Robust Adaptive Time Delay Estimation for Speaker Localisation in Noisy and Reverberant Acoustic Environments

In this paper, two adaptive algorithms are presented for robust time delay estimation (TDE) in acoustic environments where a large amount of background noise and reverberation is present. Recently, an adaptive eigenvalue decomposition (EVD) algorithm has been developed for TDE between two microphones in highly reverberant acoustic environments. In this paper, we extend the adaptive EVD algorithm to noisy and reverberant acoustic environments, by deriving an adaptive stochastic gradient algorithm for the generalised eigenvalue decomposition (GEVD) or by prewhitening the noisy microphone signals. In addition, we extend all considered TDE algorithms to the case of more than two microphones. We have performed simulations using a localised and a diffuse noise source for several SNRs (ranging from −10 dB to 10 dB), showing that the time delays can be estimated more accurately using the adaptive GEVD algorithm than using the adaptive EVD algorithm. However, the difference in performance between these two algorithms is negligible for SNRs higher than 5 dB and for a diffuse noise source. In addition, we have analysed the sensitivity of the adaptive GEVD algorithm w.r.t. the accuracy of the noise correlation matrix estimate, showing that the performance may be quite sensitive, especially for low SNR scenarios. Index Terms Time delay estimation, Acoustic source localisation, Generalised eigenvalue decomposition, stochastich gradient