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Fast estimators of time delay and Doppler stretch based on discrete-time methods

Estimation of the time delay and the Doppler stretch of a signal is required in several signal processing applications, This paper is focused on the joint fine estimation of these two parameters by a fast interpolation of the estimated ambiguity function. Four discrete-time methods (viz. multirate, piecewise scaling, linear scaling, and indirect estimators), based on an orthogonal model, are introduced. Their mean square error is mathematically derived for random signals corrupted by additive random noises. The obtained expressions have been evaluated for some typical parameter sets in the reference case of Gaussian signals and noises. The numerical results, compared with the accuracy of a continuous-time estimator, show the near efficiency of the multirate estimator for a wide range of SNRs. In fact, the adjustable multirate estimator can operate under near optimal conditions, unlike the approximate (i.e., piecewise and linear) scaling and the indirect methods based on constant sampling rates.