Kalman Filter | Why Shift the Belief Distribution I am looking at the video lecture on Kalman Filter. I got some understanding that if the robot moves that we also shift the enviornment belief model accordingly (the same mean amount the robot moved). I am quite confused that why do we move the belief model of the enviornment. The enviornment itself is stationary so if the robot moves the door will remain in place so their distribution should not be shifted. In the following snapshot, the doors are our measurements and we form the belief of where the robot is with respect to the doors. When the robot moves the doors stay stationary. Why do we move the posterior model of as shown in the image below?
The idea is that the robot is trying to figure out where it is.  The only information it can use is:


Its door sensor which says either you're next to a door or you're not next to a door.
Its map of where the doors are.


That's how we go from the "maximum confusion" (uniform) plot to the one with three humps. This uses the first you're next to a door measurement.

Then, the robot knows it moves to the right.  Therefore it must update its probability with a similar movement to the right.  However, its motion sensors are a little uncertain, so this has the effect of smoothing the three bumps (well, the whole distribution) a little bit. So the three bumps move to the right and they spread out a little.

The peaks of the three spread out humps are still the robot's best guess as to where it is on its map.

Now we get the second you're next to a door measurement.  We multiply our prior (the slightly spread out three-humped distribution) with a new three humped distribution (from our known map).  The prior second-door location and the map second-door location will align, so that will generate the largest peak.