This paper analyses the principles and the underlying mathematical model for acoustic based shooter detection systems. These systems use the muzzle blast and acoustic shock waves to compute the shooter's location. Our detection system works on a distributed sensor network where microphone arrays are used as sensors. Detection algorithms run concurrently at each node. After determining the wave directions, the information is passed to the central node. The central node fuses data coming from each sensor with our optimization algorithm. For correct georeferenced fusion, GPS, accelerometer and magnetometer data are used. A mathematical framework of the problem with possible node outputs has been developed in this study. Our framework supports all possible combinations of muzzle blast and shockwave measurements at each sensor node. The simulation for various scenarios has been performed and analyzed. Imperfections in the placements of microphones within the arrays, uncertainty of sensor locations and time uncertainty in time of arrival estimations are investigated as regards to their effect on system performance. In order to analyze the effect of these imperfections on the calculated shooter position, shooter's relative direction and bullet direction, a detailed sensitivity analysis has been done. A system calibration method has been developed in this study to reduce imperfections and enhance the shooter localization performance. In addition, acoustic-based shooter localization hardware has been designed within the study. The study involves not only the simulation but also the results of real tests. (C) 2017 Elsevier B.V. All rights reserved.