Time delay estimation via minimum entropy

Time delay estimation (TDE) is a basic technique for numerous applications where there is a need to localize and track a radiating source. The most important TDE algorithms for two sensors are based on the generalized cross-correlation (GCC) method. These algorithms perform reasonably well when reverberation or noise is not too high. In an earlier study by the authors, a more sophisticated approach was proposed. It employs more sensors and takes advantage of their delay redundancy to improve the precision of the time difference of arrival (TDOA) estimate between the first two sensors. The approach is based on the multichannel cross- correlation coefficient (MCCC) and was found more robust to noise and reverberation. In this letter, we show that this approach can also be developed on a basis of joint entropy. For Gaussian signals, we show that, in the search of the TDOA estimate, maximizing MCCC is equivalent to minimizing joint entropy. However, with the generalization of the idea to non-Gaussian signals (e.g., speech), the joint entropy-based new TDE algorithm manifests a potential to outperform the MCCC-based method.