HMM parameters estimation with inequality constraints

Parameters estimation is the most crucial and difficult problem for signals Hidden Markov Model (HMM) modeling. Success signals modeling depends to a large extent on how precisely the estimated HMM can represent the underlying signal classes. However, in the application of HMM, some known signal information is often either ignored or dealt with heuristically. For instance, state variable constraints, which may be based on physical considerations, practical engineering requirements and prior knowledge, are often neglected because they do not fit easily into the structure of the HMM parameters estimation. In this paper, a four-steps procedure for HMM parameters estimation and re-estimation with inequality constraints is proposed. An active set based Lagrange multiplier method and expectation maximization (E-M) algorithm is proposed to re-estimate the parameters when inequality constraints are not satisfied for the initial estimation value and the convergence is demonstrated. Simulation is provided to demonstrate the effectiveness of the proposed algorithm.