Hidden Markov Models

(12th-September-2020)

• A hidden Markov model (HMM) is an augmentation of the Markov chain to include observations. Just like the state transition of the Markov chain, an HMM also includes observations of the state. These observations can be partial in that different states can map to the same observation and noisy in that the same state can stochastically map to different observations at different times.

• The assumptions behind an HMM are that the state at time t+1 only depends on the state at time t, as in the Markov chain. The observation at time t only depends on the state at time t. The observations are modeled using the variable Ot for each time t whose domain is the set of possible observations. The belief network representation of an HMM is depicted in Figure 6.14. Although the belief network is shown for four stages, it can proceed indefinitely.

Localization

• Suppose a robot wants to determine its location based on its history of actions and it sensor readings. This is the problem of localization.