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This paper develops a method for estimating the flying trajectory of a turboprop or rotary-wing aircraft based on narrow-band passive acoustical technique, which measures the instantaneous frequency of the acoustical signal emitted by the target and received by three stationary sensors placed on the ground. The received instantaneous frequency varies due to the acoustical Doppler effect. Under the condition that the target flies at a constant velocity and the trajectory is a straight line, a intuitional model to describe the trajectory is proposed, which completely specifies the flight path by seven parameters. The nonlinear least-square problem of estimating the parameters is simplified by decomposing it into four steps. Computer simulations are provided to show the performance of the proposed method compared with the Cramer-Rao lower bound (CRLB) in the presence of white Gaussian measurement noise.