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We consider a setting in which a receiver uses a sequence of short, narrowband training burst signals from a transmitter to jointly estimate the time delay and frequency offset of its local clock with respect to the transmitter. A key challenge in this estimation problem is in handling cycle-slips arising from ambiguities in phase unwrapping when (a) the repetition rate of the training signal is small compared to the frequency offset, and (b) the bandwidth of the training signal is small relative to the carrier frequency. We propose a novel Bayesian filter-bank approach to handling these ambiguities. We present numerical simulations to show the effectiveness of this approach and compare our results with the fundamental posterior Cramer-Rao lower bound. The filter achieves the bound for signals between about 5 and 35 dB SNR, showing that it is optimal in this regime.