Extend Example 9.30 (page 420) so that it includes the state of the animal, which is either sleeping, foraging, or agitated.

If the animal is sleeping at any time, it does not make a noise, does not move, and at the next time point it is sleeping with probability 0.8 or foraging or agitated with probability 0.1 each.

If the animal is foraging or agitated, it tends to remain in the same state of composure (with probability 0.8), move to the other state of composure with probability 0.1, or go to sleep with probability 0.1.

If the animal is foraging in a corner, it will be detected by the microphone at that corner with probability 0.5, and if the animal is agitated in a corner, it will be detected by the microphone at that corner with probability 0.9. If the animal is foraging in the middle, it will be detected by each of the microphones with probability 0.2. If it is agitated in the middle, it will be detected by each of the microphones with probability 0.6. Otherwise, the microphones have a false positive rate of 0.05.

(a) Represent this as a two-stage dynamic belief network. Draw the network, give the domains of the variables and the conditional probabilities.

(b) What independence assumptions are embedded in the network?

(c) Implement either variable elimination or particle filtering for this problem.

(d) Does being able to hypothesize the internal state of the agent (whether it is sleeping, foraging, or agitated) help localization? Explain why.