Sparse planar arrays for azimuth and elevation using experimental data.

Sparse arrays are special geometrical arrangements of sensors which overcome some of the drawbacks associated with dense uniform arrays and require fewer sensors. For direction finding applications, sparse arrays with the same number of sensors can resolve more sources while providing higher resolution than a dense uniform array. This has been verified numerically and with real data for one-dimensional microphone arrays. In this study the use of nested and co-prime arrays is examined with sparse Bayesian learning (SBL), which is a compressive sensing algorithm, for estimating sparse vectors and support. SBL is an iterative parameter estimation method and can process multiple snapshots as well as multiple frequency data within its Bayesian framework. A multi-frequency variant of SBL is proposed, which accounts for non-flat frequency spectra of the sources. Experimental validation of azimuth and elevation [two-dimensional (2D)] direction-of-arrival (DOA)estimation are provided using sparse arrays and real data acquired in an anechoic chamber with a rectangular array. Both co-prime and nested arrays are obtained by sampling this rectangular array. The SBL method is compared with conventional beamforming and multiple signal classification for 2D DOA estimation of experimental data.

Three-dimensional source localization using sparse Bayesian learning on a spherical microphone array.

The identification of acoustic sources in a three-dimensional (3D) domain based on measurements with an array of microphones is a challenging problem: it entails the estimation of the angular position of the sources (direction of arrival), distance relative to the array (range), and the quantification of the source amplitudes. A 3D source localization model using a rigid spherical microphone array with spherical wave propagation is proposed. In this study, sparse Bayesian learning is used to perform localization in 3D space and examine the use of principal component analysis to denoise the measurement data. The performance of the proposed method is examined numerically and experimentally, which is tested both in a free-field and in a reverberant environment. The numerical and experimental investigations demonstrate that the approach offers accurate localization in a 3D domain, resolving closely spaced sources and making it possible to identify sources located at different ranges.

Alternating direction method of multipliers for weighted atomic norm minimization in two-dimensional grid-free compressive beamforming.

An algorithm is developed based on alternating direction method of multipliers to solve the weighted atomic norm minimization in two-dimensional grid-free compressive beamforming. Simulations and experiments are carried out to compare this algorithm with the off-the-shelf interior point method based sdpt3 solver in cvx toolbox. Whether a standard uniform rectangular array or a non-uniform array constructed by a small number of microphones is utilized, this algorithm is feasible and faster.

Resolution enhancement of two-dimensional grid-free compressive beamforming.

Reconstructing the acoustic source distribution via imposing a sparsity constraint on a continuum, the atomic norm minimization (ANM) based grid-free compressive beamforming can eliminate the basis mismatch of conventional grid-based compressive beamforming. However, it works well only for sufficiently separated sources, which prohibits high resolution. The drawback arises because it uses an atomic norm to measure the source sparsity, while the atomic norm is not a direct sparse metric and its minimization is equivalent to the sparsity constraint only when the sources are sufficiently separated. This paper devotes itself to overcoming the drawback for the two-dimensional ANM based grid-free compressive beamforming. First, a sparse metric that can promote sparsity to a greater extent than the atomic norm is proposed. Then, using this metric a minimization problem is formulated and the majorization-minimization (MM) solving algorithm is introduced. MM iteratively conducts atomic norm minimization with a sound reweighting strategy, and therefore the developed method can be termed as iterative reweighted atomic norm minimization (IRANM). Both simulations and experiments demonstrate that whether a standard uniform rectangular array or a non-uniform array constituted by a small number of microphones is utilized, IRANM can overcome the drawback and thus enhance the resolution.

Two-dimensional grid-free compressive beamforming.

Compressive beamforming realizes the direction-of-arrival (DOA) estimation and strength quantification of acoustic sources by solving an underdetermined system of equations relating microphone pressures to a source distribution via compressive sensing. The conventional method assumes DOAs of sources to lie on a grid. Its performance degrades due to basis mismatch when the assumption is not satisfied. To overcome this limitation for the measurement with plane microphone arrays, a two-dimensional grid-free compressive beamforming is developed. First, a continuum based atomic norm minimization is defined to denoise the measured pressure and thus obtain the pressure from sources. Next, a positive semidefinite programming is formulated to approximate the atomic norm minimization. Subsequently, a reasonably fast algorithm based on alternating direction method of multipliers is presented to solve the positive semidefinite programming. Finally, the matrix enhancement and matrix pencil method is introduced to process the obtained pressure and reconstruct the source distribution. Both simulations and experiments demonstrate that under certain conditions, the grid-free compressive beamforming can provide high-resolution and low-contamination imaging, allowing accurate and fast estimation of two-dimensional DOAs and quantification of source strengths, even with non-uniform arrays and noisy measurements.

A refined wideband acoustical holography based on equivalent source method.

This paper is concerned with acoustical engineering and mathematical physics problem for the near-field acoustical holography based on equivalent source method (ESM-based NAH). An important mathematical physics problem in ESM-based NAH is to solve the equivalent source strength, which has multiple solving algorithms, such as Tikhonov regularization ESM (TRESM), iterative weighted ESM (IWESM) and steepest descent iteration ESM (SDIESM). To explore a new solving algorithm which can achieve better reconstruction performance in wide frequency band, a refined wideband acoustical holography (RWAH) is proposed. RWAH adopts IWESM below a transition frequency and switches to SDIESM above that transition frequency, and the principal components of input data in RWAH have been truncated. Further, the superiority of RWAH is verified by the comparison of comprehensive performance of TRESM, IWESM, SDIESM and RWAH. Finally, the experiments are conducted, confirming that RWAH can achieve better reconstruction performance in wide frequency band.