A method for estimating the incident sound field inside a region containing scattering objects is proposed. The sound field estimation method has various applications, such as spatial audio capturing and spatial active noise control; however, most existing methods do not take into account the presence of scatterers within the target estimation region. Although several techniques exist that employ knowledge or measurements of the properties of the scattering objects, it is usually difficult to obtain them precisely in advance, and their properties may change during the estimation process. Our proposed method is based on the kernel ridge regression of the incident field, with a separation from the scattering field represented by a spherical wave function expansion, thus eliminating the need for prior modeling or measurements of the scatterers. Moreover, we introduce a weighting matrix to induce smoothness of the scattering field in the angular direction, which alleviates the effect of the truncation order of the expansion coefficients on the estimation accuracy. Experimental results indicate that the proposed method achieves a higher level of estimation accuracy than the kernel ridge regression without separation.

翻译：提出了一种估计包含散射体区域内部入射声场的方法。声场估计方法具有多种应用，例如空间音频采集和空间有源噪声控制；然而，现有大多方法未考虑目标估计区域内散射体的存在。尽管存在一些利用散射体属性知识或测量值的技术，但通常难以精确地预先获取这些信息，且其属性可能在估计过程中发生变化。我们提出的方法基于入射场的核岭回归，并通过球面波函数展开分离散射场，从而无需对散射体进行先验建模或测量。此外，我们引入权重矩阵来促使散射场在角度方向上的平滑性，从而减轻展开系数截断阶数对估计精度的影响。实验结果表明，所提方法比未进行分离处理的核岭回归实现了更高的估计精度。