On time delay estimation based on multichannel spatiotemporal sparse linear prediction

Noise and reverberation can significantly affect the performance of time delay estimation (TDE) in room acoustic environments. The multichannel cross-correlation coefficient (MCCC) algorithm, which extends the traditional cross-correlation method from two to multiple channels, can exploit the spatial information among multiple microphones to improve the robustness of TDE with respect to environmental noise; but this algorithm is not robust to reverberation. The multichannel spatiotemporal prediction (MCSTP) algorithm uses both the spatial and temporal information provided by the array. This algorithm improves significantly the robustness of TDE with respect to reverberation; however, it is found sensitive to noise. In this paper, we develop a multichannel spatiotemporal sparse prediction (MCSTSP) algorithm for TDE. This algorithm obtains a good compromise between robustness of TDE to noise and that to reverberation through making a tradeoff between pre-whitening and non-prewhitening. This is achieved via adjusting a regularization parameter, which is solved by an augmented Lagrangian alternating direction method of multipliers (ADMM). The property of this developed algorithm is justified with numerical experiments in both noisy and reverberant environments.