An acoustic-signature based method of estimating the flight trajectory of low-altitude flying aircraft that only requires a stationary microphone array is proposed. This method leverages the Doppler shifts of engine sound to estimate the closest point of approach distance, time, and speed. It also leverages the acoustic phase shift over the microphone array to estimate the direction of arrival of the target. Combining these parameters, this algorithm provides a total least square estimate of the target trajectory under the assumption of constant target height, direction, and speed. Analytical bounds of potential performance degradation due to noise are derived and the estimation error caused by signal propagation delay is analyzed, and both are verified with extensive simulation. The proposed algorithm is also validated by processing the data collected in field experiments.