Obtaining accurate pose of camera facing a plane

Hi everyone, I'm trying to accurately deduce the pose of my camera relative to a plane within the camera's view. By accurately, I mean I want it in real world units (meters), not in an arbitrary scale. I'm looking to do this mathematically as it is meant to be implemented on an embedded camera board, instead of using hosted programming which would grant me access to libraries such as opencv.

Here's what I have:

* coordinates of the 4 corners …

computervision mean plane scale units view world