A closed-form method for finding source locations from microphone-array time-decay estimates

1. ABSTRACT 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 conngured 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-nal location estimate is determined by a probabilistic weighting of these potential locations. The LI estima-tor 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. 2. INTRODUCTION Microphone-array systems can be used to determine the positions of active talkers and can be electronically steered to provide spatially-selective speech acquisition. Since it is steered electronically, a microphone-array's directivity pattern can be updated rapidly to follow a moving talker or to switch between several alternating or simultaneous talkers. These features make microphone-arrays an attractive alternative to single microphone systems for hands-free speech acquisition, especially those involving multiple or moving sources. The ability of microphone-array systems to determine talker location makes them attractive for use in multimedia teleconferencing systems where the location of the talker can be used not only for steering the directivity of the microphone-array, but also for pointing cameras or determining binaural cues for stereo imaging. In microphone-array systems a directly observable signal characteristic is inter-sensor delay. Extensive literature exists on the topic of inter-sensor delay estimation and subsequent source location 1]. To achieve a high update rate in real-time situations, a practical source-location procedure must be computationally inexpensive. This requirement favors closed-form solutions 2, 3, 4, 5, 6] over search-based methods. The locationing problem addressed here may be stated as follows. There are N pairs of sensors m i1 and m i2 for i 2 1; N]. The ordered triplet (x,y,z) of spatial coordinates for the sensors will be denoted by m i1 and m i2 , respectively. For each sensor pair, a time-diierence of arrival (TDOA) estimate, i , for a signal source located at s is available. The true TDOA associated with a source, s, and the i th sensor-pair is given by: T (fm i1 ; m i2 g; s) = js ? m i1 j ? js ? m i2 j c (1) where c …