In many multi-microphone algorithms, an estimate of the relative transfer functions (RTFs) of the desired speaker is required. Recently, a computationally efficient RTF vector estimation method was proposed for acoustic sensor networks, assuming that the spatial coherence (SC) of the noise component between a local microphone array and multiple external microphones is low. Aiming at optimizing the output signal-to-noise ratio (SNR), this method linearly combines multiple RTF vector estimates, where the complex-valued weights are computed using a generalized eigenvalue decomposition (GEVD). In this paper, we perform a theoretical bias analysis for the SC-based RTF vector estimation method with multiple external microphones. Assuming a certain model for the noise field, we derive an analytical expression for the weights, showing that the optimal model-based weights are real-valued and only depend on the input SNR in the external microphones. Simulations with real-world recordings show a good accordance of the GEVD-based and the model-based weights. Nevertheless, the results also indicate that in practice, estimation errors occur which the model-based weights cannot account for.

翻译：基于空间相干性的RTF向量估计在扩散声场中的偏差分析对于许多多麦克风算法，需要估计所需扬声器的相对传递函数（RTFs）。最近，针对声音传感器网络提出了一种计算有效的RTF向量估计方法，假设本地麦克风阵列和多个外部麦克风之间的噪声成分的空间相干性（SC）很低。该方法旨在优化输出信噪比（SNR），其中线性组合多个RTF向量估计，复杂值权重使用广义特征值分解（GEVD）计算。本文针对多个外部麦克风的基于SC的RTF向量估计方法进行了理论偏差分析。在假设噪声场的某种模型的前提下，我们推导出一个权重的分析表达式，表明最佳的模型基权重是实值的，并且仅依赖于外部麦克风中的输入SNR。实际录音的模拟结果表明，GEVD基于的权重和模型基的权重吻合较好。然而，结果还表明，在实践中会出现估计误差，模型基的权重无法解决。