Direction of arrival estimation using nonsingular spherical ESPRIT

The eigenbeam-ESPRIT (EB-ESPRIT) is a parametric method that estimates the direction of arrival of source signals using a recurrence relation of spherical harmonics. In EB-ESPRIT, the sound-source elevation angle is estimated from an arctangent function, which diverges near the equator in the spherical coordinate system and inevitably induces an ill-conditioning problem. Here, a nonsingular spherical ESPRIT technique based on sine-based recurrence relations is proposed, in which the elevation angles are estimated from an arcsine function. It is shown that the proposed technique can estimate more sources than the conventional EB-ESPRIT technique while also avoiding ill-conditioning problems.