Forward Algorithm

Finding probability
Definition
Example
Summary
Section 2 - Page 2
1 2 3

Then for each time step, t = 2, ..., T, the partial probability a is calculated for each state;

[Formula]

that is, the product of the appropriate observation probability and the sum over all possible routes to that state, exploiting recursion by knowing these values already for the previous time step.

Finally the sum of all partial probabilities gives the probability of the observation, given the HMM, l.

[Formula]

To recap, each partial probability (at time t > 2) is calculated from all the previous states.