I am having a hard time understanding how to use the observation matrix B for continuous HMM assuming the observation of each hidden state Normal.
So far I defined the matrix B as an Nx2 matrix where N is the number of states and 2 is mean and variance of the Normal dist. Question 1: is this correct?
Now, I want to use the values inside the matrix B in the forward algorithm (let's call b the terms inside the matrix B). The forward algorithm I am referring is the following one:
In particular, in step (b), I have to multiply the bracket by bj(Ot) and I am not sure how to define it.
Question 2: Is this formula correct to be used in the forward alg.? In this formula I know the mean and variance for each hidden state that are contained in the matrix B. By the way, I do not know how to define Ot. In fact, my initial idea was to use the single observation at time t. By the way, knowing that the continuous pdf of a single number is 0, this makes no sense. Question 3: Am I missing something? How can I formulate this?
Thank you so much in advance!