Azimuth-elevation direction finding, using three uni-axial velocity sensors as an arbitrarily sparse linear array

Abstract

A tri-axial velocity sensor measures the acoustic particle-velocity vector, by all three of its Cartesian components. This particle-velocity vector equals the spatial gradient of the acoustic pressure field. Song & Wong [1] has advanced an algorithm to estimate an incident source's azimuth-elevation (θ, Φ) direction-of-arrival using three uni-axial velocity sensors that are orthogonally oriented among themselves and placed arbitrarily in three-dimensional space. This work will focus on a particular array geometry whereby the three uni-axial velocity sensors are placed on a straight line in three-dimensional space but the inter-element spacings may be entirely arbitrary. This work will show how to estimate a far-field emitter's azimuth-elevation direction-of-arrival, despite the three elements’ spatial separation, and despite the separation's arbitrary length and possible sparseness. Furthermore, the Cramer-Rao Bounds (CRB) will be presented analytically for the case of the linear array being aligned along the x-axis. This work differs from [2], which requires an additional pressure-sensor. [1] Y. Song & K. T. Wong, “Acoustic direction finding using a spatially spread tri-axial velocity sensor,” IEEE Trans. Aerosp. Electron. Syst. 51(2), 834–842 (2015). [2] Y. Song & K. T. Wong, “Azimuth-elevation direction finding, using one four-component acoustic vector-sensor spread spatially along a straight line,” Proc. of Meetings on Acoustics—Meeting of the ASA, Pittsburgh, U.S.A., May 18–22, 2015.