Given a set of points in a plane, and series of measurements of the distances between those points, how would I go about generating a best-fit model of the position of the points?
For example, given 3 points (A, B, C) that define a 30-40-50 right triangle, the data set might look something like this:
(0, 29.1, 39.7) - at point A, measuring to B, C
(NULL, 0, 49.4) - at point B, missing measurement to A
(40.4, 50.5, 0) - at point C, measuring to A, B
What I would like to do is fit this data to a model that will make it possible to determine the distance between any two arbitrary data points, as well as determine the error (given a known error in each measurement). I'm not even sure what type of problem this is, so any pointers to methods or algorithms would be greatly appreciated.