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In this paper, we show that minimization of the statistical dependence using broadband independent component analysis (ICA) can be successfully exploited for acoustic source localization. As the ICA signal model inherently accounts for the presence of several sources and multiple sound propagation paths, the ICA criterion offers a theoretically more rigorous framework than conventional techniques based on an idealized single-path and single-source signal model. This leads to algorithms which outperform other localization methods, especially in the presence of multiple simultaneously active sound sources and under adverse conditions, notably in reverberant environments. Three methods are investigated to extract the time difference of arrival (TDOA) information contained in the filters of a two-channel broadband ICA scheme. While for the first, the blind system identification (BSI) approach, the number of sources should be restricted to the number of sensors, the other methods, the averaged directivity pattern (ADP) and composite mapped filter (CMF) approaches can be used even when the number of sources exceeds the number of sensors. To allow fast tracking of moving sources, the ICA algorithm operates in block-wise batch mode, with a proportionate weighting of the natural gradient to speed up the convergence of the algorithm. The TDOA estimation accuracy of the proposed schemes is assessed in highly noisy and reverberant environments for two, three, and four stationary noise sources with speech-weighted spectral envelopes as well as for moving real speech sources.