A maximum likelihood approach for underdetermined TDOA estimation

This paper considers the estimation of time difference of arrival (TDOA) of multiple sparse sources when the number of sources is larger than that of the microphones. White Gaussian noise is assumed present at the microphone in addition to the instantaneously mixed sources. The TDOA estimate is obtained based on a maximum likelihood (ML) criteria, and the likelihood is obtained by marginalizing the joint probability over the sources. Explicit marginalization is mathematically intractable, thus the joint probability is approximated as a summation of several Dirac delta functions by assuming the time-frequency component of the source distribution to be a complex-valued super Gaussian, and the global maximum point of the marginalized joint probability is found by Markov chain Monte Carlo sampling. Experimental results show that the proposed algorithm outperforms TDOA estimation using a well-known Gaussian based approximation method in terms of root-mean-square error (RMSE).