Sound Localization in Microphone Array Using Trigonometric Method versus Hyperbolic Equations

Localization systems are usually used for detecting moving and offensive targets of enemy. The sound localization, however, is one of the main approaches in passive defense which has an impending role to aggression of enemy. This kind of localization method is carried out in a passive way, without emission of any signals and cannot be detected easily. The acoustic signals emitted by a sound source are used to detect its position. Sound source localization is estimated by measuring the time difference of sound from the microphone array. Due to the distance between the microphones in an array, sound reaches the microphone with shifting times. There are many various methods for estimating this time difference of the sound. The locus of sound source position creates a series of hyperbolic; and the source location is obtained by solving a set of nonlinear equations of these hyperbolic. Sound positioning algorithms generally solve these equations by linearization and geometric symmetry. In this study, instead of nonlinear hyperbolic equations, the trigonometric relations of geometric symmetry in a four microphone array are used to obtain the position of sound source. The results show that the trigonometric method is more accurate and less sensitive to noise as well as lower computation load, compared to the sophisticated hyperbolic equations. The mean error induced by noise is about 8.9% and 13.1% in the trigonometric and hyperbolic method respectively.