We explore the possibility of using an emerging tool in statistical signal processing, sequential importance sampling (SIS), for joint estimation and decoding of space-time trellis codes (STTC). First, we provide background on SIS, and then we discuss its application to space-time trellis code (STTC) systems. It is shown through simulations that SIS is suitable for joint estimation and decoding of STTC with time-varying flat-fading channels when phase ambiguity is avoided. We used a design criterion for STTCs and temporally correlated channels that combats phase ambiguity without pilot signaling. We have shown by simulations that the design is valid.