In this contribution we address the problem of MIMO equalisation and transmit diversity. More specifically, we develop a method that jointly decodes space time trellis coded modulation (STTCM) encoded signals and equalises the MIMO channels. The optimal solution for such a setup would require construction of a super-trellis that describes a finite state machine resulting from the combination of MIMO channel and STTCM trellises. However, the number of states in this super-trellis is typically gigantic and as such prohibits practical application. Our solution is based on sequential Monte Carlo technique (aka particle filter), which has gained much interest recently in the communications community. The structure of the STTCM code is incorporated into the proposal distribution of the particle filter. As a results a significant reduction in complexity has been achieved as compared not only to the brute force super-trellis approach, but also when compared to the conventional "turbo" solution.