Localizing impulse sources in an open space by time reversal with very few transducers

Localizing impulse point sources is a problem of major practical importance for numerous applications in security or equipment monitoring. It is difficult to solve when posed in a strongly congested propagation medium. This paper concerns the case where, in an open space, obstructing bodies are of a sufficient size and number to impede reception of certain direct paths from the source to the receivers. They produce reflected or diffracted paths. A low number of point receivers is used, 2-5, depending on the case. This fits practical constraints one meets in the field. The localization principle being time reversal, the aim is therefore to model the time reversed signal propagation from the receivers. From a direct signal obtained from measurements or computer simulations, the reversed propagation computation is made in the frequency domain or in the time domain. Despite the low number of receivers, which we would expect not to give good refocusing of the reversed wave, we are able in each case to localize the source with a conveniently chosen criterion, based on the time shortness of the signal. The advantage of this technique is its simplicity and speed: in a time formulation, a unique computation allows the localization. This result opens the way to economical measurement techniques for localizing impulse sources in congested or disturbed media, as long as a propagation model allowing integration of refraction, diffraction and reflection effects is available. (C) 2006 Elsevier Ltd. All rights reserved.