An overdetermined system of linear equations can be solved by approximation as described in https://en.wikipedia.org/wiki/Overdetermined_system.
I also need to solve such a system $P_{act} = T * P_{nom}$, where the transformation matrix $T$ between nominal 2D positions $P_{nom}$ and actual 2D positions $P_{act}$ of a point cloud is searched.
The transformation matrix is 2x2, and the number of points is 3 or more.
The currently implemented calculation method uses the pseudo-inverse, which works well, if the goal is getting equally low errors on each point. As the related wikipedia article says,
A common use of the pseudoinverse is to compute a "best fit" (least squares) solution to a system of linear equations that lacks a solution ...
Now, I have a different goal when calculating the transformation matrix: The orientation of a grid of dots is searched. Outliers in this grid should be weightes less. Therefore, the goal is not reducing large errors anymore (least squares), but reducing small errors at the cost of increasing large errors, a least square roots method, so to speak.
When I search for that term, I only found
https://stats.stackexchange.com/questions/34237/least-square-root-fitting-a-fitting-method-with-multiple-minima
but I don't see how this could help.
How can I calculate a transformation matrix between the nominal and actual positions of a point cloud, using a least square roots method?
