A method for the direct outdoor localization of multiple impulse acoustic sources by a distributed microphone array is proposed. This localization problem is of great interest for gunshot, firecracker and explosion detection localization in a civil environment, as well as for gun, mortar, small arms, artillery, sniper detection localization in military battlefield monitoring systems. Such a kind of localization is a complicated technical problem in many aspects. In such a scenario, the permutation of impulse arrivals on distributed microphones occurs, so the application of classical two-step localization methods, such as time-of-arrival (TOA), time-difference-of-arrival (TDOA), angle-of-arrival (AOA), fingerprint methods, etc., is faced with the so-called association problem, which is difficult to solve. The association problem does not exist in the proposed method for direct (one-step) localization, so the proposed method is more suitable for localization in a given acoustic scenario than the mentioned two-step localization methods. Furthermore, in the proposed method, direct localization is performed impulse by impulse. The observation interval used for the localization could not be arbitrarily chosen; it is limited by the duration of impulses. In the mathematical model formulated in the paper, atmospheric factors in acoustic signal propagation (temperature, pressure, etc.) are included. The results of simulations show that by using the proposed method, centimeter localization accuracy can be achieved.
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