) is investigated. The receiving array is oriented as an inverted pyramid and we assume that the receiving USBL array is mounted rigidly on the lower part of the carrier hull. The article presents a design approach where the coordinates of an underwater object are determined by using a complete set of the elemental (three-element) USBL arrays. The total number of the elemental USBL arrays used is eighteen (six orthogonal three-element USBL arrays and twelve skew (non-orthogonal) three-element USBL arrays). The Cartesian coordinates of the underwater object are calculated in the reference coordinate system bounded up with the USBL system´s carrier. The proposed design method is based on determination of the object´s coordinates for all eighteen basic three-element USBL receiving arrays with subsequent reduction of these coordinates to the carrier coordinate system and averaging of the reduced coordinates. It is assumed that the receiving USBL array can have significant inclination, which is controlled by the measurement of the array´s pitch and roll angles. It is shown that utilization of the full set of the elemental three-element arrays of receiving antenna provides noticeable improvement of the object´s position-determination accuracy.