Azimuth-elevation direction finding using one four-component acoustic vector-sensor spread spatially as a parallelogram array

An acoustic vector-sensor (also called a "vector hydrophone") consists of three uni-axial velocitysensors (which are oriented perpendicularly with respect to each other) and one pressure-sensor. Song and Wong (Journal of the Acoustical Society of America, vol. 133, no. 4, pp. 1987-1995, April 2013) has advanced direction-finding formulas that allow these four component-sensors to be spaced apart in three-dimensional space, in order to extend the overall spatial aperture spanned by them, while improving the accuracy in the azimuth-elevation angle-of-arrival estimation of an acoustic emitter impinging from the far field. Whereas Song and Wong advances estimation formulas for any general arbitrary placement of the four component-sensors, this paper will focus on a special spatial geometry - where the four component-sensors occupy the four corners of a parallelogram in three-dimensional space - thereby simplifying the earlier formulas in Song and Wong.