Cross-term rejection in the Wigner-Ville distribution for velocity estimation of a narrowband sound source

Doppler shift of the sound wave is widely used to passively estimate the velocity of the narrowband moving source by a single sensor. The performance largely depends on the instantaneous frequency estimation accuracy. The Wigner-Ville distribution provides a high-resolution tool in time-frequency analysis, but it is hardly used for instantaneous frequency estimation due to the existence of the cross-terms. To tackle this inconvenience, a method for cross-term rejection in the Wigner-Ville distribution is proposed to passively estimate the velocity of a narrowband sound source by using a single sensor. A rejection term is introduced to Wigner-Ville distribution, which is formulated based on the relation between the cross-term and the source velocity. The method updates the source velocity estimate iteratively, making the rejection term and the cross-term opposite in phase so as to cancel the cross-term. The experiment results show that the estimation error for a truck at the speed of 6.07 m/s (signal to noise ratio is approximately 29 dB) is 0.1 m/s and the run time of the method is 4.6 s. Furthermore, the error for a helicopter at the speed of 28.90 m/s (signal to noise ratio is approximately 16 dB) is 0.46 m/s and the run time is 1.2 s. The performance of the proposed method is superior to matched Wigner transform and Doppler chirplet transform both in terms of the precision and the computational efficiency.