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.
The eigenbeam estimation of signal parameters via the rotational invariance technique (EB-ESPRIT) is a well-known subspace-based beamforming algorithm for a spherical microphone array. EB-ESPRIT uses a recurrence relation to directly estimate directional parameters expressing directions-of-arrival (DOAs) of sound sources without an exhaustive grid-search. In the conventional EB-ESPRIT, the directional parameter along the elevational direction is given by a tangent function, which inevitably produces two shortcomings. First, the tangent function becomes singular for sources near the equator in spherical coordinates. Furthermore, two sources lying in exactly opposite directions in the spherical coordinates are indistinguishable and a strong ambiguity problem arises. In this work, an EB-ESPRIT technique based on generalized eigenvalue decomposition (GEVD) is proposed to resolve the singularity and ambiguity problems. The proposed technique uses three independent recurrence relations for spherical harmonics, thus the singularity problem due to the tangent function can be completely avoided. A common transformation matrix for extracting DOAs from recurrence relations are found from the GEVD, and the use of cosine and sine functions makes it possible to find DOAs without ambiguity and without extra transforms or angle-pairing processes. It is demonstrated that the proposed method not only overcomes the singularity and ambiguity problems, but also outperforms conventional techniques in terms of DOA accuracy.
The estimation of direction of arrivals (DoAs) from spherical microphone array data is one of the key issues in extracting source information from all-around audio recordings. One such technique is the eigenbeam estimation of signal parameters via the rotational invariance technique (EB-ESPRIT), which separates the signal subspace related to the stationary sound field and then directly estimates DoAs of multiple sound sources. EB-ESPRIT has been evolved in many different ways by involving different types of recurrence relations of spherical harmonics, all of which are able to identify DoAs of a limited number of sources that are noticeably smaller than the number of finite-order spherical harmonic coefficients recorded. In this work, we report that it is possible to go beyond the known limits of detectable sources. The proposed formula is also based on conventional recurrence relations and probably permits to reach the ultimate limit by additional constraints of the signal parameters that can better exploit the highest-order coefficients. Monte-Carlo simulations conducted with various source positions and signal-to-noise ratios (SNRs) reveal that the proposed technique can detect more sources with insignificant loss in estimation performance and robustness.
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