Study On The Improvement Of Two-dimensional Grid-free Compressive Beamforming For Acoustic Source Identification

Two-dimensional compressive beamforming based on a planar microphone array measurement is a promising method for acoustic source identification.The on-fixed-grid compressive beamforming proposed earlier assumes that the acoustic sources fall on the fixed grid points which are preset as bases.When the acoustic source does not fall on the grid point,the real basis of the source does not match the preset basis,and the acoustic source identification performance is deteriorated,that is,the basis mismatch problem occurs.Although the newly proposed two-dimensional grid-free compressive beamforming can fundamentally overcome the basis mismatch problem,it has two disadvantages:one is that the existing methods require a priori noise parameter,and the other is that the array geometry is limited to uniform rectangular array and sparse rectangular array.The above shortcomings limit the popularization and application of the two-dimensional grid-free compressive beamforming.Therefore,this paper focuses on the above two problems.Firstly,the on-fixed-grid compressive beamforming is derived based on the plane wave assumption and the iterative weightedl₁ minimization algorithm is established.The basis mismatch problem is discussed through simulations.To overcome the problem,two-dimensional grid-free compressive beamforming based on the atomic norm minimization is proposed.The existing methods based on the interior point method and the alternating direction method of multiplier involve a prior noise parameter,which is challenging to accurately estimate in many situations.To circumvent this prior parameter,an iterative Vandermonde decomposition and shrinkage-thresholding based two-dimensional grid-free compressive beamforming is proposed.It implements the atomic norm minimization by iteratively performs smoothing,gradient descent,and proximal mapping based on accelerated proximal gradient framework without invoking SDP.The simulation and experiments results show that compared to the existing methods with accurately estimated noise,the proposed method achieves an equivalent direction-of-arrival estimation accuracy and a higher source strength quantification accuracy and is more robust.However,due to the limitation of the mathematical model,the two-dimensional grid-free compressive beamforming is limited to measuring with regular rectangular arrays and not suitable for arbitrary array geometries,which limits its popularization and application.To break this limitation,a new two-dimensional grid-free compressive beamforming strategy for arbitrary planar array geometries is proposed.The core is to transform the microphone pressure into the two-dimensional Fourier series expansion based on the two-dimensional discrete Fourier transform.The term truncation method of Fourier series polynomials is established.Then,the atomic norm minimization problem is proposed for acoustic source identification.The effectiveness and feasibility of the proposed method in the acoustic source identification are verified by simulation and experiment.The simulation results show that the proposed method can achieve accurate source identification,but it has a lower applicable upper frequency,higher computational complexity and is not robust to noise.These are subjects worthy of further study.