A time delay estimation approach with low computational complexity for speaker localization

Time delay estimation (TDE), which aims at estimating the time difference of arrival using the signals captured by an array of microphones, plays an essential role in hands-free speech communication systems for localizing and tracking speakers. The sparse linear prediction model, which is based on the l1-norm optimization with respect to the prediction-error vector and the coefficient vector of the linear predictor, can be effectively used to prefilter the microphone signals so as to establish a time delay estimator robust to background noise and reverberation. In the course to solve this model, however, a high-dimension cross-correlation matrix has to be inverted, indicating that the corresponding TDE algorithm has huge computational load. In this paper, we propose a new solution approach to this dual l1-norm optimization model. The original prediction-error filter is decomposed by Kronecker product into two short subpredictors. Accordingly, the size of the cross-correlation matrix in the TDE algorithm is degraded, which significantly reduces the computational complexity for prewhitening microphone signals. Simulation experiments in room acoustic environments demonstrate the computational efficiency of the proposed TDE algorithm as well as its estimation precision.