Focusing and frequency smoothing for arbitrary arrays with application to speaker localization

The coherent signal subspace method (CSSM) enables the direction-of-arrival (DoA) estimation of coherent sources with subspace localization methods. The focusing process that aligns the signal subspaces within a frequency band to its central frequency is central to the CSSM. Within current focusing approaches, a direction-independent focusing approach may be more suitable for reverberant environments since no initial estimation of the sources' DoAs is required. However, these methods use integrals over the steering function, and cannot be directly applied to arrays around complex scattering structures, such as robot heads. In this article, current direction-independent focusing methods are extended to arrays for which the steering function is available only for selected directions, typically in a numerical form. Spherical harmonics decomposition of the steering function is then employed to formulate several aspects of the focusing error. A case of two coherent sources is studied and guidelines for the selection of the frequency smoothing bandwidth are suggested. The performance of the proposed methods is then investigated for an array that is mounted on a robot head. The focusing process is integrated within the direct-path dominance (DPD) test method for speaker localization, originally designed for spherical arrays, extending its application to arrays with arbitrary configurations. Finally, experiments with real data verify the feasibility of the proposed method to successfully estimate the DoAs of multiple speakers under real-world conditions.