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This paper develops a Rao-Blackwellised particle filtering algorithm for blind system identification. The state space model under consideration uses a time-varying autoregressive (AR) model for the sources, and a time-varying finite impulse response (FIR) model for the channel. The multi-sensor measurements result from the convolution of the sources with the channels in the presence of additive noise. A numerical approximation to the optimal Bayesian solution for the nonlinear sequential state estimation problem is implemented using sequential Monte Carlo (SMC) methods. The Rao-Blackwellisation technique is applied to improve the efficiency of the particle filter by marginalizing out the AR and FIR coefficients from the joint posterior distribution. Simulation results are given to verify the performance of the proposed method.