Abstract In the paper, to exploit the temporal information of signal, an autoregressive (AR) process is adopted to model the time structure of each source signal. Then variational Bayesian (VB) approach is used to separate noisy mixtures of temporally correlated sources. We express noisy mixing model and AR source model in a state space form and employ variational Kalman smoother to estimate source. The advantage of our algorithm is that it exploits the temporally correlated nature of source signal. Experiments on artifact and real-world speech signals are used to verify our proposed algorithm. As a result, AR source model improves the separation. The performance of our algorithm is compared with that of VB separation algorithm based on independent and identically distributed (i.i.d.) assumption which each source satisfies and the second-order blind identification (SOBI) algorithm.