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In a previous work, we considered time-reversal refocusing for localizing a sound source in a highly reverberant urban environment with non-line-of-sight (NLOS) receivers. The approach involved a virtual (computer-based) time-reversal propagation calculation using a priori knowledge of the receiver and scatterer positions. Among the errors that affect the quality of refocusing is the imperfect accuracy of the assumed scatterer locations. Some practical analogues of changing scatterer positions are (a) the building coordinate errors (or mistakes) and (b) the random movement of vehicles on the street of an urban setting. We address these issues by conducting a time-reversal analysis of a set of numerically generated synthetic acoustic pressure recordings after intentionally introducing errors by altering the position of the scatterers. The numerical experiment results indicate that, for a realistically complicated urban setting, coordinate errors in the position of only a few scatterers have little detrimental effect. The effect of coordinate errors in one or a few scatterers is suppressed by the constraints imposed by correct propagation features (both kinematic and dynamic) generated by multiple reflections and diffractions from other precisely located scatterers. The dependence of source localization accuracy on the relative error in scatterer coordinates, the relative number of scatterers with coordinate errors and the number of receivers is quantitatively assessed in this paper. In general, time-reversal refocusing with a large number of receivers can compensate for more severe errors. Even for only three non-line-of-sight receivers, building location errors in the order of 3 m still give good results. Adding small scatterers (like vehicles) close to a receiver is more critical than adding scatterers relatively far from the receivers.

The effect of changing scatterer positions on acoustic time-reversal refocusing in a 2D urban environment at low frequencies