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A systematic study of threat effectiveness for anti-aircraft artillery (AAA) systems requires the development of a mathematical model for the gunner's tracking response. An anti-aircraft gunner model based on the Luenberger reduced-order observer theory is developed in this paper. It is composed of three main parts - a reduced-order observer, a feedback controller, and a remnant element. The highlights of this model are simplicity in model structure and accuracy in the tracking error predictions. A parameter identification program based on the least squares curve-fitting method and the Gauss-Newton gradient algorithm is developed to systematically determine the model parameters. Computer simulation results of the AAA tracking task with this model are in excellent agreement with the empirical data obtained from manned AAA simulation experiments conducted at the Aerospace Medical Research Laboratory, Wright-Patterson Air Force Base, Ohio. A comparison between this model and the optimal control model by Kleinman, Baron, Levison is also given.