This paper studies the estimation of fast fading channel in the presence of impulse noise. The fast fading channel in a wireless communications system is typically modeled as an autoregressive (AR) process. The least-squares algorithm and Kalman filter have been previously proposed for estimating the AR parameters and the channel impulse response respectively using a training sequence. The performance of these algorithms, however, is very sensitive to impulse noise. In this paper, a robust Kalman filter and a robust recursive least M-estimate algorithm are employed to jointly estimate the channel impulse response and the AR parameters of fast fading channel under impulse noise. Simulation showed that the proposed algorithms are much less sensitive to impulse noise than the conventional algorithms.