We have described three policies for the vacuum robot: (1) a uniform random walk, (2) a bias for wandering southeast, as described in Exercise hmm-robust-exercise, and (3) the policy described in Exercise roomba-viterbi-exercise. Suppose an observer is given the observation sequence from a vacuum robot, but is not sure which of the three policies the robot is following. What approach should the observer use to find the most likely path, given the observations? Implement the approach and test it. How much does the localization accuracy suffer, compared to the case in which the observer knows which policy the robot is following?
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