Recursive Spatial Covariance Estimation with Sparse Priors for Sound Field Interpolation

Recent advances have shown that sound fields can be accurately interpolated between microphone measurements when the spatial covariance matrix is known. This matrix may be estimated in various ways; one promising approach is to use a plane wave formulation with sparse priors, although this may require the use of a many microphones to suppress the noise. To overcome this, we introduce a time domain formulation exploiting multiple time samples, posing the problem as an identification problem of a recursively estimated sample covariance matrix. A computationally efficient method is proposed to solve the resulting identification problem. Using both numerical experiments and anechoic data, the proposed method is shown to yield preferable performance as compared to current state of the art methods, notably for high frequencies sources and/or in cases when using few microphones.