Reestimation of Observation PDF's

In order to update the observation PDF's, it is necessary to maximize

$\displaystyle Q_j = \sum_{t=1}^T w_{tj} \log b_j(O_t).

over the PDF $ b_j$, where

$\displaystyle w_{t,j} = \frac{\displaystyle \alpha_t(j)\; \beta_t(j) }{\displaystyle \sum_{i=1}^{N} \alpha_t(i)\; \beta_t(i) }.$ (13.18)

This is a weighted maximum likelihood (ML) procedure since if $ w_{tj} = c_j$, the results are the strict ML estimates. The weights $ w_{tj}$ are interpreted as the probability that the Markov chain is in state $ j$ at time $ t$.

Baggenstoss 2017-05-19