I would like to find the coordinates of a set of points in 3D from a distance matrix that may contain (experimental) errors.
The approach suggested here is not symmetric (treats the first point differently), and that is not adequate when there are uncertainties. These uncertainties may lead to numerical instabilities as suggested here. But the answer to this question also assumes exact data.
So I would like to see if there is any statistical approach that best uses the redundancy of the data to minimize the error in the predicted coordinates and avoids potential instabilities due to inconsistent distances.
I am aware that the final result is invariant to rigid body translations and rotations.
It would be great if you can suggest algorithms present in or based on numpy/scipy, but general suggestions are also welcome.
After asking this same question in cross correlated @wuber edited my post by adding the multidimensional-scaling keyword. With this keyword I could find many algorithms, starting from the wikipedia: https://en.wikipedia.org/wiki/Multidimensional_scaling