  De-interleaving of the mixtures of Hidden Markov Processes (HMPs) generally
depends on its representation model. Existing representation models consider
Markov chain mixtures rather than hidden Markov, resulting in the lack of
robustness to non-ideal situations such as observation noise or missing
observations. Besides, de-interleaving methods utilize a search-based strategy,
which is time-consuming. To address these issues, this paper proposes a novel
representation model and corresponding de-interleaving methods for the mixtures
of HMPs. At first, a generative model for representing the mixtures of HMPs is
designed. Subsequently, the de-interleaving process is formulated as a
posterior inference for the generative model. Secondly, an exact inference
method is developed to maximize the likelihood of the complete data, and two
approximate inference methods are developed to maximize the evidence lower
bound by creating tractable structures. Then, a theoretical error probability
lower bound is derived using the likelihood ratio test, and the algorithms are
shown to get reasonably close to the bound. Finally, simulation results
demonstrate that the proposed methods are highly effective and robust for
non-ideal situations, outperforming baseline methods on simulated and real-life
data.
