Parameters estimation of point moving source with time-frequency transformation

A new parameter estimation method for a point moving harmonic source with unknown moving velocity and frequency is presented in this paper. The time-frequency representation of the source signal is taking the place of traditional time correlation estimation methods. For a harmonic source moving at constant velocity, the received signal which is amplitude and frequency modulated has no spatial correlation between microphone pairs in time or frequency domain which make the estimation problem become complicated. Besides, it is observed that the Doppler shifted frequency of the signal correlate well between spatial distributed microphone signals. Moreover, the second time derivative of the Doppler shifted frequency gives the reference time for the estimation of the source parameters in time domain. In this paper, the algorithm for estimation based on time-frequency transformation is presented. The adaptability of short -time Fourier transform (STFT), filtered short-time Fourier transform (FSTFT) and Polynomial Phase Estimation (PPE) method are also illustrated. In addition, the performance of the analysers on difference source velocity, frequency and signal to noise ratio in computer simulations is presented. The results demonstrate the validity of the proposed method to give a rigid estimation in constant speed moving source. This paper concludes with further investigation and discussion about the proposed method. INTRODUCTION The estimation of moving sound sources parameters through measurement is a significant process in acoustics. It is obvious that direct measurement of sound pressure from a moving source which is amplitude and frequency modulated of the original signal, signal information is unavailable to extract if no prior knowledge of the source. Pre-processing of the measured data is required for the parameter estimation. A commonly used method, sweeping focus method employed by Barsikow and King [1], Barsikow [2] and To and Yung [3] to eliminate the Doppler effect by adjusting the direction of focus to the source with a directional microphone array at the same speed of the source which assumed to be known. Besides, instantaneous frequency based methods has been used for moving source localization by Ferguson and Quinn [4,5] with Wigner-Ville transformation. The instantaneous frequency change also done by Poisson et al [6] with bilinear time-frequency transformation which simplifies the frequency modulation by linear approximation. Three parameters are estimated including source velocity, frequency and power (amplitude). The harmonic source is travelling through a line trajectory which parallel to the array with constant speed. Under this situation, the received frequency and pressure remain a linear relationship at particular time instant, and only depend on the speed and the closest source microphone distance. The general way is to make use of the highest sound pressure time as the reference time. However, if the source velocity is unknown, the estimated frequency and power would be biased. Thus, the estimation of source velocity and representative time reference for the estimation problem are necessary. This paper is organized as follows. Section 2 gives the review of the harmonic moving source model. The new reference time for the estimation based on maximum rate of change of received source frequency is presented in section 3. Three time-frequencies based instantaneous frequency estimators were reviewed including, short-time Fourier transforms (STFT), filtered short-time Fourier transforms (FSTFT), and Polynomials phase estimation (PPE) in section 4. Simulation results with various source speed, frequency and signal to noise ratio (SNR) are discussed in section 5.