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What is the difference of gaussian HMM and gaussian mixture HMM (the emission is gaussian or gaussian mixture)? I want to know if it is the same thing. What is the point when estimating the parameters using Baum Welch algorithm.

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Suppose you have a d-dimensional observation vector. You may assume that your emission probabilities come from a single d-dimensional Gaussian density or a mixture of M Gaussians in which case the density is a linear combination of M component Gaussian densities. In the first case you estimate mean vector and cov. matrix for each state, in the second case you do this for all M component densiites together with their mixing weights.

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