For tracking time-varying underwater acoustic (UWA) channels, a state-space model based scheme generally outperforms a direct adaptive method. The success for the former depends on the choice of a proper state transition model as well as accurate estimation of the model parameters. The autoregressive (AR) transition model has proven to be useful and the key is to determine the AR coefficients so as to achieve a good channel tracking performance. In this paper, we revisit the problem of determining the AR coefficients via Yule-Walker equation, for which the required autocorrelations are estimated as an ensemble average of estimated channel impulse responses (CIRs). Different from existing scheme employing least squares (LS) channel estimation, we propose to obtain a sequence of CIR estimations via adaptive schemes. The advantage is twofold: first, complexity reduction is achieved and the saving can be significant for a UWA channel with extensive delay spread; second, improved tracking performance is achieved as the implicit assumption by the LS method that the channel remains constant over a block is not required. We also propose to dynamically update the autocorrelations and AR coefficients as the channel tracking progresses, such that the variation in the channel statistical property can be captured. Both simulations and experimental results verify the performance gain of the proposed model-based channel tracking scheme.