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On section 2.4.2. of the "Probabilistic robotics" book, there is an example to demonstrate the way a Bayes filter works. I only can't understand one point in the example, I hope you help to get it.

This is the whole example:

The point I can't get to, is the formula (2.42). I think there is assumptions that are not mentioned there. I guess that for 2.42, the Writer assumption is that the door is functioning well and the robot actuator is also working correctly, and finally, the Xt is a sensing output, because the 0.2 is exactly the same error I see in the formula, one line above the formula 2.40, when the door is closed but is sensing open (sensory noise). From the other side, from reading the text it seems to me that P(X=x | Ut, Xt-1) is at all not about the sensing, but about the control, action and this together with assuming Xt an output of the sensor brings me to contradiction.

I would be very happy to know what is the reason behind 2.42.

From that point onward or backward, all is clear.

Thank you,

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# Probablity robotics, Bayes filter reasoning problem

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