I've been reading about hidden Markov models and stumbled upon A Tutorial on Hidden Markov Models and Selected Applications in Speech Recognition by Lawrence R. Rabiner (Proc. IEEE, 77(2):257–286, 1989; PDF). The following appears as equation 49 in the section about continuous observations in hidden Markov models:

$$b_j(O) = \sum_{m=1}^M c_{jm}\mathfrak{N}[O, \mu_{jm}, U_{jm}], \quad 1\leq j\leq N\,.$$

What I want to know is how to use this equation given an estimation of the transition, emission, initial probabilities and a given continuous observed sequence to train the hidden Markov model using the Baum–Welch algorithm.

Also I haven't read the rest of the paper, since I already have a good amount of knowledge about discrete hidden Markov models. I'm just trying to learn how to use continuous time series data to train an HMM.

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    $\begingroup$ Welcome to CS.SE! Can you be more specific about what you do and don't understand? Do you know what the symbols mean? Do you understand everything else in the paper before that? What specifically has you confused? Can you edit the question to clarify? $\endgroup$ – D.W. Jun 29 '16 at 15:24
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    $\begingroup$ If you haven't read the rest of the paper, your first step should be to read the first 11 pages of the paper (everything before that equation that might be relevant to understanding it) before asking here. It's better to exhaust all reasonably available resources on your own before asking here. $\endgroup$ – D.W. Jun 29 '16 at 15:47

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