A modified Baum-Welch algorithm for hidden Markov models with multiple observation spaces

In this paper, a new algorithm based on the Baum-Welch algorithm for estimating the parameters of a hidden Markov model (HMM) is presented. It allows each state to be observed using a different set of features rather than relying on a common feature set. Each feature set is chosen to be a sufficient statistic for discrimination of the given state from a common "white-noise" state. Comparison of likelihood values is possible through the use of likelihood ratios. The new algorithm is the same in theory as the algorithm based on a common feature set, but without the necessity of estimating high-dimensional probability density functions (PDFs). A simulated data example is provided showing superior performance over the conventional HMM.