A closed-form approach to acoustic source localization

Acoustic source location is determined by the intersection of a set of hyperbolic curves defined by Time Difference of Arrival (TDOA). Many researchers consider that the closed-form solution of the intersection is cumbersome as the equations are nonlinear, so few researchers focus on solving the equations. However, we find that the closed-form solution can be found easily and directly by Matlab. Three typical four-sensor arrays are mainly concerned in this paper. We find that in some special directions, the error of planar arrays raises sharply. For planar arrays and pyrometric cone array, there are some totally different attributes for their closed-form solutions. These differences are analyzed in detail. In practical applications, as the closed-form solution includes two possible sources, four-sensor array can´t provide the unique source as the existence of ambiguity. Finally, we present a five-sensor array to exclude the ambiguous source.