Source localization in reverberant environments: modeling and statistical analysis

Room reverberation is typically the main obstacle for designing robust microphone-based source localization systems. The purpose of the paper is to analyze the achievable performance of acoustical source localization methods when room reverberation is present. To facilitate the analysis, we apply well known results from room acoustics to develop a simple but useful statistical model for the room transfer function. The properties of the statistical model are found to correlate well with results from real data measurements. The room transfer function model is further applied to analyze the statistical properties of some existing methods for source localization. In this respect we consider especially the asymptotic error variance and the probability of an anomalous estimate. A noteworthy outcome of the analysis is that the so-called PHAT timedelay estimator is shown to be optimal among a class of crosscorrelation based time-delay estimators. To verify our results on the error variance and the outlier probability we apply the image method for simulation of the room transfer function.