Broadband Source Localization From an Eigenanalysis Perspective

Broadband source localization has several applications ranging from automatic video camera steering to target signal tracking and enhancement through beamforming. Consequently, there has been a considerable amount of effort to develop reliable methods for accurate localization over the last few decades. Essentially, the localization process consists in finding the candidate source location that maximizes the synchrony between the properly time-shifted microphone outputs. In addition to using well known cross-correlation-based criteria such as the steered response power (SRP), minimum variance (MV), and multichannel cross-correlation (MCCC), this synchrony can also be measured using the averaged magnitude difference function (AMDF) and the averaged magnitude sum function (AMSF) whose calculations involve low computational cost. In earlier related works, the latter techniques have been used for time delay estimation (TDE) of a target source observed by only one pair of microphones. Their generalization to the multiple microphone case and application to source localization have not been studied yet. In this paper, we consider both categories, i.e., cross-correlation and AMDF (with AMSF)-based approaches, using an arbitrary number of microphones, and analyze their performance. Specifically, we first provide a unifying study of the most popular cross-correlation-based techniques, such as the SRP, MV, and MCCC. In this paper, we use the eigenanalysis of the parameterized spatial correlation matrix (PSCM) to classify these methods and gain some insight into their performance. We demonstrate, for instance, that the MV and SRP consist in searching the major eigenvalue of the PSCM, while the MCCC, essentially, combines its minor eigenvalues when scanning for the source location. Inspired by this analysis, we show, in the second part of this work, the efficiency of the AMDF and AMSF in localizing an acoustic source using multiple microphones. Indeed, we propose two new paramet- - erized matrices named as the parameterized averaged magnitude difference matrix (PAMDM) and the parameterized averaged magnitude sum matrix (PAMSM). The eigenanalysis of these matrices also reveals new criteria for acoustic source localization. Simulation results are provided to illustrate the effectiveness of all the investigated and proposed methods.