Abstract: Two premises need to be satisfied for conventional two-dimensional (2D) on-grid compressive beamforming with a planar microphone array to obtain accurate source identification results. One is that the direction of arrivals (DOAs) of the acoustic source are consistent with the discretized grid points (basis match); the other is that the related prior parameters need to be accurately estimated. However, the above two premises are difficult to meet in practical applications. In this case, the source identification performance of conventional 2D on-grid compressive beamforming will be significantly degraded due to the combined effects of the basis mismatch issue and inaccurate estimation of prior parameters. A 2D off-grid compressive beamforming acoustic source identification method based on orthogonal matching pursuit is proposed to solve this problem. It uses the first-order Taylor expansion of the transfer vector at the grid point to approximate the real transfer vector at the off-grid source, takes the on-grid coordinates, off-grid deviations and strengths of the sources as the unknown parameters to construct the equations, and solves them by orthogonal matching pursuit and least squares method to obtain the off-grid coordinate and strength estimates of the acoustic sources. Both simulations and experiments demonstrate that the proposed method can effectively alleviate the basis mismatch issue, obtain high accuracy of DOAs and source strengths estimation, and achieve better acoustic source identification performance than the conventional on-grid compressive beamforming. It enjoys high computational efficiency. Besides, the proposed method does not require prior knowledge of signal-to-noise ratio and/or regularization parameters and is insensitive to sparsity estimation and the grid spacing, and its acoustic source identification performance is robust.

Key words: acoustic source identification, planar microphone array, compressive beamforming, off-grid, orthogonal matching pursuit