This work considers joint channel estimation and data detection of Space-Time Trellis Codes (STTCs) over timevarying flat fading channels with unknown normalized Doppler shift, f d T . An algorithm based on an improved Per Survivor Processing (PSP) technique, where the survivor branch decision is formulated in the symbol by symbol Maximum A Posteriori Probability (MAP) framework, is presented. An Adaptive Kalman Predictor (AKP) is employed to track the fading channel and f d T . In the AKP, the sequence of channel estimates produced by the Kalman Predictor (KP) is utilized for f d T estimation. In turn, the estimated f d T is used in the KP for channel tracking. This coupled process adaptively estimates both the channel coefficients and Doppler shift. The performance of STTC using the proposed receiver is robust against f d T mismatch, and it is within 0.3 dB from the known f d T case.