The joint estimation of differential delay, Doppler, and phase
Abstract
In radio and sonar applications it sometimes happens that narrow-band signals, originated from a remote source and observed at a pair of receivers, differ by unknown differential phase and Doppler shift in addition to the differential delay corresponding to the range difference. The correspondence presents the joint maximum likelihood (ML) estimate of the differential delay, Doppler, and phase and examines their accuracy by deriving the Cramer-Rao bound. It is shown that joint ML estimators are the values of the delay and Doppler that maximize the magnitude of a generalized ambiguity function analogous to the one used in radar. It is also shown that for long observation time and high enough signal-to-noise ratio there is no degradation in the accuracy of the time-delay estimator due to the additional phase and Doppler uncertainty and that the differential Doppler is uncorrelated with the differential delay and phase estimators.
- Publication:
-
IEEE Transactions on Information Theory
- Pub Date:
- September 1982
- Bibcode:
- 1982ITIT...28..817W
- Keywords:
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- Doppler Effect;
- Maximum Likelihood Estimates;
- Radio Transmission;
- Signal To Noise Ratios;
- Sonar;
- Time Lag;
- Extremum Values;
- Frequency Shift;
- Phase Shift;
- Probability Theory;
- Signal Processing;
- Stochastic Processes;
- Communications and Radar