Moving sound source parameter estimation using a single microphone and signal extrema samples

Estimating the parameters of moving sound sources using only the source signal is of interest in low-power, and contact-less source monitoring applications, such as, industrial robotics and bio-acoustics. The received signal embeds the motion attributes of the source via Doppler effect. In this paper, we analyze the Doppler effect on mixture of time-varying sinusoids. Focusing, on the instantaneous frequency (IF) of the received signal, we show that the IF profile composed of IF and its first two derivatives can be used to obtain source motion parameters. This requires a smooth estimate of IF profile. However, the numerical implementation of traditional approaches, such as analytic signal and energy separation approach, gives oscillatory behavior hence a non-smooth IF estimate. We devise an algorithm using non-uniformly spaced signal extrema samples of the received signal for smooth IF profile estimation. Using the smooth IF profiles for a source moving on a linear trajectory with constant velocity, an accurate estimate of moving source parameters is obtained. We see promise of this approach for an arbitrary trajectory motion parameter estimation.