Functional generalized inverse beamforming with regularization matrix applied to sound source localization

Abstract

Microphone arrays have become a popular technique to identify sound sources. They can be utilized to localize the sources for various applications. The most common application is the conventional beamforming that provides the source maps with strong side lobes and poor spatial resolution at low frequencies. To overcome these problems, the focus is set on deconvolution and generalized inverse techniques such as a deconvolution approach for the mapping of acoustic sources (DAMAS) and generalized inverse beamforming (GIB). Although the source maps are clearly improved, these methods have the shortcomings of expensive computing and limited dynamic range. In this paper, we propose a source localization method called functional generalized inverse beamforming with regularization matrix (FGIBR) based on an inverse problem. Compared with GIB, the accuracy of FGIBR could be improved by introducing a new beamforming regularization matrix and a scaling parameter c 0 . Also the dynamic range of the source maps can be increased by applying FGIBR with an exponent parameter called order v. Several simulated examples are given to illustrate that the side lobes are suppressed and the main lobe becomes much narrow; moreover, if order v is increased, the beamforming side lobes can be sharply reduced and the actual position of the noise source can be precisely located. Then FGIBR is implemented to deal with experimental data in the free field. In the case of the experiment, the source is correctly located. The proposed FGIBR demonstrates a good performance in terms of resolution and side lobe rejection compared with other beamforming methods. Furthermore, the computation time is shown to be low if the iteration and order are reasonable.