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Suppose we have a robot that can be in one of two states: state 1 or state 2. The robot moves between states according to the following rules:

If the robot is in state 1, it has a 70% chance of staying in state 1 and a 30% chance of transitioning to state 2.

If the robot is in state 2, it has a 60% chance of staying in state 2 and a 40% chance of transitioning to state 1.

The robot has two sensors: sensor 1 and sensor 2. The sensors are not perfect and sometimes give incorrect readings. The emission probabilities for each sensor are as follows:

If the robot is in state 1, sensor 1 gives the correct reading with a probability of 0.8 and an incorrect reading with a probability of 0.2. If the robot is in state 2, sensor 1 gives the correct reading with a probability of 0.4 and an incorrect reading with a probability of 0.6.

If the robot is in state 1, sensor 2 gives the correct reading with a probability of 0.3 and an incorrect reading with a probability of 0.7. If the robot is in state 2, sensor 2 gives the correct reading with a probability of 0.9 and an incorrect reading with a probability of 0.1.

Assume that the robot starts in state 1 with equal probability and generates the following sensor readings over time:

sensor 1: correct, correct, incorrect

sensor 2: incorrect, correct, correct

What is the most likely sequence of states that the robot went through to generate these observations?
in HMM by Active (276 points)

1 Answer

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I assumed you meant the robot starts in state 1 or 2 with equal probabilities and I also assumed that two sensor's readings are independent of each other.

The answer is State 1, State 1, and State 2.

Please find the worksheet here.

Google Sheet

by (164 points)
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