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Let's say I have a robot, located in a box. The robot can move in the x and y and rotate.

The robot has 4 rangefinders, mounted 90 degrees apart, that measure the distance to the walls of the box (I think it would be possible with just 3 but let's use 4 as an example). The robot also has an "approximate" +-10 degree estimate of its heading, so it knows in general which quadrant its bearing should be in.

Given this information, how can I calculate the "exact" position and bearing of the robot?

Intuitively I know this should easily be possible as there are three degrees of freedom for the system (x,y, and the angle), but I can't think of a way to actually calculate the position.

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Suppose your coord axis is at the center of the box and the axes parallel to the walls o the box. Distance to the min-y-wall tells you y. Distance to the min-x wall gives you x, with the obvious offsets added in. Crazy-easy unless I misunderstood.

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