HMM Procedure

The Gaussian hidden Markov model (Gaussian HMM) is a type of finite-state-space and homogeneous HMM where the observation probability distribution is the normal distribution,

where and are mean and covariance parameters at state . Hence, the initial state probability vector (ISPV) , the transition probability matrix (TPM) , and the observation parameter (, which consists of mean and covariance parameters) together specify the Gaussian HMM; that is, the parameter of the Gaussian HMM is .

Because the Gaussian HMM is a type of finite-state-space and homogeneous HMM, the six common problems—the filtering, smoothing, forecasting, evaluating, decoding, and learning problems—can be solved using the three algorithms introduced in the section Hidden Markov Model. That is, you can solve the evaluating, filtering, and forecasting problems by using the forward algorithm; the smoothing problem by using the forward algorithm and backward algorithm; the decoding problem by using the Viterbi algorithm; and the learning problem, if solved through the maximum likelihood or maximum a posteriori method, by using the forward algorithm to calculate the likelihood.