I'm currently taking Udacity's AI for robotics course and came across a question that stumped me. The problem plays on localization probability given uncertainty in our measurement updates. enter image description here

The first measurement distribution I was able to solve no problem. Original distribution was [0.2, 0.2, 0.2, 0.2, 0.2], multiply greens by 0.1, reds by 0.9, normalize and I get [0.04761904761904762, 0.04761904761904762, 0.4285714285714286, 0.04761904761904762, 0.4285714285714286]. What's confusing me is how to manage the move. If the world was cyclic, I would just shift all the probabilities to the right by one. But since he says there is a wall blocking the right side...I'm not sure if the fifth element of resulting shifted matrix should be P(red) * P(green) or P(red) + P(green). I've tried both and neither have worked.

Any advice would be appreciated!

  • $\begingroup$ at the fifth place the robot moves to the right, this movement results in "returning" to the same red square and measuring again. So I would multiply the prior belief with P(red) = 0.9 as you are in fact on a red square. It is the same case as if another sixth red square would be present after the fifth last square $\endgroup$ – 50k4 Jun 8 at 7:25

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