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A major challenge while communicating in dynamic channels, such as the underwater acoustic channel, is the large amount of time-varying inter-symbol interference (ISI) due to multipath. In many realistic channels, the fluctuations between different taps of the sampled channel impulse response are correlated. Traditional least-squares algorithms used for adapting channel equalizers do not exploit this correlation structure. A channel subspace post-filtering algorithm is presented that treats the least-squares channel estimate as a noisy time series and exploits the channel correlation structure to reduce the channel estimation error. The improvement in performance of the post-filtered channel estimator is predicted theoretically and demonstrated using both simulation and experimental data. Experimental data is also used to demonstrate the improvement in performance of a channel estimate-based decision feedback equalizer that uses this post-filtered channel estimate to determine the equalizer coefficients.