Sound Field Estimation With Moving Microphones Using Kernel Ridge Regression

Sound field estimation with moving microphones can increase flexibility, decrease measurement time, and reduce equipment constraints compared to using stationary microphones. In this paper a kernel ridge regression (KRR)-based method is presented for sound field estimation with moving microphones. The proposed KRR method is constructed to estimate room impulse response (RIR) as a function of receiver position, using a discrete time continuous space sound field model based on the discrete Fourier transform and the Herglotz wave function. The proposed method allows for the inclusion of prior knowledge as a regularization penalty, similar to KRR methods for sound field estimation with stationary microphones, which is then novel for moving microphones. Using a directional weighting for the proposed method, the estimates are improved, which is demonstrated on both simulated and real data. Due to the high computational cost of sound field estimation with moving microphones, an approximate KRR method is also proposed, using random Fourier features (RFF) to approximate the kernel. The RFF method is shown to decrease computational cost while obtaining less accurate estimates compared to the KRR method, providing a trade-off between cost and performance.