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.

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.

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.

A novel approach for signal parameter estimation, named the non-linear instantaneous least squares (NILS) estimator, is proposed and a high SNR statistical analysis of the estimates is presented. The algorithm is generally applicable to deterministic signal in noise models. However, it is of particular interest in applications where the "conventional" non-linear least squares criterion suffers from numerous local minima. The key idea here is to apply a sliding window to estimate the instantaneous amplitude, which is then used in a separable least squares criterion-function. Hereby the radius of attraction of the global minimum is under the control of the user, which makes the NILS approach advantageous to use in practical applications. Numerical results using polynomial-phase signals validate the theoretical results.

In this paper an instrumental variable based subspace tracking algorithm is proposed. The basic idea of the algorithm is to reduce the amount of computations using a certain perturbation/approximation strategy. The complexity is reduced to O(mn/sup 2/), which should be compared to O(ml/sup 2/) for the SVD, where m, l/spl Gt/n in general (m denotes the number of sensors, l denotes the number of instruments, and n denotes the number of signals). The proposed algorithm turns out to be related to Karasalo's subspace averaging approach (1986). In a series of simulations we demonstrate that the detection, stationary estimation, and tracking performance of the proposed algorithm is essentially equivalent to that achieved by the truncated SVD.