I'm working on an Augmented Reality project, and I have five markers whose positions will vary somewhat every use, and I need to measure the distances between them to scale the 3D model I'm using. The markers are arranged in a pentagon like so:

    A
E      B
  D  C

I use the AR library to measure the orthonormal affine transformations between A>B, B>C and A>E,E>D in order to construct a new orthonormal basis in the middle. The problem is that the AR library isn't capable of measuring the affine transformations with enough precision, so the errors accumulate, and the values I end up with for D>C don't line up and are about 1cm off. I can measure D>C, but I have no idea what sort of strategy I might use from there to adjust the previous matrices to make them more precise while keeping them orthonormal. Are there some techniques out there that could accomplish this?