This paper considers the problem of estimating time delay and Doppler shift based on the maximum likelihood criteria. Joint estimation of time delay and Doppler stretch of a random signal received by two (or more) sensors is required in many signal processing applications. This problem can be viewed as the determination of the effects of a time-varying channel on the emitted signal. It is shown that discrete time-frequency (time-scale) techniques provide the correct system characterization. Theses techniques are simple, fast and efficient. Moreover, in areas where the measurements are repeatable, such as ultrasonic imaging and nondestructive evaluation, the process of averaging can be used to improve the SNR. In order to implement the simultaneous estimation of time delay and Doppler coefficient according to the maximum likelihood criterion, two practical problems are investigated: the interpolation method used to obtain a fine resolution of the estimates and the scaling procedure which is not a trivial problem.