The estimate of time delay between two signals with random relative phase shift
M. Wax · IEEE Transactions on Acoustics Speech and Signal Processing · 1981
This paper presents the maximum likelihood estimate of the time delay between two signals with random relative phase shift. The analysis applies for narrow-band signals and incorporates a parametric representation of the spread of the phase variation which allows the examination of all cases ranging from uniformly distributed phase shift to known phase shift. A realization of the ML estimator is presented which illustrates the difference between optimum processing for random phase shift and pure delay. The Cramér-Rao bound is also derived and the performance degradation with respect to the pure delay case is discussed.