What Bayesian model should I use for posterior room identification?

Question

I have n rooms (which can be considered as states) and a sensor on my robot which gives me a probability array of what room it is in (this array is of size n and its sum is 1). At every timestamp (the timestamps are regularly spaced, say 5 seconds) the robot takes a measurement and stores it.

Moreover, I know my robot is quite slow and the rooms are quite large, so the robot should stay in the same room during x timestamps (for example with x = 12, it should stay in the same room for 60 seconds).

Now here is the tricky part:

• the sensor is rather noisy so the right room should be in the worst case at the third place in the sensor array (if you order by decreasing probability)
• fortunately, I only need to know about the rooms where the robot was after he has finished travelling (hence the "posterior room identification"), meaning that the robot does not take advantage of this sensor when it travels
• there is no prior on room topology, you could consider that the rooms are all connected to each other.

One last piece of information: I can train the model with a groundtruth dataset.

I don't think there needs to be more data added to design a model. I was planning to go for a simple Markov state model but the three observations I made make me doubt it would apply correctly, since the present depends on the past and on the future.

What model would you use?

Answer 1

I would use a first-order hidden Markov model. The transition distribution of the model corresponds to the room topology, as well as the probability of lingering in the same room. I would learn that from the training data. Given a prior on the initial state and the sensor readings at each time step, I would use a forward-backward algorithm to estimate the posterior probability of being in each room at each time step.