How to adjust/convert/transform set of points with unknown crs using reference points

Question

I have a set of points in an unknown crs. How can I convert (not guess) this to a given crs? I know, or rather I can determine the actual coordinates of each point in order to have some reference points to match against. How can I convert the rest of the points using these reference points? I have done this with raster images (using qgis + georeferencer plugin) , but I don't seem to find any tools for doing this with points. I don't need great accuracy.

I have managed to center it and scale it in a very naive and linear based on a single reference point (near the center) but the accuracy is pretty bad, specially with points far away from the reference point.

Answer 1

I finally managed to transform the points using OpenJump.

First I load the layer with my reference points. Then I load the layer with the local coordinates (I had to do some manual transformations before so that it would overlap the reference layer).

Form the main menu, "Tools"->"Warp"->"Warping...".
A dialog appears. On the source layer you select the unadjusted layer. I checked Warp incrementally and Auto-hide layers. Then you select the green arrow in the dialog and start drawing vectors from the unadjusted points to the actual reference points.

You can even load additional layers, after having warped the layer and you can apply the same transformation using the "Copy Layer To Vectors" button. A new layer will appear with your transformed points.

Nice and easy, no thorough knowledge or math needed.

Hope this helps someone else.