用可学习内积核的高斯过程，实现任意麦克风分布下的外场声场插值。
Exterior sound field estimation based on physics-constrained kernel
- 基于可训练内积的点源核，构建物理约束的高斯过程模型。
- 在100Hz至2.5kHz频段平均误差降低约2dB，重建更贴近真实声场。
- 无需特定阵列布局，自动抑制高阶谐波，适合复杂麦克风分布场景。
外部声场插值是一个挑战性问题，通常需要特定的麦克风阵列配置和声源先验知识。本文提出一种基于高斯过程的插值方法，采用具有可训练内积形式的点源再生核，以适应外部声场特性。该方法虽无闭式解，但能定义灵活的估计器，不依赖麦克风分布，并通过直接从录音中优化参数，自动衰减高阶谐波。在模拟实验中，与基于球面波函数的传统方法及已有的物理信息机器学习模型相比，在100 Hz至2.5 kHz频率范围内平均插值误差降低约2 dB，且在目标区域更一致地重构出真实声场。
原文摘要 · Abstract (English)
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.
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