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A Bayesian multi-task model is developed for radar automatic target recognition (RATR) using high-resolution range profile (HRRP). The aspect-dependent HRRP sequence is modeled using a stick-breaking hidden Markov model (SB-HMM) with time-evolving transition probabilities, in which the spatial structure across range cells is described by the hidden Markov structure and the temporal (or orientational) dependence between HRRP samples is described by the time evolution of the transition probabilities. This framework imposes the belief that temporally proximate HRRPs are more likely to be drawn from similar HMMs, while also allowing for possible distant repetition or "innovation" associated with abrupt fluctuation in the HRRP sequence. In addition, as formulated the stick-breaking prior and multi-task learning (MTL) mechanism are employed to infer the number of hidden states in an HMM and learn the target dependent states collectively for all targets. The form of the proposed hierarchical model allows efficient variational Bayesian (VB) inference. The experimental results based on the measured HRRP data are compared with the MTL HMMs without time evolution and also some other existing statistical models.