Impairment caused by Doppler frequency shift and harsh channel condition distinguish underwater acoustic communications from radio communications. Slow speed of acoustic waves produces relatively high Doppler shift and result in expansion or compression in time samples, which is known as Doppler scaling. In particular, the Doppler scaling causes significant carrier frequency offset (CFO) in orthogonal frequency division modulation (OFDM). To compensate the CFO, it is essential to resample signal samples according to the Doppler scale. In theory, the Doppler scale can be estimated by measuring the distance between peaks of the matched filter output of consecutive Doppler-invariant preambles. In practice, multi-path reflections and non-orthogonality between the HFM and OFDM payload produce large numbers of local false peaks. In this paper, we propose a robust Doppler estimation technique by employing constant false alarm rate (CFAR) filter to remove false peaks. We validate the performance of the proposed scheme through two sea-trials carried out in shallow water near Jervis Bay, Australia. In the sea-trials, a slow-moving towed hydrophone array was deployed as the receiver and the source was a stationary, low source level, vertical transmit array. Sea-trial results demonstrated up to 112bps information rate using bit-interleaved coded OFDM over 400 Hz bandwidth.