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In this paper, we present a channel equalization scheme for time-division multiple access (TDMA) satellite communications with burst digital transmission. We show that each channel states of the multipath satellite channel follows a Gaussian distribution, which means a Bayesian equalization can be implemented. The parameters of the Bayesian equalization are determined using an unsupervised clustering method - the fuzzy c-means (FCM) method. An extremely small number of training symbols (about 1% of a burst) are used to determine the category of each channel state with the aid of data mining. Simulation results show that our Bayesian equalizer performs much better than the recently proposed nearest neighbor classifier-based equalizer at moderate to high signal-to-noise ratio (SNR).