Exterior sound field estimation based on physics-constrained kernel

TL;DR

This paper introduces a physics-constrained Gaussian process kernel for exterior sound field interpolation, enabling flexible microphone configurations and automatic attenuation of higher harmonics, with improved accuracy over traditional methods.

Contribution

It presents a novel kernel-based interpolation method that does not depend on microphone arrangement and optimizes parameters directly from recordings, enhancing exterior sound field estimation.

Findings

Achieves approximately 2 dB lower interpolation error than conventional methods.

Provides more consistent reconstruction of the ground truth sound field.

Works effectively across frequencies from 100 Hz to 2.5 kHz.

Abstract

Exterior sound field interpolation is a challenging problem that often requires specific array configurations and prior knowledge on the source conditions. We propose an interpolation method based on Gaussian processes using a point source reproducing kernel with a trainable inner product formulation made to fit exterior sound fields. While this estimation does not have a closed formula, it allows for the definition of a flexible estimator that is not restricted by microphone distribution and attenuates higher harmonic orders automatically with parameters directly optimized from the recordings, meaning an arbitrary distribution of microphones can be used. The proposed kernel estimator is compared in simulated experiments to the conventional method using spherical wave functions and an established physics-informed machine learning model, achieving lower interpolation error by approximately 2 dB on average within the analyzed frequencies of 100 Hz and 2.5 kHz and reconstructing the ground truth sound field more consistently within the target region.