Multi-Source Direction-of-Arrival Estimation Using Steered Response Power and Group-Sparse Optimization

In this paper, a method is proposed for estimating the direction of arrival (DOA) of multiple broadband sound sources. This is achieved through the solution of a group-sparse optimization problem, which models an observed broadband steered response power (SRP) map as a linear function of power spectral densities (PSDs), corresponding to a set of candidate DOAs, and forming a PSD vector. Given the assumption of spatial sparsity, the estimation of the source DOAs is then accomplished by identifying peaks in the resulting spatial power density, i.e., the estimated direction-specific PSDs integrated over frequency. The motivation behind the proposed method lies in its potential to reveal more distinct peaks in the estimated spatial power density than those directly observed in the broadband SRP map, which can be beneficial to the robustness in DOA estimation performance when multiple sources need to be distinguished under varying acoustic conditions. An implementation of the proposed method using the alternating direction method of multipliers (ADMM) is presented, and the DOA estimation performance is evaluated with both simulated and experimental data. Results show that, especially in reverberant scenarios, the proposed method presents an advantage in locating closely spaced sources when compared to the conventional SRP-PHAT, the group-sparse iterative covariance-based estimation (GSPICE) method, and the wideband MUSIC method with geometric averaging. Furthermore, it is observed that for a compact microphone array, the proposed method overall maintained its performance even when using SRP maps computed with grid resolutions that are lower than the sampling requirements of the broadband SRP function. Finally, results obtained with experimental data showed the validity and applicability of the proposed method in a practical meeting room environment.