A Closed-Form Method for Finding Source Locations from Microphone-Array Time-Decay Estimates

The linear intersection (LI) estimator, a closed-form method for the localization of source positions given only the sensor array time-delay estimate information, is presented. The array is constrained to be composed of 4-element sub-arrays configured in 2 centered orthogonal pairs. A bearing line in 3-space is estimated from each sub-array and potential source locations are found via closest intersection of bearing line pairs. The final location estimate is determined by a probabilistic weighting of these potential locations. The LI estimator is shown to be robust and accurate, to closely model the ML estimator, and to outperform a representative algorithm. The computational complexity of the LI estimator is suitable for use in real-time microphone-array applications