Suppose I have a large sample of the function f(x,y), for many x's and y's.

I believe that the function should be radial, i.e: f(r^2=(x-x0)^2+(y-y0)^2) = constant.

It is difficult to estimate the errors in each point in the sample, so I don't particularly trust a least square analysis to find x0,y0.

Is there a different more robust way to estimate x0 and y0 (center of the radial function), using some sort of symmetry methods?