We introduce a novel family of adaptive robust channel estimators for highly chal- lenging underwater acoustic (UWA) channels. Since the underwater environment is highly non-stationary and subjected to impulsive noise, we use adaptive ltering techniques based on minimization of a logarithmic cost function, which results in a better trade-off between the convergence rate and the steady state performance of the algorithm. To improve the convergence performance of the conventional rst and second order linear estimation methods while mitigating the stability issues related to impulsive noise, we intrinsically combine different norms of the error in the cost function using a logarithmic term. Hence, we achieve a com- parable convergence rate to the faster algorithms, while signi cantly enhancing the stability against impulsive noise in such an adverse communication medium. Furthermore, we provide a thorough analysis for the tracking and steady-state performances of our proposed methods in the presence of impulsive noise. In our analysis, we not only consider the impulsive noise, but also take into account the frequency and phase offsets commonly experienced in real life experiments. We demonstrate the performance of our algorithms through highly realistic experi- ments performed on accurately simulated underwater acoustic channels.