Estimation of delay and Doppler by wavelet transform

This paper studies the use of wavelet transform for delay and Doppler estimation between a sensor pair with relative motion between source and/or receivers. In passive sonar or radar estimation, the optimum wavelet is one of the receiver outputs and a method which scales the wavelet in discrete form is proposed. In active estimation, the maximum-likelihood (ML) estimator is shown to be equivalent to performing a wavelet transform of one of the receiving signals followed by a cross-correlation. The optimum wavelet in this case is equal to the weighting in the ML cost function. The wavelet approach combines noise filtering and scaling together, yielding a reduction in complexity. The proposed estimators were shown to approach the Cramer-Rao lower bound for delay and Doppler estimation.