I am learning to use HMM and I am trying to solve the following problem. There is a robot moving around the nodes in graph. The robot can move to adjacent nodes with certain probabilities. Each time the robot steps into a new "node", a (noisy) information about the node is generated. That is, I do not know the exact node.
I have the following data:
- Each node node is a hidden state (finite number)
-
A transition matrix that defines the probabilies for the transitions between nodes. $A$
-
Emission probabilities for each hidden node
Using HMM standard functions I should be able to predict the "hidden state" at time t if I have "t observations" (observations from $1,\dots,t$) $P(X_t|O_{1,\dots,t})$.
Is there a way to predict the next move (hidden state at t+1)? If I have "$t$-observations" (all observations at time $t$), is it possible to predict the most probable "hidden state" at time "$t+1$"?
Which HMM principle should I use?
Best Answer
You use the forward algorithm to predict $P(X_{t+1})$.
$P(X_{t+1}|X_t, Y_{1:t} ) = \sum_{X} P(X_{t+1}|X_t) \cdot P(X_t|Y_{1:t}) $
So, you use the same principle for predicting $P(X_{t})$, but without being able to incorporate $Y_{t+1}$, since it is not observed yet.