Time delay estimation for closely spaced echoes

The Cramer-Rao bound (CRB) for the time delays of closely spaced echoes is derived. It is shown that the variance of the ith echo delay estimate depends on the relative delays of all other echoes, but not on their amplitudes. This results from the restriction that the estimator must be unbiased. A single replica correlation algorithm is suggested for the case of two echoes with highly unequal amplitudes, and its performance is evaluated. For echo spacings below some threshold, the estimate for the dominant echo is slightly biased, but its mean square error is significantly lower than the CRB. The estimation of the weak echo is discussed