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Maximum-likelihood estimation of time-varying delay--Part I

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1 Author(s)
Stuller, J.A. ; University of Missouri, Rolla, MO

This paper presents, for the first time, the exact theoretical solution to the problem of maximum-likelihood (ML) estimation of time-varying delay d(t) between a random signal s(t) received at one point in the presence of uncorrelated noise, and the time-delayed, scaled version αs(t - d(t)) of that signal received at another point in the presence of uncorrelated noise. The signal is modeled as a sample function of a nonstationary Gaussian random process and the observation interval is arbitrary. The analysis of this paper represents a generalization of that of Knapp and Carter [1], who derived the ML estimator for the case that the delay is constant, d(t) = d0, the signal process is stationary, and the received processes are observed over the infinite interval (-∞, +∞). We show that the ML estimator of d(t) can be implemented in any of four canonical forms which, in general, are time-varying systems. We also show that our results reduce to a generalized cross correlator for the special case treated in [1].

Published in:

Acoustics, Speech and Signal Processing, IEEE Transactions on  (Volume:35 ,  Issue: 3 )

Date of Publication:

Mar 1987

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