A novel training method for HMM2 with multiple observation sequences

Second-order hidden Markov models (HMM2) have been widely used in pattern recognition, especially in speech recognition. Their main advantages are their capabilities to model noisy temporal signals of variable length. In this paper, we introduce a novel training method for HMM2 with multiple observable sequences, assuming that all the observable sequences are driven by a common hidden sequence. By generalizing Baum's auxiliary function into this framework and building up an associated objective function using Lagrange multiplier method, several new formulae solving model parametric estimation are theoretically derived.