In this style of model training, a set of training observations
is used to estimate the
parameters of a single HMM. The
basic formula for the reestimation of the transition probabilities is
where 1<i<N and 1<j<N and 
is the total probability
of the r'th observation.
The transitions from the non-emitting entry state are reestimated by
where 1<j<N and the transitions from the emitting states to the final non-emitting exit state are reestimated by
where 1<i<N.
For a HMM with 
mixture components in stream s, the means, covariances
and mixture weights for that stream are reestimated as follows.
Firstly, the probability of occupying the m'th mixture component in stream
s at time t for the r'th observation is
where
and
For single Gaussian streams, the probability of mixture component occupancy is equal to the probability of state occupancy and hence it is more efficient in this case to use
Given the above definitions, the re-estimation formulae may
now be expressed in terms of 
as
follows.
