Motion parameter estimation of a radiating point source with multiple tonals using acoustic Doppler analysis

Abstract

The sound emitted by distant moving sources, such as air crafts, submarines and ships contain time-varying Doppler-shifted tonals when observed from a stationary sensor. This temporal variation in the Doppler shift of the tonal can be used for the estimation of time of closest approach, distance between the source and the sensor at the closest approach instant, the relative speed of the source and the rest frequency of the emitted tonal. The existing methods model the radiating source as a point source under uniform linear motion, and estimate the frequency of a single dominant tonal as it undergoes Doppler shift due to the relative motion of the source as compared to a stationary sensor. However, the received signal may consist of multiple tonals and their harmonics. In this case, the tonals exhibit dissimilar Doppler shifts as the Doppler shift depends on the rest frequency of the tonal. In this paper we consider the motion parameter estimation of a point source when the received signal is composed of multiple Doppler-shifted tonals, which may or may not be harmonically related. The frequencies corresponding to the multiple Doppler-shifted tonals present in the received signal are estimated over short intervals. We propose the use of the average of the estimated Doppler-shifted tonals for the estimation of the motion parameters. The average of the estimated frequencies preserves the temporal variation in the Doppler shift and hence it can be used for the estimation of the motion parameters. Once the motion parameters are estimated, it is also possible to extract the line spectrum, which is often used in applications such as the classification of the moving source. Simulations are used to demonstrate the efficacy of proposed algorithm, which utilizes the Doppler variation corresponding to multiple tonals as compared with the monotone case. The performance of the proposed algorithm in the presence of noise is assessed under several signal-to-noise ratios. The proposed algorithm is applied to actual pass-by sound of an aircraft and an underwater signal recorded for a ship.