The problem of estimating the time delay and the Doppler stretch for wideband signals from a moving target is considered. The Cramér-Rao bound and the maximum likelihood (ML) method of estimation are derived. Due to the uncertainty of the reflection coefficient, the ML method may not be practicable. An alternative method involving the location of the peak of the wideband ambiguity function of the signal is suggested. The performance of the method is analysed, and, under high signal-to-noise ratios (SNR's), the method is asymptotically unbiased, and the variances of the estimates are closed to the Cramér-Rao bound for a large variety of signals. Optimum signals for the joint estimation of the time delay and the Doppler stretch under practical constraints are designed and, through computer simulations, their performance are shown to be superior to the commonly used signals.