Hidden Markov model parameters estimation with independent multiple observations and inequality constraints

In this study, the authors focus on hidden Markov model (HMM) parameters estimation with independent multiple observations and non-linear inequality constraints. The parameters estimation process is divided into four steps: initialisation, parameters pre-estimation, parameters re-estimation and termination. The pre-estimation results are used to approximate non-linear inequality constraints to linear inequality constraints. In parameters re-estimation step, the active-set optimisation is combined with the expectation maximisation (EM) algorithm in M-step and the active set-based EM algorithm is proposed to re-estimate HMM parameters when inequality constraints are not satisfied in pre-estimation. An auxiliary function is devised for reconstructing the optimisation objective function and the convergence of the proposed algorithm is also demonstrated. Simulation results indicate that the proposed algorithm provides better performance by modifying the random error of observation data appropriately and it is powerful for industry process fault diagnosis.