Sound field estimation for source-included region based on Gaussian process using prior source information

Estimating a sound field in a region that includes sources (i.e., an inhomogeneous sound field) is challenging. This paper proposes the Gaussian process (GP) for estimating an inhomogeneous sound field in the case of anechoic condition. A kernel function is formulated as a weighted spatial correlation of free-field transfer functions in the modal domain. The weights for the kernel function are derived by introducing the probability distribution of source positions in spherical regions containing the sound sources. Here, a weight obtained by analytically solving the spherical integral with the probability distribution as Gaussian is proposed. Schemes of order truncation and hyperparameter optimization for the kernel function are also proposed. Compared with conventional methods, numerical experiments reveal that the proposed method achieves higher sound field estimation accuracy. In addition, Gaussian process regression, using the kernel function with the proposed weight, achieves higher estimation accuracy with lower computational cost than those using the kernel functions with other weights. Moreover, the advantages of the proposed method, which are obtained by treating the sound source as a distribution rather than a point source, are revealed.