An update rule for multiple source variances estimation using microphone arrays

This paper addresses the problem of time-varying variance estimation in scenarios with multiple speech sources and background noise using a microphone array, which is an important issue in speech enhancement. Under the optimal principle of maximum likelihood (ML), the variance estimation under the general cases occurs no explicit formula, and all the variances require to be updated iteratively. Inspired by the fixed-point iteration (FPI) method, we derive an update rule for variance estimation by introducing a dummy term and exploiting the ML condition. Insights into the update rule is investigated and the relationship with the variance estimates under least-squares (LS) principle is presented. Finally, by simulations, we show that the resulting variance update rule is very efficient and effective, which requires only a few iterations to converge, and the estimation error is very close to the Cramér–Rao Bound (CRB).