Linear Least Squares Fit of Sphere to Points

Question

I\'m looking for an algorithm to find the best fit between a cloud of points and a sphere.

That is, I want to minimise

where C is the centre

Answer 1

The linked thesis contains a problem : it doesn't handle noise properly and overestimates the radius. (Centre is OK). It looks like it should be possible to come up with a correction based upon the estimate of the applied noise.