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Space-time codes have been proposed as an efficient way for improving the data rates over fading channels by employing multiple transmit/receive antennas in wireless digital communications links. To realize these gains, channel state information is assumed to be available and approximated to be constant during a data transmission burst. In this paper, a per-survivor processing (PSP) which incorporates statistical channel modeling and Kalman filtering to perform maximum-likelihood sequence estimation (MLSE) is presented to jointly estimate the channels and detect the transmitted symbols in a fast fading environment. The fading channel is modeled to be a Gauss-Markov random process to characterize the time variation. A space-time pilot symbol sequence to achieve the diversity/coding gains is also designed to initialize the channel estimates. Simulation results demonstrate this optimal Kalman-based approach could achieve better tracking performance in terms of bit error probability than that of recursive least squares (RLS) tracking method over fast Rayleigh flat fading channels.