Closed-form multiple source direction-of-arrival estimator under reverberant environments

Accurate direction-of-arrival (DOA) estimation of multiple sources, simultaneously active in a reverberant environment, remains a challenge, as the multi-path acoustic reflections and overlapped periods dramatically distort the direct-path wave propagation. This article proposes a prominent solution localizing multiple sources in a reverberant environment using closed-form estimates, circumventing any exhaustive search over the two-dimensional directional space. Apart from a low complexity cost, the algorithm has robustness to reverberant, inactive, and overlapped periods and an ease of operation in practice, achieving sufficient accuracy compared to state-of-the-art approaches. Specifically, this algorithm localizes an unknown number of sources through four steps: (i) decomposing the frequency domain signals on a spherical array to the spherical harmonics domain; (ii) extracting the first-order relative harmonic coefficients as the input features; (iii) achieving direct-path dominance detection and localization using closed-form estimation; and (iv) estimating the number of sources and their DOAs based on those pass the direct-path detection. Experimental results, using extensive simulated and real-life recordings, confirm the algorithm with a significantly reduced computational complexity, while preserving competitive localization accuracy as compared to the baseline approaches. Additional tests confirm this low-complexity algorithm even with a potential capacity for online DOA tracking of multiple moving sources.