Enhancement of direction-of-arrival estimation performance of spherical ESPRIT via atomic norm minimisation

Abstract

Estimation of signal parameters via rotational invariance technique (ESPRIT) with spherical microphone arrays (abbreviated as spherical ESPRIT) has recently attracted considerable attention because it can panoramically estimate the direction-of-arrivals of acoustic sources and avoid the degradation in accuracy due to discretisation of the region of interest. However, the state-of-the-art spherical ESPRIT still fails to perform well at high frequencies and under the cases involving coherent sources, a small number of data snapshots, or low signal-to-noise ratios (SNRs). To overcome these limitations, an atomic norm minimisation (ANM) method is proposed, which can measure the source sparsity in a continuous domain. Hence, a novel covariance matrix can be obtained by solving the positive semidefinite programming that is equivalent to the ANM. It is not only independent of the orthogonality of the sampled spherical harmonics but can also decorrelate the sources and denoise the measured signals. The principle involves using the novel covariance matrix as opposed to the original covariance matrix as the spherical ESPRIT input. The simulations and experiments demonstrate that the cooperation with ANM aids the spherical ESPRIT in overcoming or mitigating the aforementioned limitations. Furthermore, the experiments demonstrate that the proposed method is effective in a typical reverberant environment.