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基于球谐域四阶累积量的混响相干声源定位

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

  • 摘要: 针对室内混响环境下相干声源定位精度低、空间谱出现伪峰及混叠的问题,提出一种基于球谐域四阶累积量多重矩阵重构的波达方向(DOA)估计方法。该方法利用球形阵列的旋转不变性及球谐域频率平滑特性抑制混响多径干扰,结合四阶累积量扩展阵列虚拟孔径并抑制高斯白噪声,通过多重矩阵重构技术恢复相干信号协方差矩阵的秩。首先对阵列接收信号进行短时傅里叶变换(STFT),筛选高信噪比时频点;将其变换至球谐域并构建四阶累积量矩阵;随后采用随机Krylov奇异值分解获取高阶信号子空间与噪声子空间;最后构建空间谱函数实现DOA估计。仿真实验表明,在不同混响时间及信噪比条件下,该方法相比传统球谐域MUSIC算法及频率平滑类算法,具有更高的定位精度、更窄的主瓣宽度及更好的鲁棒性,尤其是在高混响场景下,定位误差(均方根误差为7.38°)显著低于对比算法(21.40°),有效解决了混响环境下相干声源的高分辨率定位问题。

     

    Abstract: 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°).

     

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