From my understanding you can use the transition matrix to predict the probability of going from the last predicted hidden state(state t), to the t+1 hidden state. My confusion is how in code format do I go from the hidden state predicted at time t+1 to the predicted observed state at time t+1.
For each state of continuous HMM, an emission probability distribution is defined. It can be a Gaussian distribution or a Gaussian Mixture Model (GMM). After computing the state variable, you can get the emission probability distribution of observed variables using corresponding state distribution. Note that there is no deterministic value for observed variables and just a probability distribution conditioned on the predicted state variable. In hmmlearn, you can get the means, covars and priors of the GMM using means_, covars_ and weights_ attributes of the model, respectively.