Fourth-order cumulant multiple matrix reconstruction to estimate direction of arrival for coherent sound source under low signal-to-noise ratio

A direction of arrival (DOA) estimation method that adopts higher-order matrix transformation, named fourth-order cumulant multiple matrix reconstruction (FOC-MMR), is proposed to effectively estimate the DOA of the coherent sound sources which cause the subspace energy dispersion and under-rank of the covariance matrix. Firstly, short-time Fourier transform is performed on the array sound pressure data in frames. Secondly, singular value decomposition (SVD) of the fourth-order cumulant-expanded higher-order covariance matrix is calculated to obtain the higher-order noise eigenvectors, which are orthogonally matched with the expanded higher-order array manifold vector. Finally, DOA estimation of the coherent signals is achieved. The simulation results of coherent single-frequency rectangular pulse signal show that when the signal-to-noise ratio (SNR) ≥ −15 dB, applying the proposed method to the uniform linear array (ULA, M = 4), the root mean square error (RMSE) of coherent signals (θ₁ = −20° and θ₂ = 20°) remains within 1.5°. The correctly resolved azimuth interval \Delta \theta can be as low as 5° when the SNR = 10 dB. The coherent pulse sound source experiment mixed with SNR = 5 dB Gaussian white noise verifies that when applying the FOC-MMR algorithm to a rectangular area array composed of multiple ULAs, it can distinguish adjacent sound sources with a high degree of ability to suppress Gaussian noise. The proposed method achieves full-rank high-order covariance matrix by reconstructing the virtual sound pressure array data, which not only solves the problem of energy diffusion between noise and signal eigenvectors caused by signal coherence, but also the DOA estimation of multiple groups of coherent sound sources with wide-angle incidence is achieved with higher direction measurement accuracy and spatial resolution.