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PM-PO, but you need to make sure you are not simply "subtracting", as you have to take care about the orientation of the frames as well.

As a simple example, assume PM = (10,0,0) in (x,y,yaw), PO = (2,0,0), you'd get MO = (8,0,0).

In amcl it is solved like this , e.g.