Reverberant Coherent Sound Source Localization Based on Fourth-Order Cumulants in Spherical Harmonic Domain

To address the issues of low localization accuracy and spatial spectrum aliasing caused by coherent sound sources in indoor reverberant environments, a Direction-of-Arrival (DOA) estimation method based on Fourth-Order Cumulant Multi-Matrix Reconstruction in the Spherical Harmonic Domain (SHFOC-MMR) is proposed. By leveraging the rotational invariance of spherical arrays and the frequency-smoothing characteristics of the spherical harmonic domain, the method effectively suppresses multipath reverberation. Furthermore, fourth-order cumulants are employed to extend the virtual aperture and suppress Gaussian noise, while matrix reconstruction is used to restore the rank of the covariance matrix for coherent signals. Specifically, the received signals are first processed using the Short-Time Fourier Transform (STFT) to select high-energy time–frequency points. These points are then transformed into the spherical harmonic domain to construct fourth-order cumulant matrices, followed by Randomized Krylov Subspace-based Singular Value Decomposition (SVD) to separate signal and noise subspaces for spatial spectrum search. Simulation results under varying reverberation conditions demonstrate that the proposed method achieves higher localization accuracy, improved directivity, and enhanced robustness compared with traditional algorithms. In particular, in high-reverberation scenarios, the localization error—measured as root-mean-square error—is 7.38°, significantly lower than that of the compared algorithm (21.40°).