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SOURCE LOCALIZATION PROBLEM
The localization of a radiant point source is a common problem to many scientific research areas, such as seismology and astronomy, and it is the basis for the development of technologies like GPS, radar and sonar devices. In particular, the acoustic source localization has been a leading research topic in the audio and acoustics communities for quite a few decades. The ability to locate a sound source is a prerequisite for the proper functioning of many relevant applications, e.g., automatic camera tracking for video--conferencing and beamformer steering for suppressing noise and reverberation in voice processing systems.
In general, given an array of sensors located at known positions and synchronized in time, there are two different kind of data that are considered in literature: the time of arrival (TOA) of the signal at a fixed sensor and the time difference of arrival (TDOA) between two distinct sensors. TOA is used if both the transmitted signal is known and source and sensors are syncronized, such as in underwater sonar technology, and it is possible to extrapolate the time delay between the original signal and the measured one. On the other hand, TDOA is used if there is no explicit knowledge of a reference signal, which is the typical situation in audio processing, where the sound emitted by the source is completely unknown. In this case, first one measures the signal with two sensors located at distinct positions, then it is possible to extrapolate the relative TDOA.
The main contributions to the study of the TDOA--based localization problem come from the engineering literature, where the researchers focus on the development of algorithms for locating the source starting from empirical TDOA data, affected by (mainly, Gaussian distributed) noise. A classification of the different methods can be done according to the proposed solution: maximum likelihood principle versus least--squares estimators, linear approximation versus numerical optimization, and finally iterative versus closed forms--algorithms. However, they all are based on the geometric acoustic model in an anechoic homogeneous medium: the acoustic rays propagate in rectilinear paths and every echo and reverberation is considered negligible. On the other hand, the geometric acoustic model for the TDOA--localization has never been studied in itself in a satisfactory way.
The aim of our research is to to explore the source localization problem through an in-depth study of the geometric acoustic model, with particular emphasis on its statistical properties. See our publications list for recent developments on the subject.
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