Spatial Covariance Estimation for Sound Field Reproduction Using Kernel Ridge Regression

Many sound field reproduction methods require knowledge of the spatial covariance, a quantity derived from room impulse responses in a region. The spatial covariance is commonly computed as the sample covariance, even though this often leads to poor estimates in practice due to spatial undersampling. This paper proposes a method for estimating sound fields generated by multiple sound sources, with the goal of improving spatial covariance estimation. The method includes prior knowledge, which allows for previous covariance estimates to be combined with new sound field measurements. A sound zone control problem is considered where the estimated spatial covariance is used to generate sound in a simulated room. The experiment shows that the proposed method provides an improvement in sound field reproduction performance when both sound field data and spatial covariance data can be combined.