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

Ryo Matsuda1, Makoto Otani1

  • 1Department of Architecture and Architectural Engineering, Graduate School of Engineering, Kyoto University, Kyoto-daigaku-katsura, Nishikyo-ku, Kyoto, 615-8540, Japan.

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This study introduces Gaussian process (GP) regression for accurate sound field estimation in anechoic conditions. The novel method improves accuracy and reduces computational cost by modeling sound sources as distributions.

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Area of Science:

  • Acoustics
  • Signal Processing
  • Machine Learning

Background:

  • Estimating inhomogeneous sound fields, especially those containing sources, presents significant challenges in acoustics.
  • Conventional methods often struggle with accuracy and computational efficiency in complex sound environments.

Purpose of the Study:

  • To propose a novel Gaussian process (GP) based method for accurately estimating inhomogeneous sound fields under anechoic conditions.
  • To enhance the accuracy and reduce the computational cost of sound field estimation by treating sound sources as probability distributions.

Main Methods:

  • Developed a kernel function for GP regression based on weighted spatial correlation of free-field transfer functions in the modal domain.
  • Derived weights for the kernel function by introducing a probability distribution of sound source positions within spherical regions.
  • Proposed analytical solutions for spherical integrals using Gaussian probability distributions and introduced schemes for order truncation and hyperparameter optimization.

Main Results:

  • Numerical experiments demonstrated that the proposed GP method significantly outperforms conventional techniques in sound field estimation accuracy.
  • The GP regression utilizing the proposed kernel function achieved superior accuracy with a lower computational cost compared to other weighting schemes.
  • The benefits of modeling sound sources as distributions, rather than point sources, were clearly revealed, enhancing estimation performance.

Conclusions:

  • The proposed Gaussian process regression method offers a robust and efficient solution for inhomogeneous sound field estimation in anechoic environments.
  • Treating sound sources as probability distributions is a key factor in achieving higher accuracy and computational efficiency.
  • This approach provides a valuable advancement for acoustic analysis and signal processing applications.