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We present a joint channel estimation and detection method of space-time trellis codes (STTC) in the context of an unknown flat fading multiple-input multiple-output (MIMO) channel. A combined state-space model for the space-time code and the Rayleigh fading MIMO channel is introduced, in order to use deterministic particle filtering at the receiver side. An important feature of the proposed method is that the fading rate need not be known to the receiver. Monte-Carlo simulations show that the performances of the proposed scheme are close to decoding with perfect channel state information (CSI) using the Viterbi algorithm (VA).