Methods based on wavelets for time delay estimation of ultrasound signals

It is well known that classical time delay estimation gives an inexact estimation of the true delay between two signals delayed by non integral multiple of the sample period. For more accurate estimation, new methods are proposed to estimate small time delay with regard to the sample period of ultrasonic signals. In this paper, we focus on two methods based on the wavelet transform for time delay estimation between an ultrasound emitted pulse and the received signal. The first technique consists of computing at a fixed frequency (which is the emitting frequency of the ultrasonic signal) the difference of maximum time argument between wavelet coefficients of the two signals (the reference and the delayed signal). The second technique, based on a crosswavelet representation, directly provides the time delay between the two signals. The performance of these methods in terms of bias and variance are compared to classical correlation using polynomial interpolation. Numerical results show the superior performance of the crosswavelet approach for time delay estimation.