## Introduction to HMM's

The fundamental assumption of an HMM is that the process to be modeled is governed by a finite number of states and that these states change once per time step in a random but statistically predictable way. To be more precise, let be the probability that the system transitions into state at time . The Markovian assumption says that depends only on , the true state at time . Furthermore, if this distribution does not depend on the absolute time , then the state probabilities can be described completely by a fixed state transition matrix where .
Figure 13.20 illustrates a hidden Markov model (HMM). At each time step (time running from left to right), the Markov model is in one of the five possible states. According to the Markovian assumption, the probability that the model is in state at time is governed only by the transition probability , where is the true state at time . The Markov model is hidden" from view by the observer who can only observe measurements whose PDF is governed by the true state at each time step. The mathematics of the HMM are reviewed in section 13.3.2.

Subsections
Baggenstoss 2017-05-19