Multi-Source Position and Direction-of-Arrival Estimation Based on Euclidean Distance Matrices

Abstract

A popular method to estimate the positions or directions-of-arrival (DOAs) of multiple sound sources using an array of microphones is based on steered-response power (SRP) beamforming. For a three-dimensional scenario, SRP-based methods require joint optimization of three continuous variables for position estimation or two continuous variables for DOA estimation, which can be computationally expensive when high localization accuracy is desired. In this paper, we propose novel methods for multi-source position and DOA estimation by exploiting properties of Euclidean distance matrices (EDMs) and their respective Gram matrices. All methods require estimated time-differences of arrival (TDOAs) between the microphones. In the proposed multi-source position estimation method, only a single continuous variable per source, representing the distance to a reference microphone, needs to be optimized. For each source, the optimal distance variable and set of candidate TDOA estimates are determined by minimizing a cost function defined using the eigenvalues of the Gram matrix. The estimated relative source positions are then mapped to absolute source positions by solving an orthogonal Procrustes problem. The proposed multi-source DOA estimation method eliminates the need for continuous variable optimization. The optimal set of candidate TDOA estimates is determined by minimizing a cost function defined using the eigenvalues of a rank-reduced Gram matrix. For two sources in a noisy and reverberant environment, experimental results for different source and microphone configurations with six microphones show that the proposed EDM-based method consistently outperforms the SRP-based method in terms of position and DOA estimation accuracy and run time.