Tony Gustafsson

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 time-delay estimator is shown to be optimal among a class of cross-correlation 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.

Source localization in reverberant environments: performance bounds and ML estimation

The main obstacle for designing robust microphone-based source localization systems is the effects of room reverberation. Based on well known results from statistical room acoustics, we present an analysis of the problem of localizing acoustical sources in the presence of room reverberation. In this context we derive the Cramer-Rao lower bound and also relevant ML estimators.

Estimation of acoustical room transfer functions

Presents a method to obtain room transfer functions for applications in the design of intelligent systems for video conferencing. In these applications the acoustical dynamics, for example, affects the quality of the recorded speech signal and the ability to achieve accurate source localization. The first part of the paper gives results on the identification of parameterized room transfer functions. The second part presents a method to extrapolate room transfer functions from the identified models. The extrapolation is achieved by getting a functional form of the transfer function parameters which depends on the speaker and the microphone locations.

Analysis of time-delay estimation in reverberant environments

The main obstacle for designing robust microphone-based source localization systems is the effects of room reverberation. Utilizing results from statistical room acoustics, we analyze the performance of GCC-based methods for time-delay estimation. An interesting outcome of the analysis is that the so-called PHAT time-delay estimator is shown to be optimal among a class of cross-correlation based time-delay estimators.

Statistical analysis of a signal separation method based on second order statistics

This paper explores an existing method for signal separation, which is based on second order statistics. Here, statistical analysis of a generalized version of the original algorithm is given. The generalized method includes a weighting matrix, and a result of the statistical analysis is that the best possible weighting is found. The problem of initialization of the involved non-linear optimization is also discussed.

Weighting in Subspace-Based System Identification

Abstract Subspace-based methods for system identification are often based on an estimate of the range space of the extended observability matrix. It is thus of great interest to investigate, and also optimize, the accuracy of the estimated subspace. Especially, the influence of certain weighting matrices is an unresolved issue. Here, an asymptotic analysis of the accuracy of the estimated subspace is presented. The main result of the analysis is that statistically sound weighting matrices are found.

Optimal weighting for MOESP type of procedures

Abstract In this paper we discuss the asymptotic properties of the MOESP type of subspace methods with respect to certain user-defined parameters. A new instrumental variables interpretation of these algorithms is given. This leads to a lower bound on the achievable estimation accuracy, which is different from the Cramer Rao lower bound. Some facts about the asymptotic covariance matrix are derived.