Closed-Form DOA Estimation Using First-Order Differential Microphone Arrays via Joint Temporal-Spectral-Spatial Processing

Sound source direction-of-arrival (DOA) estimation in reverberant environments with low-computational complexity remains a challenging problem, especially for small-sized microphone arrays. To address the problem, a promising method is based on the sound intensity (SI) measurement using differential microphone arrays (DMAs), which can give a closed-form solution and, hence, is computationally efficient. Unfortunately, the SI-based method has been shown to be sensitive to room reverberation, and therefore, more works need to be done to improve its performance in reverberant environments. In this paper, we propose an SI-based closed-form DOA estimation algorithm through the joint temporal-spectral-spatial processing by using two orthogonal first-order DMAs. The proposed method consists of two stages. In the first stage, it focuses on temporal-spectral processing to improve the SI-based DOA estimation, and a preliminary DOA estimate is made through a dual-threshold technique inspired by the local DOA variance weighting scheme in the time-frequency domain. In the second stage, the preliminary DOA estimate is then refined through the spatial processing, where the two first-order orthogonal DMAs are further utilized to construct a first-order steerable DMA for dereverberation, which is shown to be useful when the signal to noise ratio is not too low. Simulations and real-world experiments in reverberant environments have demonstrated the superior performance of the proposed closed-form DOA estimation method.