Nonsingular EB-ESPRIT for the localization of early reflections in a room

Abstract

The eigenbeam-ESPRIT (EB-ESPRIT) can directly identify the direction of arrivals (DoAs) of sound sources through the parametric estimation process. This parametric estimation is beneficial for identifying directions of early echoes in an enclosed space, because it does not need an extra peak searching step for finding dominant peak locations from a beamforming power map. Nevertheless, the use of EB-ESPRIT for echo localization has been hindered due to its ill-conditioning problem for sources positioned near the equator of the spherical coordinates. Room reflections in a reverberant room can impinge from any direction, and hence, the ill-conditioning is highly likely to occur. In this work, a nonsingular EB-ESPRIT technique is utilized for the echo localization without the ill-conditioning problem. The technique is based on new recurrence relations of spherical harmonics that express DoA parameters in form of sinusoidal functions. Therefore, the ill-conditioning due to the use of arctangent function can be avoided. The performance is demonstrated using the room impulse responses simulated and measured for a rigid spherical microphone array. Frequency smoothing is applied to localize echoes that are highly coherent to each other, and results demonstrate that accurate localization of echoes is possible irrespective of their incidence angles.