Application of the short-time Fourier transform and the Wigner-Ville distribution to the acoustic localization of aircraft

The dominant feature in the acoustic spectrum of a propeller-driven aircraft is the spectral line corresponding to the propeller blade rate that is equal to the product of the propeller shaft rotation rate and the number of blades on the propeller. The frequency of this line, when measured by a stationary observer on the ground, changes with time due to the acoustical Doppler effect. In this paper, the short-time Fourier transform and the Wignet-Ville distribution are used to estimate the propeller blade rate at short time intervals for a turbo-prop aircraft flying at a constant altitude and speed over an acoustic sensor located just above ground level. The temporal variation in the observed blade rate is then used to estimate the speed and altitude of the aircraft, together with the source (or rest) frequency of the blade rate. Finally, the estimated values for these parameters are compared with the actual values recorded onboard the aircraft during each of the eighteen transits formed by pairing each element of a set of speeds: 150, 200, and 250 kn, with each element of a set of aircraft altitudes: 250, 500, 750, 1000, 1250, and 1500 ft.