The linear intersection (LI) estimator, which is a closed-form method for the localization of source positions given sensor array time-delay estimate information, is presented. The LI estimator is shown to be robust and accurate, to closely model the search-based ML estimator, and to outperform a benchmark algorithm. The computational complexity of the LI estimator is suitable for use in real-time microphone-array applications where search-based location algorithms may be infeasible